ARMSTRONG, W., J. COCHRANE, et al. (1981). “THETA-PINCH IONIZATION FOR FIELD-REVERSED CONFIGURATION FORMATION.”

ARMSTRONG, W., D. HARDING, et al. (1982). “FLUX-TRAPPING DURING THE FORMATION OF FIELD-REVERSED CONFIGURATIONS.”

Asai, T., Y. Suzuki, et al. (2000). “Experimental evidence of improved confinement in a high-beta field-reversed configuration plasma by neutral beam injection.”

The first experimental result of high power (14 kV, 23 A) neutral beam (NB) injection into a high-beta field-reversed configuration (FRC) is demonstrated. The result makes it clear that the NB injection improves the plasma performance, increasing the configuration lifetime more than 200% in comparison with the ordinary FRC under similar conditions. A novel NB injection system is presented for application to FRC plasmas. A set of three concave electrodes for beam extraction is used to focus the beam enabling to pass through a narrow port. The target of beam injection is a large bore FRC plasma contained in a mirror field with a mirror ratio of 2-9. (C) 2000 American Institute of Physics. [S1070-664X(00)04106-9].

BARNES, D. (1979). “STABILITY AND TRANSPORT IN A FIELD REVERSED CONFIGURATION.”

BARNES, D., A. AYDEMIR, et al. (1980). “NON-LINEAR SIMULATION OF THE IDEAL MHD TILTING MODE IN A PROLATE FIELD REVERSED CONFIGURATION.”

BARNES, D., J. SCHWARZMEIER, et al. (1986). “KINETIC TILTING STABILITY OF FIELD-REVERSED CONFIGURATIONS.”

BARNES, D., J. FERNANDEZ, et al. (1990). “SUMMARY OF THE UNITED-STATES-JAPAN WORKSHOP ON FIELD-REVERSED CONFIGURATIONS WITH STEADY-STATE HIGH-TEMPERATURE FUSION PLASMAS AND THE 11TH UNITED-STATES-JAPAN WORKSHOP ON COMPACT TOROIDS, LOS-ALAMOS, NEW-MEXICO, NOVEMBER 7-9, 1989.”

BARNES, D. and R. MILROY (1991). “STABILIZATION OF THE FIELD-REVERSED CONFIGURATION (FRC) TILT INSTABILITY WITH ENERGETIC ION-BEAMS.”

The stabilization of the internal tilt mode of a field-reversed configuration by injecting a minority energetic ion component has been investigated numerically. Calculations that follow ion orbits in a specified three-dimensional magnetic field configuration, corresponding to a partially tilted field-reversed configuration, demonstrate how a beam can provide a restoring force to the n = 1 tilt instability. A fully self-consistent three-dimensional numerical model, which treats the background plasma as a Hall fluid and the energetic ions as a collisionless Vlasov species, has also been developed. Calculations have been made for a variety of beam injection parameters, and indicate that the tilt mode can be stabilized with a beam energy of about 40% of the total, beam plus plasma, energy.

Barnes, D. (2001). “Profile consistency of an elongated field-reversed configuration. I. Asymptotic theory.”

An asymptotic theory of field-reversed configuration (FRC) equilibrium is developed, where the small expansion parameter is the square of the inverse elongation of the separatrix. It is shown that equilibrium alone completely determines the closed-field pressure profile of an elongated FRC in terms of the open-field profile. Examples show that the closed profile is insensitive to details of the open profile. A surprising result is that the open outflow plasma (axially beyond closed region) is always totally diamagnetic on the axis (beta =1, where beta is measured in the theta -pinch sense). The separatrix shape (axial variation) depends uniquely on the first-order pressure profile, and any separatrix shape may be realized within the limitations of the asymptotic theory. This sensitive dependence of shape on pressure profile explains extreme stiffness of the FRC equilibrium problem which was reported earlier. These results are compared favorably with experimental observations. (C) 2001 American Institute of Physics.

Barnes, D. (2001). “Profile consistency of an elongated field-reversed configuration. II. Two-dimensional solutions.”

An asymptotic theory of field-reversed configuration equilibrium, where the small expansion parameter is the square of the inverse elongation of the separatrix, was previously developed [D. C. Barnes, Phys. Plasmas 8, 4856 (2001)]. This theory is used to compute consistent pressure profiles which are then used to obtain two-dimensional solutions of the Grad-Shafranov equation. Solutions are obtained for a range of normalized separatrix radii, elongations, and shapes. These solutions confirm the predictions of the asymptotic theory. Elongations up to 25:1 are obtained, and the shape is shown to assume any previously specified value. (C) 2001 American Institute of Physics.

Barnes, D. (2002). “Stability of long field-reversed configurations.”

The stability of very elongated field-reversed configurations is solved by an expansion in the small parameter epsilon (inverse elongation). It is first shown that all possible unstable modes have small growth rates (gamma similar toepsilon). The internal tilt mode is considered in detail. An explicit form for deltaW in leading order is derived, and leads to a quadratic form including Hall terms. A sufficient condition for stability is obtained by minimizing deltaW, leading to a field-line ordinary differential equation. Sufficient stability conditions are obtained from this formulation, and indicate stability for S-*/E<2 (where S-* is the ratio of separatrix radius to collisionless ion skin depth and E the elongation of the separatrix), if the local criterion is used. It is argued that a volume-averaged condition is more appropriate when finite ion orbit effects are included. This leads to S-*/E<3.5-4 for stability, independent of separatrix shape or x(s) (separatrix radius to wall radius at the midplane). This condition for stability compares favorably with experimental observations. (C) 2002 American Institute of Physics.

Barnes, D. (2002). “Stability of long field-reversed configurations (vol 9, pg 560, 2002).”

BEKLEMISHEV, A., V. GORDIN, et al. (1993). “TOROIDAL PLASMA REACTOR WITH A LOW EXTERNAL MAGNETIC-FIELD.”

The Lyapunov conditions for plasma stability are shown to be met in a toroidal pinch configuration with the safety factor q < 0.5, decreasing from the centre to the periphery without field reversal. This magnetic configuration is capable of containing high pressure plasma with only a small external toroidal magnetic field. Stable configurations are found with average beta near 15% and with the magnetic field associated mainly with the plasma current. The beta value calculated with the external magnetic field can be > 100%. Fast charged particles produced by fusion reactions are asymmetrically confined by the poloidal magnetic field (owing to the lack of a strong toroidal field). They thus generate a current in the non-central part of the plasma volume, which reinforces the poloidal field. This current drive can sustain the monotonic decrease of q with radius. The plasma stability is studied by constructing the Lyapunov functional and investigating its extrema both analytically and numerically. This can be justified by either a qualitative argument about the hierarchy of the relaxation processes or a straightforward search for equilibria that are stable against non-linear perturbations. The results of the Lyapunov approach lead to an additional restriction on the equilibria as compared to the conventional linear theory, namely that a stable equilibrium should correspond to an extremum of an integral of motion. This restriction can be expressed as an additional equation involving the arbitrary functions of the Grad-Shafranov equilibrium.

Belova, E., S. Jardin, et al. (2000). “Numerical study of tilt stability of prolate field-reversed configurations.”

Global stability of the field-reversed configuration (FRC) has been investigated numerically using both three-dimensional magnetohydrodynamic and hybrid (fluid electron and deltaf particle ion) simulations. The stabilizing effects of velocity shear and finite ion Larmor radius (FLR) on the n = 1 internal tilt mode in the prolate FRCs have been studied. Sheared rotation is found to reduce the growth rate, however a large rotation rate with Mach number of M greater than or similar to 1 is required in order for significant reduction in the instability growth rate to occur. Kinetic effects associated with large thermal ion orbits have been studied for different kinetic equilibria. The simulations show that there is a reduction in the tilt mode growth rate due to FLR effects, but complete linear stability has not been found, even when the thermal ion gyroradius is comparable to the distance between the field null and the separatrix. The instability existing beyond the FLR theory threshold could be due to the resonant interaction of the wave with ions whose Doppler shifted frequency matches the betatron frequency. (C) 2000 American Institute of Physics. [S1070-664X(00)01612-8].

Belova, E., S. Jardin, et al. (2001). “Numerical study of global stability of oblate field-reversed configurations.”

Global stability of the oblate (small elongation, E <1) Field-Reversed Configuration (FRC) has been investigated numerically using both three-dimensional magnetohydrodynamic (MHD) and hybrid (fluid electrons and kinetic ions) simulations. For every nonzero value of the toroidal mode number n, there are three MHD modes that must be stabilized. For n=1, these are the interchange, the tilt and the radial shift; while for n >1 these are the interchange and two co-interchange modes with different polarization. It is shown that the n=1 tilt mode becomes an external mode when E <1, and it can be effectively stabilized by close-fitting conducting shells, even in the small Larmor radii (MHD) regime. The tilt mode stability improves with increasing oblateness, however at sufficiently small elongations the radial shift mode becomes more unstable than the tilt mode. The interchange mode stability is strongly profile dependent, and all n greater than or equal to1 interchange modes can be stabilized for a class of pressure profile with separatrix beta larger than 0.035. Our results show that all three n=1 modes can be stabilized in the MHD regime, but the stabilization of the n >1 co-interchange modes still remains an open question. (C) 2001 American Institute of Physics.

BERK, H. (1987). “PLASMA CURRENT SUSTAINED BY FUSION-CHARGED PARTICLES IN A FIELD-REVERSED CONFIGURATION.”

BERK, H., H. MOMOTA, et al. (1987). “PLASMA CURRENT SUSTAINED BY FUSION CHARGED-PARTICLES IN A FIELD-REVERSED CONFIGURATION.”

Bhattacharyya, R., M. Janaki, et al. (2001). “Field-reversed configuration (FRC) as a minimum-dissipative relaxed state.”

The field-reversed configuration (FRC) with a completely null toroidal field and finite plasma beta is shown to result from a relaxation mechanism based on the principle of minimum dissipation of energy. (C) 2001 Published by Elsevier Science B.V.

Bhattacharyya, R., M. Janaki, et al. (2003). “Relaxation phenomenon in the field reversed configuration.”

The relaxation phenomenon for a driven plasma system is studied using minimum dissipation rate principle. For the class of equilibria supporting field-aligned flows the Euler-Lagrange equations are shown to support bifurcated solutions. One of the branches depicts the topology of the field reversed configuration sustaining flow whereas the other branch resembles the classical spheromak configuration.

Binderbauer, M. and N. Rostoker (1996). “Turbulent transport in magnetic confinement: How to avoid it.”

From recent tokamak research, there is considerable experimental evidence that superthermal ions slow down and diffuse classically in the presence of turbulent fluctuations that cause anomalous transport of thermal ions. Furthermore, research on field-reversed configurations at Los Alamos is consistent with the view that kinetic effects suppress instability growth when the ratio of plasma radius to ion orbital radius is small; turbulence is enhanced and confinement degrades when this ratio increases. Motivated by these experiments, we consider a plasma consisting of large-orbit non-adiabatic ions and adiabatic electrons. For such a plasma, it is possible that the anomalous transport characteristic of tokamaks can be avoided and a compact reactor design becomes viable.

Bora, M. (2000). “Resistive axisymmetric equilibria with arbitrary flow.”

An analysis of axisymmetric equilibria with arbitrary incompressible flow and finite resistivity is presented. It is shown that with large aspect ratio approximation or vanishing poloidal current, a uniform conductivity profile is consistent with equilibrium flows. Also a comment is made on coexistence of both toroidal and poloidal flows in an axisymmetric field-reversed configuration. (C) 2000 American Institute of Physics. [S1070-664X(00)02207-2].

BOSE, M. (1995). “LOWER-HYBRID DRIFT WAVES IN A PLASMA WITH NEGATIVE-IONS.”

The dispersion relation for the lower hybrid drift mode is analytically obtained for a warm plasma containing negative ions. It is found that the lower hybrid drift frequency is directly proportional to the population density of negative ions. Moreover, it is found that the growth rate of the lower hybrid drift instability can be controlled by appropriate selection of the density inhomogeneity scale length, the external magnetic field and the number density of negative ions.

BROWNING, J., R. MAJESKI, et al. (1988). “INTERCHANGE STABILIZATION OF A MIRROR PLASMA USING RADIO-FREQUENCY WAVES BELOW THE ION-CYCLOTRON FREQUENCY.”

BROWNING, J., N. HERSHKOWITZ, et al. (1989). “RADIO-FREQUENCY WAVE INTERCHANGE STABILITY EXPERIMENTS BELOW THE ION-CYCLOTRON FREQUENCY.”

BUDKO, A., E. KARLSON, et al. (1993). “SELF-SIMILAR SOLUTIONS FOR TRAPPING AND DIFFUSION OF MAGNETIC-FLUX DURING FORMATION OF FIELD-REVERSED CONFIGURATION.”

Self-similar solutions are given that represent an analytical theory of implosion and extension stages of a THETA pinch before the magnetic field lines reconnection in course of formation of field-reversed configuration. Effects of Ohmic dissipation, thermal conductivity, and plasma turbulence are included. The self-similar solutions, obtained in an explicit analytical form, demonstrate that magnetic flux is trapped during the implosion and expansion stages for a classical plasma, and that losses of magnetic flux are possible for a turbulent plasma during the expansion stage. The rate of flux trapping and diffusion is expressed in terms of experimental parameters.

BURTSEV, V., I. ARTYUGINA, et al. (1992). “D-HE-3-FUELED FUSION POWER-PLANT BASED ON THE PULSATORY FIELD-REVERSED CONFIGURATION.”

Some physical and engineering aspects of a D-He-3 fueled fusion power plant based on the pulsatory field-reversed configuration are considered. The results of preliminary technical and economical factors and optimization calculations are given. An increase in the "aneutronics factor" of such a reactor is shown to result in higher costs.

BURTSEV, V., V. KOZHEVIN, et al. (1992). “THE PULSATOR CONCEPT AS A POSSIBLE TECHNIQUE FOR FORMATION OF A FIELD-REVERSED CONFIGURATION.”

The PULSATOR concept for the formation of a quasi-stationary magnetoplasma field-reversed configuration (FRC) by means of cyclic injection and merging of toroids in the confinement chamber is analyzed. The possible use of quasi-stationary plasma accelerators for the formation of high-[beta] toroids is considered. The requirements for the formation of FRCs with fusion parameters are evaluated. The possibility of the existence of an FRC with a finite toroidal field value is shown. The SAPFIR experimental installation for FRC formation investigations is briefly described, and the results of preliminary experiments are given.

CAMPOS, D., M. MACHIDA, et al. (1995). “ANALYTIC STUDY ON HIGH-VOLTAGE CROWBAR SYSTEM.”

Crowbar switches are largely used in plasma devices, such as field-reversed configuration (FRC) machines and tokamaks, to avoid energy return from the discharge coil to the capacitor bank. A method of identification of all resistances, inductances and currents involved in capacitor bank discharges using a crowbar is proposed based on the derivation of the general analytical form of the coil current. This analysis can also be used for optimization of the discharge, reducing the ripple amplitude inherent in the crowbar-switched current. Fitting results of the TC-1 UNICAMP FRC device are also presented in this work.

CARLSON, A. (1987). “A SEARCH FOR LOWER-HYBRID-DRIFT FLUCTUATIONS IN A FIELD-REVERSED CONFIGURATION USING CO2 HETERODYNE SCATTERING.”

Chacon, L. and G. Miley (1996). “IEC breeder for D-He-3 satellite systems.”

D-He-3 fusion minimizes neutrons and maximizes charged fusion products, enabling Increased energy recovery efficiency by direct conversion However, scarce He-3 terrestrial resources(1) have deterred research & development (R&D) on this alternative. Here, we explore He-3 production through inertial electrostatic confinement (IEC) breeders, which supply He-3 to field-reversed configuration (FRC) satellite reactors.(2) The breeder-satellite system is analyzed in terms of energy balance. taking the net energy gain of the overall system as the key parameter. An economic study determines the competitiveness of breeding with respect to He-3 lunar mining, already shown to be an attractive route for commercial exploitation.(3)

CHAN, C., T. INTRATOR, et al. (1982). “THE EFFECT OF SECONDARY ELECTRONS ON PLASMA POTENTIAL IN A MULTI-DIPOLE DEVICE.”

CHAN, C., M. CHO, et al. (1984). “LABORATORY EVIDENCE FOR ION-ACOUSTIC TYPE DOUBLE-LAYERS.”

CHAN, C., M. CHO, et al. (1986). “EXPERIMENTAL-OBSERVATION OF SLOW ION-ACOUSTIC DOUBLE-LAYERS.”

CHANCE, M., J. GREENE, et al. (1992). “THE FIELD LINE TOPOLOGY OF A UNIFORM MAGNETIC-FIELD SUPERPOSED ON THE FIELD OF A DISTRIBUTED RING CURRENT.”

A magnetic field line topology with nulls, generated by superimposing a uniform magnetic field onto the field from a distributed ring current, is analyzed. This simple model, which is reminiscent of the structures found in laboratory field reversed configurations and detached plasmoids, is amenable to substantial analytical progress and also facilitates the visualization of the three dimensional field geometry. Four nulls are seen to exist and representative field lines and tubes of flux found by numerical integration are presented. An infinite number of topologically distinct flux bundles is found. These are distinguished by the number of times they encircle a circular magnetic field line. A convenient mapping is described which proves very useful in distinguishing between and following the paths of the different tubes of flux as they traverse through the null system. The separatrices that divide these flux bundles are described. The complexities already present in this simple but nontrivial configuration serve to emphasize the difficulties in analyzing more complicated geometries, but the intuition gained from this study proves beneficial in those cases. One such example is the comparison of the generic features of our model with those found in a topologically different model of plasmoid formations in the earth's magnetotail.

CHAPMAN, R., G. MILEY, et al. (1989). “FUSION SPACE PROPULSION WITH A FIELD REVERSED CONFIGURATION.”

CHIANG, P. and M. HSIAO (1992). “ELECTRIC-FIELD IN THE EDGE LAYER OF FIELD-REVERSED CONFIGURATIONS.”

A particle-tracing routine is used to find the boundary surface of the confinement region in velocity space. This numerical boundary surface is then imposed on the distribution function to calculate the electric potential profile around the X point in field-reversed configurations (FRC's). The model eliminates the original assumptions of the fast loss of the unconfined particles and free end-throat electric field in deriving the analytical confinement criteria in the velocity-space particle loss (VSPL) model. Electric potential profiles over the whole region with different particle-tracing times are presented. According to the calculated results, a new hypothetical electrostatic confinement in the edge layer is proposed. Effects resulting from this electrostatic confinement are investigated. It is found that several physical issues in the edge layer can be explained by this hypothetical electrostatic confinement.

CHIYODA, K. (1984). “SUFFICIENT CRITERION FOR MHD STABILITY OF A FIELD-REVERSED CONFIGURATION.”

CHIYODA, K. (1985). “A STABILITY ANALYSIS AGAINST THE INTERCHANGE MODE OF THE HILL VORTEX MODEL IN A FIELD-REVERSED CONFIGURATION.”

CHO, M., C. CHAN, et al. (1984). “MEASUREMENT OF VACUUM SPACE POTENTIAL BY AN EMISSIVE PROBE.”

CHO, M., N. HERSHKOWITZ, et al. (1988). “TEMPORAL EVOLUTION OF COLLISIONLESS SHEATHS.”

CHRIEN, R. (1985). “FIELD-REVERSED CONFIGURATION TRANSLATION INTO A COMPRESSION COIL.”

CHRIEN, R. and S. OKADA (1987). “FIELD-REVERSED CONFIGURATION PROFILES AND RESISTIVITIES INFERRED FROM THE RADIAL LINE-INTEGRAL DENSITY PROFILE.”

CHRIEN, R. (1991). “NEUTRON CALIBRATION FOR THE FRX-C LSM MAGNETIC COMPRESSION EXPERIMENT.”

Neutron source strength and yield from field-reversed configurations have been measured in the FRX-C/LSM magnetic compression experiment using plastic scintillators, indium activation samples, and moderated rhodium activation counters. The calibration of these neutron detectors is complicated by the changing shape and position of the plasma and by the presence of the massive aluminum compression coils. The overall uncertainty in the neutron measurements is estimated to be 45%.

CHUNG, C., N. HERSHKOWITZ, et al. (1984). “EXPERIMENTAL-OBSERVATIONS OF SELF-SIMILAR PLASMA EXPANSION.”

CLAUVEL, J., C. TCHOBROUTSKY, et al. (1986). “SPONTANEOUS RECURRENT FETAL WASTAGE AND AUTOIMMUNE ABNORMALITIES - A STUDY OF 14 CASES.”

CLEMENTE, R. and J. MILOVICH (1981). “THE TILTING MODE IN FIELD-REVERSED CONFIGURATIONS.”

CLEMENTE, R. and J. MILOVICH (1983). “THE TILTING MODE IN RIGIDLY ROTATING FIELD-REVERSED CONFIGURATIONS.”

CLEMENTE, R. (1983). “A BIFURCATION PROBLEM IN FIELD-REVERSED CONFIGURATIONS.”

CLEMENTE, R. and C. GRILLO (1984). “INTERNAL TILTING AND CLASSICAL TRANSPORT FOR FIELD-REVERSED CONFIGURATIONS BASED ON THE MASCHKE-HERNEGGER SOLUTION.”

CLEMENTE, R., P. SAKANAKA, et al. (1989). “PLASMA DECAY IN FIELD REVERSED CONFIGURATIONS.”

CLEMENTE, R. (1991). “RIGID ROTOR MODEL FOR FIELD-REVERSED CONFIGURATIONS, REVISITED.”

It is shown that the ratio between ion and electron macroscopic rotational frequencies in rigid rotor profiles, OMEGA-i/OMEGA-e, is not a free parameter when global charge neutrality is taken into account. For most applications of interest OMEGA-i/OMEGA-e less-than-or-equal-to - T(i)/T(e) and depends on global characteristics of the confined plasma, as number of confined particles per unit length, T(i)/T(e) and the diamagnetism. Global charge neutrality is justified on the facts that in weakly coupled plasmas, the electrostatic energy of each species should be much lower than the respective thermal energy on average, and that no experimental evidence of any net charge of the plasma in theta-pinches or field-reversed configurations is reported. Connections of the present results with previous stability studies based on the rigid rotor model are discussed and some comparison with experimental results, supporting the hypothesis of global charge neutrality, are presented.

CLEMENTE, R. and L. STEINHAUER (1994). “RESISTIVE ANISOTROPIC FLOW FOR EDGE-LAYER AND JETS IN FIELD-REVERSED CONFIGURATIONS.”

A fluid model allowing for plasma resistivity and anisotropic temperatures, for describing edge-layer and jets in field-reversed configurations, is presented. Jet velocity can be predicted in terms of drops in parallel and perpendicular temperatures, from the separatrix to the throat, and the edge-layer broadness should depend on plasma conductivity. Comparison with experimental measurements suggests that the conductivity should be an order of magnitude lower than classical.

Clemente, R., P. Sakanaka, et al. (1995). “On the stability of anisotropic field-reversed configurations.”

The stability of a class of anisotropic field-reversed configurations (FRCs) is studied using an extension of the energy principle. When a family of incompressible plasma displacements xi satisfying B . (B . del xi) = 0, with B the equilibrium magnetic field, is considered, the general result that the stability problem is equivalent to that of scalar pressure FRCs is obtained. The formalism allows us to predict the existence of global modes for toroidal mode number n greater than unity, with growth rates faster than for the n = 1 case, which corresponds to tilting instability.

CLEMENTE, R. and R. CESAR (1995). “ANISOTROPIC EFFECTS ON CLASSICAL PARTICLE CONFINEMENT TIME IN FIELD-REVERSED CONFIGURATIONS.”

A global particle transport calculation for field-reversed configurations with possible anisotropy in the kinetic stress tenser is presented. The resulting particle confinement times may be greater or smaller than in the scalar pressure case, depending on the amount and behaviour of anisotropy. The calculation is restricted to a special quasi-equilibrium model we named 'anisotropic' Hill's vortex; however, similar effects should also arise for other anisotropic models. Comparison with experimental results is of limited meaning due to lack of measurements of any eventual anisotropy.

Clemente, R. (1998). “Anisotropic magnetic confinement, applications to field-reversed configurations.”

Introducing an auxiliary function of the usual poloidal magnetic stream function, it is possible to obtain axisymmetric solutions of the ideal anisotropic magnetohydrodynamic equations for steady rotating plasmas, in terms of solutions of the Maschke and Perrin equation for isotropic plasmas, with temperature as a surface function. For vanishing rotation, the problem is reduced to the classical Grad-Schluter-Shafranov equation for static equilibria. Some applications of the equilibrium models to the study of tilting stability and classical particle transport in field-reversed configurations are presented.

Clemente, R. (1998). “On current drive in field-reversed configurations.”

The problem of current drive in field-reversed configurations, by apl,lying two transverse magnetic fields rotating in opposite sense: is analyzed within the framework of two-fluid collisional equations. It is shown that it is possible to generate opposite torques on electron and ions, while the net externally applied torque is vanishing. In this scenario, wall interactions, collisions with neutrals and diffusion effects are not required in order to maintain the steady stale. It is also shown that, when electrons and ions are almost in phase with the two rotating fields, the injected power is mainly dissipated by collisions associated with the azimuthal motion of both species, which should permit the achievement of significant plasma current drive efficiency in field-reversed configurations.

COBB, J., T. TAJIMA, et al. (1993). “PROFILE STABILIZATION OF TILT MODE IN A FIELD-REVERSED CONFIGURATION.”

The possibility of stabilizing the tilt mode in field-reversed configurations without resorting to explicit kinetic effects such as large ion orbits is investigated. Various pressure profiles, P(PSI), are chosen, including ''hollow'' profiles, where current is strongly peaked near the separatrix. Numerical equilibria are used as input for an initial value simulation, which uses an extended magnetohydrodynamic (MHD) model that includes viscous and Hall terms. Tilt stability is found for specific hollow profiles when accompanied by high values of separatrix beta, beta(sep). The stable profiles also have moderate to large elongation, racetrack separatrix shape, and lower values of sBAR, average ratio of Larmor radius to device radius. The stability is unaffected by changes in viscosity, but the neglect of the Hall term does cause stable results to become marginal or unstable. Implications for interpretation of recent experiments are discussed.

Cohen, S. and A. Glasser (2000). “Ion heating in the field-reversed configuration by rotating magnetic fields near the ion-cyclotron resonance.”

The trajectories of ions confined in a field-reversed configuration (FRC) equilibrium magnetic geometry and heated with a small-amplitude, odd-parity rotating magnetic field (RMF) have been studied with a Hamiltonian computer code. When the RMF frequency is in the ion-cyclotron range, explosive heating occurs. Higher-energy ions are found to have betatron-type orbits, preferentially localized near the FRC's midplane. These results are relevant to a compact magnetic-fusion-reactor design.

Cohen, S. and R. Milroy (2000). “Maintaining the closed magnetic-field-line topology of a field-reversed configuration with the addition of static transverse magnetic fields.”

The effects on magnetic-field-line structure of adding various static transverse magnetic fields to a Solov'ev-equilibrium field-reversed configuration are examined. It is shown that adding fields that are antisymmetric about the axial midplane maintains the closed field-line structure, while adding fields with planar or helical symmetry opens the field structure. Antisymmetric modes also introduce pronounced shear. (C) 2000 American Institute of Physics. [S1070-664X(00)03705-8].

COMMISSO, R., C. EKDAHL, et al. (1980). “PREIONIZATION STUDIES FOR FIELD-REVERSED CONFIGURATIONS.”

CRAWFORD, E. (1992). “A MULTIFRAME SOFT-X-RAY CAMERA WITH FAST VIDEO CAPTURE FOR THE LSX FIELD REVERSED CONFIGURATION (FRC) EXPERIMENT.”

Soft x-ray pinhole imaging has proven to be an exceptionally useful diagnostic for qualitative observation of impurity radiation from field reversed configuration plasmas. We used a four frame device, similar in design to those discussed in an earlier paper [E. A. Crawford, D. P. Taggart, and A. D. Bailey III, Rev. Sci. Instrum. 61, 2795 (1990)] as a routine diagnostic during the last six months of the Large s Experiment (LSX) program. Our camera is an improvement over earlier implementations in several significant aspects. It was designed and used from the onset of the LSX experiments with a video frame capture system so that an instant visual record of the shot was available to the machine operator as well as facilitating quantitative interpretation of intensity information recorded in the images. The camera was installed in the end region of the LSX on axis approximately 5.5 m from the plasma midplane. Experience with bolometers on LSX showed serious problems with "particle dumps" at the axial location at various times during the plasma discharge. Therefore, the initial implementation of the camera included an effective magnetic sweeper assembly. Overall performance of the camera, video capture system, and sweeper is discussed.

DASGUPTA, B., T. SATO, et al. (1995). “FORMATION OF A FIELD-REVERSED CONFIGURATION BY COALESCENCE OF SPHEROMAKS.”

DEGNAN, J., R. PETERKIN, et al. (1993). “COMPACT TOROID FORMATION, COMPRESSION, AND ACCELERATION.”

Research on forming, compressing, and accelerating milligram-range compact toroids using a meter diameter, two-stage, puffed gas, magnetic field embedded coaxial plasma gun is described. The compact toroids that are studied are similar to spheromaks, but they are threaded by an inner conductor. This research effort, named MARAUDER (Magnetically Accelerated Ring to Achieve Ultra-high Directed Energy and Radiation), is not a magnetic confinement fusion program like most spheromak efforts. Rather, the ultimate goal of the present program is to compress toroids to high mass density and magnetic field intensity, and to accelerate the toroids to high speed. There are a variety of applications for compressed, accelerated toroids including fast opening switches, x-radiation production, radio frequency (rf) compression, as well as charge-neutral ion beam and inertial confinement fusion studies. Experiments performed to date to form and accelerate toroids have been diagnosed with magnetic probe arrays, laser interferometry, time and space resolved optical spectroscopy, and fast photography. Parts of the experiment have been designed by, and experimental results are interpreted with, the help of two-dimensional (2-D), time-dependent magnetohydrodynamic (MHD) numerical simulations. When not driven by a second discharge, the toroids relax to a Woltjer-Taylor equilibrium state that compares favorably to the results of 2-D equilibrium calculations and to 2-D time-dependent MHD simulations. Current, voltage, and magnetic probe data from toroids that are driven by an acceleration discharge are compared to 2-D MHD and to circuit solver/slug model predictions. Results suggest that compact toroids are formed in 7-15 musec, and can be accelerated intact with material species the same as injected gas species and entrained mass greater-than-or-equal-to 1/2 the injected mass.

Degnan, J., J. Taccetti, et al. (2001). “Implosion of solid liner for compression of field reversed configuration.”

The design and first successful demonstration of an imploding solid liner with height to diameter ratio, radial convergence, and uniformity suitable for compressing a field reversed configuration is discussed. Radiographs indicated a very symmetric implosion with no instability growth, with similar to 13 x radial compression of thp inner liner surface prior to impacting a central measurement unit. The implosion kinetic energy was 1.5 megajoules, 34% of the capacitor stored energy of 4.4 megajoules,

DIEBOLD, D., N. HERSHKOWITZ, et al. (1987). “SELF-SIMILAR POTENTIAL IN THE NEAR WAKE.”

DIEBOLD, D., N. HERSHKOWITZ, et al. (1988). “EMISSIVE PROBE CURRENT BIAS METHOD OF MEASURING DC VACUUM POTENTIAL.”

FARENGO, R., P. GUZDAR, et al. (1988). “THE EFFECT OF MAGNETIZED IONS ON THE LOWER HYBRID DRIFT INSTABILITY IN FIELD REVERSED CONFIGURATIONS.”

FARENGO, R., P. GUZDAR, et al. (1989). “COLLISIONLESS ELECTRON-TEMPERATURE GRADIENT-DRIVEN INSTABILITY IN FIELD-REVERSED CONFIGURATIONS.”

FARENGO, R., P. GUZDAR, et al. (1989). “STABILIZATION OF LOWER HYBRID DRIFT MODES BY FINITE PARALLEL WAVENUMBER AND ELECTRON-TEMPERATURE GRADIENTS IN FIELD-REVERSED CONFIGURATIONS.”

FARENGO, R. and R. BROOKS (1991). “CURRENT LIMIT IN OHMICALLY HEATED HIGH-BETA PLASMAS - APPLICATION TO FIELD REVERSED CONFIGURATIONS.”

The power balance in slowly formed, Ohmically heated, field reversed configurations is considered. It is shown that a critical current exists above which the radiated power (from impurities) exceeds the Ohmic dissipation. The basic physics is introduced by analyzing the case of a linear Z pinch. Two-dimensional equilibria corresponding to a conventional field reversed configuration and the coaxial slow source [Nucl. Fusion 27, 1478 (1987)] are also considered.

FARENGO, R. and R. BROOKS (1992). “PLASMA-HEATING AND DYNAMICS IN THE COAXIAL SLOW SOURCE.”

Simple semi-analytical models are presented to calculate the temporal evolution of the plasma temperature and length or thickness in the Coaxial Slow Source (Nucl. Fusion 27 (1987) 1478) for both tearing formation and programmed formation. It is assumed that energy is delivered to the plasma via Ohmic heating and compressional work and is lost through impurity line radiation. The plasma is considered to be always fully ionized and in pressure balance; the external magnetic field is taken to be a known function of time, and particle losses are neglected. In tearing formation, a long and thin plasma sheet is initially formed. This can be studied using a 1-D model; it is shown that the higher the external field and the smaller the line integrated density, the faster the temperature increases. In programmed formation, an axial equilibrium is quickly established and a 2-D model is required. It is shown that when the external magnetic field exceeds a critical value, which depends on the temperature, the impurity fraction and the effective plasma thickness, the radiated power overcomes Ohmic heating and a radiative collapse occurs. Various time histories of the external magnetic field are analysed in order to determine the conditions that result in the fastest increase in plasma temperature.

FARENGO, R. (1992). “INTERNAL TILTING INSTABILITY IN ANNULAR FIELD-REVERSED CONFIGURATIONS.”

The energy principle is used to show that elongated annular field-reversed configurations with a conductor linking the torus are unstable to an internal tilt mode. The critical elongation increases with the aspect ratio and the growth rate decreases with plasma length for very elongated plasmas.

Farengo, R. and R. Clemente (2001). “Rotating magnetic field current drive in a hollow plasma column with a steady toroidal field.”

The effect of a steady azimuthal magnetic field on rotating magnetic field current drive is studied. The configuration considered consists of an infinitely long plasma column with a finite radius conductor, which carries a steady longitudinal current, running along its axis. The ions are assumed to be fixed and the electrons are described using an Ohm's law that contains the Hall term. A fully two-dimensional computer code is developed to solve the resulting time-dependent equations. For some values of the steady azimuthal field, two steady-state solutions with different efficiencies are found. (C) 2001 American Institute of Physics.

Farengo, R., A. Lifschitz, et al. (2002). “Theoretical studies of non inductive current drive in compact toroids.”

Three non inductive current drive methods that can be applied to compact toroids axe studied. The use of neutral beams to drive current in field reversed configurations and spheromaks is studied using a Monte Carlo code that includes a complete ionization package and follows the exact particle orbits in a self-consistent equilibrium calculated including tile beam and plasma currents, Rotating magnetic fields are investigated as a current drive method for spherical tokamaks by employing a two dimensional model with fixed ions and massless electrons. The time evolution of the axial components of the magnetic field and vector potential is obtained by combining an Ohm's law that includes the Hall term with Maxwell's equations. The use of helicity injection to sustain a flux core spheromak is studied using the principle of minimum rate of energy dissipation. The Euler-Lagrange equations obtained using helicity balance as a constraint axe solved to determine the current and magnetic field profiles of the relaxed states.

FERRON, J., R. GOULDING, et al. (1987). “ELECTROSTATIC END PLUGGING ACCOMPANIED BY A CENTRAL-CELL DENSITY INCREASE IN AN AXISYMMETRICAL TANDEM MIRROR.”

FINN, J. and R. SUDAN (1978). “MHD STABILITY OF FIELD REVERSED CONFIGURATIONS WITH A TOROIDAL FIELD.”

FINN, J. and R. SUDAN (1978). “RESONANT EFFECTS ON LOW-FREQUENCY VLASOV STABILITY OF AXISYMMETRIC FIELD-REVERSED CONFIGURATIONS.”

FINN, J. and R. SUDAN (1982). “FIELD-REVERSED CONFIGURATIONS WITH A COMPONENT OF ENERGETIC PARTICLES.”

FUENTES, N. and H. GAVARINI (1995). “ECMC, A PORTABLE 2-DIMENSIONAL CODE FOR PLASMA EQUILIBRIUM COMPUTATION ON COAXIAL-MULTIPLE-COIL SYSTEMS.”

A two-dimensional code ECMC for computing field-reversed configuration equilibria is described. Equilibrium states are found by solving the finite difference form of Grad-Shafranov equation by means of a successive over-relaxation method. Plasma rotation and the existence of a toroidal magnetic field component are not taken into account. Plasma trapped current is used as a constraint parameter to achieve an equilibrium state. The code computes any coaxial-multiple-coil system from the input data of coil positions in laboratory coordinates and their respective currents. It was written assuming neither a particular experimental device geometry nor a specific shape for the magnetic flux function in order to simulate the coils. Plasma pressure dependence as a function of the magnetic flux may be changed by providing a routine to replace that given by default. The code simulation includes the possibility of taking into account the infinite axial and radial coordinates. ECMC allows parameters (coil positions and currents, plasma trapped current, data to be written in output files, convergence criteria) to be changed interactively. Examples of simulated equilibria on different experimental devices are given.

Fujimoto, K., A. Hoshikawa, et al. (2002). “Control of a global motion on field-reversed configuration.”

An n=1 mode global motion on a field-reversed configuration (FRC) plasma is observed by means of a newly developed optical system. The deviation of the FRC from the coil axis reaches 20%-40% of the plasma radius. In order to push back the FRC to the equilibrium position, a multipole field (quadrupole or hexapole field) is applied. The n=1 motion can be easily controlled by the quadrupole field, the critical field strength of which is required to be about 15% of the confinement field. It is found that the n=2 rotational instability can also be stabilized by strength of the same order. The critical strength for the n=1 motion is theoretically obtained from a model such that the driving energy of the motion given at the formation phase balances with the work done by the multipole field. The theoretical estimation agrees within a factor of 2 with the experimental results. (C) 2002 American Institute of Physics.

Fundamenski, W. and A. Harms (1996). “Evolution and status of D-He-3 fusion: A critical review.”

Advanced fuels for nuclear fusion - of which deuterium and He-3 mixture is the leading candidate - could reduce tritium inventory, neutron fluence, structural damage, and activation in future reactors as well as allow for direct energy conversion. The feasibility of D-He-3 fusion is assessed based on recent developments in the areas of fuel resources, fusion and plasma physics, magnetic and inertial reactors, space propulsion, reactor safety, and waste disposal. It appears that D-He-3 fusion is not well suited to the conventional tokamak design (beta similar to 10%) because of excessive synchrotron loss and closed field topology. High-beta and/or non-Maxwellian plasma configurations are promising but at present lack a sufficient experimental database to predict reactor-relevant behavior. Space propulsion appears to be a most advantageous application of D-He-3 fusion.

GLADD, N., A. SGRO, et al. (1985). “MICROSTABILITY PROPERTIES OF THE SHEATH REGION OF A FIELD-REVERSED CONFIGURATION.”

Glasser, A. and S. Cohen (2002). “Ion and electron acceleration in the field-reversed configuration with an odd-parity rotating magnetic field.”

The method for accelerating ions and electrons in the field-reversed configuration using odd-parity rotating magnetic fields (RMFs) in the ion-cyclotron range-of-frequencies (ICRF) is studied. The approach is based on long, accurate numerical integration of Hamilton's equations for single-particle orbits. Rapid ion heating to thermonuclear conditions occurs in <0.1 ms in a modest-sized FRC. Strong variation of the magnetic-field strength over the confinement region prevents a true cyclotron resonance, resulting in stochastic though effective heating. Lyapunov exponents are computed to demonstrate chaotic orbits. Electrons are also effectively heated in this frequency range, primarily by a mechanism involving trapping in the wells of the azimuthal electric field. Odd-parity RMF promotes oppositely directed ion and electron motion near the minor axis, appropriate for supporting the plasma current. (C) 2002 American Institute of Physics.

Gota, H., T. Akiyama, et al. (2003). “Separatrix shape measurement on field-reversed configuration plasmas.”

In order to determine the separatrix shapes of field-reversed configuration plasmas with high accuracy, an iterative method that compares measured magnetic fluxes with the solution of the Grad-Shafranov equation is discussed in detail. Several suggestions for successfully treating the iterative method are given using numerical simulation and a mock-up experiment where conductors with three kinds of shape are inserted into the coil instead of the plasma. The iterative method is also applied to the field-reversed configuration plasma, and it is found that the separatrix shape has distinct ends and the axial location of the X point can be determined. (C) 2003 American Institute of Physics.

GOTTSCHO, R., G. SCHELLER, et al. (1988). “SPACE-TIME RESOLVED KINETICS OF MIXED RARE-GAS-ATTACHING GAS PLASMAS.”

GOTTSCHO, R., G. SCHELLER, et al. (1989). “THE EFFECT OF ELECTRODE AREA RATIO ON LOW-FREQUENCY GLOW-DISCHARGES.”

GOUAULTHEILMANN, M., D. PAYEN, et al. (1985). “THROMBOCYTOPENIA RELATED TO SYNTHETIC HEPARIN ANALOG THERAPY.”

GOUAULTHEILMANN, M., L. INTRATOR, et al. (1987). “CIRCULATING LUPUS ANTICOAGULANT - A RETROSPECTIVE STUDY OF 134 CASES.”

GOUAULTHEILMANN, M., Y. HUET, et al. (1987). “LOW-MOLECULAR-WEIGHT HEPARIN FRACTIONS AS AN ALTERNATIVE THERAPY IN HEPARIN-INDUCED THROMBOCYTOPENIA.”

GOUAULTHEILMANN, M., T. GADELHAPARENTE, et al. (1988). “TOTAL AND FREE PROTEIN-S IN NEPHROTIC SYNDROME.”

GOUAULTHELLMANN, M., Y. HUET, et al. (1986). “LOW-MOLECULAR-WEIGHT HEPARIN FRACTIONS AS AN ALTERNATIVE THERAPY IN HEPARIN-INDUCED THROMBOCYTOPENIA.”

Grabowski, C., J. Degnan, et al. (2002). “Development of a high-current low-inductance crowbar switch for FRX-L.”

The design and test results of a crowbar switch developed for the formation of long-lifetime field-reversed configurations are presented. These research efforts are being pursued at the FRX-L facility at Los Alamos National Laboratory using the "Colt" capacitor bank (a 36 muF Shiva Star bank module capable of storing up to 250 U) and at the Air Force Research Laboratory using the "Formation" capacitor bank (consisting of three parallel banks identical to Colt). The crowbar switch design includes four Maxwell rail-gap switches mounted on a cable header that transitions from the capacitor bank bus plates to 48 RG 17/14 coaxial cables. For the testing performed at AFRL, a dummy load was set up to simulate the magnetic field coils of the actual experiment. Tests thus far have demonstrated the crowbarring of peak currents up to 1.25 MA. Breakdown within the cable header due to the initial high voltage applied from the bank has been successfully suppressed by the cable feed-through design, proper placement of Mylar sheets around the switch for insulation, and replacement of air in the header with SF6. Timing for the triggering of the crowbar is somewhat critical, as inductance in the switch increases when the switch is triggered with lower voltages across the switch rails. At the higher bank charge voltages, the charge-flow ratings on the rail-gap switches are exceeded; however, other than requiring that the rail electrodes in the switches be cleaned more frequently, no detrimental effects have been observed from the excessive charge flow.

Greenwald, M. (2002). “Density limits in toroidal plasmas.”

In addition to the operational limits imposed by MHD stability on plasma current and pressure, an independent limit on plasma density is observed in confined toroidal plasmas. This review attempts to summarize recent work on the phenomenology and physics of the density limit. Perhaps the most surprising result is that all of the toroidal confinement devices considered operate in similar ranges of (suitably normalized) densities. The empirical scalings derived independently for tokamaks and reversed-field pinches are essentially identical, while stellarators appear to operate at somewhat higher densities with a different scaling. Dedicated density limit experiments have not been carried out for spheromaks and field-reversed configurations, however 'optimized' discharges in these devices are also well characterized by the same empirical law. In tokamaks, where the most extensive studies have been conducted, there is strong evidence linking the limit to physics near the plasma boundary: thus, it is possible to extend the operational range for line-averaged density by operating with peaked density profiles. Additional particles in the plasma core apparently have no effect on density limit physics. While there is no widely accepted, first principles model for the density limit, research in this area has focussed on mechanisms which lead to strong edge cooling. Theoretical work has concentrated on the consequences of increased impurity radiation which may dominate power balance at high densities and low temperatures. These theories are not entirely satisfactory as they require assumptions about edge transport and make predictions for power and impurity scaling that may not be consistent with experimental results. A separate thread of research looks for the cause in collisionality enhanced turbulent transport. While there is experimental and theoretical support for this approach, understanding of the underlying mechanisms is only at a rudimentary stage and no predictive capability is yet available.

GROSSMANN, W. and H. WEITZNER (1980). “STABILITY OF FIELD REVERSED CONFIGURATIONS.”

GUDEL, M. and P. ZLOBEC (1991). “POLARIZATION AND EMISSION MODE OF SOLAR RADIO SPIKES.”

Observational polarization characteristics of solar millisecond decimetric and microwave spike emission and implications on the emission mode are discussed. The data are based on a large sample of spike observations recorded in Trieste and Zurich, covering the 100 - 3000 MHz range; 38 include polarization information. The main results are: 1. Contrary to the widespread assumption, spikes are not always strongly polarized; indeed, any polarization degree may be observed with similar probability. 2. The spike polarization follows a distinct center-to-limb variation; very strong (> 90%) polarization originates from near the center; toward the limb, the polarization degree tends to zero. 3. The sense of the polarization is opposite to that of associated type III bursts for almost all bursts considered. It is also systematically dependent on the magnetic field configuration of the underlying magnetic spots. This suggests that one of the magnetoionic emission modes dominates. Under the additional assumption that complicated magnetic field reversal configurations are not present, extraordinary mode is found for the majority of the events. 4. The time delay between the RCP and the LCP emission is less than 30 ms, and in one case, RCP and LCP were simultaneous within 0.5 ms. Implications on the emission process, on the depolarization along the ray paths, and on the site of depolarization are discussed.

Gulec, K., M. Abdou, et al. (2000). “Novel liquid blanket configurations and their hydrodynamic analyses for innovative confinement concepts.”

Hydrodynamics analyses as a part of the APEX (advanced power extraction) study demonstrates the potential application of applying swirling thick liquid walls to innovative confinement concepts such as field reversed configuration (FRC), spherical torus (ST) and heavy-ion fusion (HIF). This paper addresses the design and the hydrodynamic aspects of fusion relevant swirling flow including 3-D velocity distribution, variations of the flow height in axial and azimuthal directions and hydrodynamic flow stability. Numerical hydrodynamic analyses using a 3-D code with Flibe as the working fluid, shows that a thick liquid first-wall/blanket (> 0.6 m) can be maintained in a circular vacuum chamber of 2 m radius by injecting the liquid layer from one side through a swirl flow generating inlet with axial (7 m/s) and azimuthal (10 m/s) velocity components. Parametric computational study indicated that the liquid layer thickness in axial and azimuthal directions is strongly dependent on the inlet axial, azimuthal velocity values and gravitational acceleration. It also shows that a uniform liquid layer thickness can be maintained for axial and azimuthal inlet velocities of 11 and 13 m/s in a cylindrical chamber with a 2 m radius and 12 m length. The swirling liquid wall idea is applied successfully to ST and HIF configurations. A 2D linear stability analysis using potential flow theory (Reynolds number is similar to 10(6) for liquid wall thickness of similar to 0.5 m) of the swirling flow in the azimuthal flow direction suggested that mean flow is stable when the surface tension, gravitational acceleration, and the centrifugal force effects are considered. (C) 2000 Published by Elsevier Science B.V.

Guo, H., A. Hoffman, et al. (2002). “Formation and steady-state maintenance of field reversed configuration using rotating magnetic field current drive.”

Rotating magnetic fields (RMF) have been used to both form and maintain field reversed configurations (FRC) in quasisteady state. These experiments differ from steady-state rotamaks in that the FRCs are similar to those formed in theta-pinch devices, that is elongated and confined inside a flux conserver. The RMF creates an FRC by driving an azimuthal current which reverses an initial positive bias field. The FRC then expands radially, compressing the initial axial bias flux and raising the plasma density, until a balance is reached between the RMF drive force and the electron-ion friction. This generally results in a very high ratio of separatrix to flux conserver radius. The achievable final conditions are compared with simple analytic models to estimate the effective plasma resistivity. The RMF torque on the electrons is quickly transferred to the ions, but ion spin-up is limited in these low density experiments, presumably by ion-neutral friction, and does not influence the basic current drive process. However, the ion rotation can result in a rotating n=2 distortion if the separatrix radius is too far removed from the plasma tube wall. (C) 2002 American Institute of Physics.

HAMADA, S. (1986). “A MODEL OF EQUILIBRIUM TRANSPORT AND EVOLUTION OF FIELD REVERSED CONFIGURATIONS.”

HAMADA, S. and M. AZEVEDO (1988). “STUDY OF A MODEL OF FIELD REVERSED CONFIGURATION WITH THE LOWER HYBRID DRIFT ANOMALOUS RESISTIVITY.”

HAMASAKI, S. and R. LINFORD (1979). “MODELING FOR DIFFUSION OF PLASMA IN FIELD REVERSED CONFIGURATIONS.”

HAMASAKI, S., N. GLADD, et al. (1986). “ONE-DIMENSIONAL TRANSPORT MODELS WITH LOCAL AND NONLOCAL LOWER-HYBRID-DRIFT WAVES IN FIELD-REVERSED CONFIGURATIONS.”

HARNED, D. (1983). “ROTATIONAL INSTABILITIES IN THE FIELD-REVERSED CONFIGURATION - RESULTS OF HYBRID SIMULATIONS.”

HARNED, D. and D. HEWETT (1984). “THE ORIGIN OF ROTATION IN FIELD-REVERSED CONFIGURATIONS.”

HARNED, D. (1984). “SUPPRESSION OF THE M=2 ROTATIONAL INSTABILITY IN THE FIELD-REVERSED CONFIGURATION BY MEANS OF QUADRUPOLE FIELDS.”

HASSAM, A. (1984). “COLLISIONAL TEARING IN FIELD-REVERSED CONFIGURATIONS.”

Hassam, A., R. Kulsrud, et al. (1999). “Steady state thermoelectric field-reversed configurations.”

It is shown that the cross-field thermoelectric force of magnetized plasmas can maintain field-reversed configurations against resistive diffusion, resulting in a steady state device attractive for thermonuclear fusion. If a peaked radial temperature profile is maintained, the thermoelectric force is in the opposite direction to the usual resistive friction, thus maintaining the field configuration. The field maintenance is tantamount to dynamo action, operating even in two dimensions. We show that a steady state device can be made by simply heating the O-point: no external electric fields or particle sources are needed. The feasibility of this scheme for fusion is discussed.

HERSHKOWITZ, N. and T. INTRATOR (1981). “IMPROVED SOURCE OF COLD-PLASMA ELECTRONS AND NEGATIVE-IONS.”

HERSHKOWITZ, N., C. FOREST, et al. (1987). “PUMPING POTENTIAL WELLS.”

HERSHKOWITZ, N., M. CHO, et al. (1988). “LANGMUIR PROBE CHARACTERISTICS IN RF GLOW-DISCHARGES.”

HESLAN, J., J. LAUTIE, et al. (1982). “IMPAIRED IGG SYNTHESIS IN PATIENTS WITH THE NEPHROTIC SYNDROME.”

HEWETT, D. and R. SPENCER (1983). “TWO-DIMENSIONAL EQUILIBRIA OF FIELD-REVERSED CONFIGURATIONS IN A PERFECTLY CONDUCTING CYLINDRICAL-SHELL.”

HIMURA, H., S. OKADA, et al. (1995). “TRANSLATION EXPERIMENTS OF FIELD-REVERSED CONFIGURATION PLASMA.”

Translation dynamics of field-reversed configuration (FRC) plasmas are studied in the FRC Injection Experiment (FIX) machine. FRC plasmas have been formed in, and launched from, a field-reversed theta-pinch source, and subsequently translated into reduced external magnetic fields. When translated into an adjacent confinement region, incident velocity of the formed FRC exceeds the Alfven velocity. Moreover, the translated FRC cools less than the prediction of an adiabatic theory. The plasma reflects from an external mirror, and some of its axial kinetic energy is lost during every reflection. In this reflection process, significant plasma heating is observed in the case where the translation velocity exceeds the sound velocity.

HIMURA, H., S. OKADA, et al. (1995). “RETHERMALIZATION OF A FIELD-REVERSED CONFIGURATION PLASMA IN TRANSLATION EXPERIMENTS.”

Himura, H., H. Wada, et al. (1997). “Drift motion of field-reversed-configuration plasma across a curved magnetic field.”

We report the first observation of the behavior of a field-reversed-configuration (FRC) plasma translated into a curved magnetic field B-cur. The FRC shows a unique behavior in B-cur. The plasma splits into two parts: one is a bulk plasma confined in a field-reversed magnetic geometry, deflecting strongly across B-cur despite beta(E) (the ratio of directed to transverse magnetic-field energy density) much greater than 1; the other is probably a peripheral plasma outside the separatrix, propagating rigidly along B-cur. This motion of the FRC may be due to E x B drifting, rather than displacement of the vacuum field by diamagnetic currents.

Himura, H., S. Ueoka, et al. (1998). “Observation of collisionless thermalization of a plasmoid with a field-reversed configuration in a magnetic mirror.”

A systematic translation study of field-reversed configurations (FRCs) has been conducted on the FRC Injection Experiment (FIX) machine [Okada et al., in Fusion Energy 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 2, p. 229]. Plasma density and temperature of a translated FRC moving at supersonic speed are measured in the downstream magnetic mirror of FIX to verify a shock jump there when the FRC is reflected. A significant jump is observed. Moreover, the time evolution of the Carbon V Doppler profile is measured both quasi-parallel and perpendicular to the direction of FRC motion. Distinct transitions from Gaussian to non-Gaussian shapes are clearly seen in both profiles before and after the shock jump. Also, the ion mean-free path in the downstream magnetic mirror is calculated to be much longer than the characteristic width of the shock jump. These results indicate that the thermalization of flow energy in the translated FRC in the mirror is produced by a collisionless process, implying that this heating mechanism can be realized even in a reactor regime. (C) 1998 American Institute of Physics. [S1070-664X(98)00212-2].

HIRANO, K. (1988). “SLOW FORMATION OF FIELD REVERSED CONFIGURATIONS BY COLLIDING HIGH-BETA COUNTER FLOWS.”

HIRANO, K. (1989). “IGNITION AND REACTOR APPLICATION OF DEUTERIUM BASED FUEL-CYCLES IN FIELD REVERSED CONFIGURATIONS.”

HOFFMAN, A. and R. MILROY (1983). “PARTICLE LIFETIME SCALING IN FIELD-REVERSED CONFIGURATIONS BASED ON LOWER-HYBRID-DRIFT RESISTIVITY.”

HOFFMAN, A., J. SLOUGH, et al. (1983). “SUPPRESSION OF THE N = 2 ROTATIONAL INSTABILITY IN FIELD-REVERSED CONFIGURATIONS.”

HOFFMAN, A. and J. SLOUGH (1986). “FLUX, ENERGY, AND PARTICLE LIFETIME MEASUREMENTS FOR WELL FORMED FIELD REVERSED CONFIGURATIONS.”

HOFFMAN, A., R. MILROY, et al. (1986). “FORMATION OF FIELD-REVERSED CONFIGURATIONS USING SCALABLE, LOW-VOLTAGE TECHNOLOGY.”

HOFFMAN, A. and J. SLOUGH (1993). “FIELD REVERSED CONFIGURATION LIFETIME SCALING BASED ON MEASUREMENTS FROM THE LARGE S-EXPERIMENT.”

Flux, energy and particle lifetimes have been measured in the new Large s Experiment field reversed configuration (FRC) facility. By careful control of the formation process, it was possible to form symmetric, quiescent FRCs, with s values higher than 4, in the one year of operation of the device. A wide range of plasma conditions was achieved, with ion temperatures varying between 0.1 and 1.5 keV. The lifetimes continue to scale approximately with the r(s)2/rho(i) parameter found in earlier work, with a coefficient proportional to x(s) to a power between 0.5 and 1.

HOFFMAN, A., L. CAREY, et al. (1993). “THE LARGE-S FIELD-REVERSED CONFIGURATION EXPERIMENT.”

The Large-s Experiment (LSX) was built to study the formation and equilibrium properties of field-reversed configurations (FRCs) as the scale size increases. The dynamic, field-reversed theta-pinch method of FRC creation produces axial and azimuthal deformations and makes formation difficult, especially in large devices with large s (number of internal gyroradii) where it is difficult to achieve initial plasma uniformity. However, with the proper technique, these formation distortions can be minimized and are then observed to decay with time. This suggests that the basic stability and robustness of FRCs formed, and in some cases translated, in smaller devices may also characterize larger FRCs. Elaborate formation controls were included on LSX to provide the initial uniformity and symmetry necessary to minimize formation disturbances, and stable FRCs could be formed up to the design goat of s = 8. For s less-than-or-equal-to 4, the formation distortions decayed away completely, resulting in symmetric equilibrium FRCs with record confinement times up to 0.5 ms, agreeing with previous empirical scaling laws (tau is-proportional-to sR). Above s = 4, reasonably long-lived (up to 0.3 ms) configurations could still be formed, but the initial formation distortions were so large that they never completely decayed away, and the equilibrium confinement was degraded from the empirical expectations. The LSX was only operational for 1 yr, and it is not known whether s = 4 represents a fundamental limit for good confinement in simple (no ion beam stabilization) FRCs or whether it simply reflects a limit of present formation technology. Ideally, s could be increased through flux buildup from neutral beams, thus avoiding dynamic formation disturbances at high s. Since the addition of kinetic or beam ions will probably be desirable for heating, sustainment, and further stabilization of magnetohydrodynamic modes at reactor-level s values, neutral beam injection is the next logical step in FRC development. Efficient ion current buildup requires low-density and high-temperature target plasmas, and low fill pressure (sub-mTorr) formation methods to produce such FRCs were also developed, for the first time, on LSX.

HOFFMAN, A. (1995). “REACTOR PROSPECTS AND PRESENT STATUS OF FIELD-REVERSED CONFIGURATIONS.”

Ffield-Reversed Configurations (FRC) have an ideal geometry for a reactor, combining high beta toroidal confinement, with a linear external geometry. Present small diameter FRCs are thought to be stabilized by kinetic effects, but recent experiments in the Large a Experiment (LSX) have demonstrated stability well into the MHD regime. Present empirical transport coefficients are already sufficient for a small pulsed reactor, but small steady state reactors will require about an order of magnitude reduction in plasma diffusivity.

Hoffman, A. (1996). “An ideal compact fusion reactor based on a field-reversed configuration.”

Field-reversed configurations (FRC) have been recognized as possessing almost ideal fusion reactor characteristics from the point of view of engineering simplicity and maintainability. The external geometry is cylindrical while the internal magnetic field configuration is toroidal, allowing for both a simple magnetic confinement design and the possibility of good plasma confinement. FRCs are unique among all toroidal confinement concepts in not possessing any significant toroidal field. This necessitates a very high plasma beta, which provides for extreme compactness, but imposes very non-standard requirements for basic stability. Recent experimental results have gone far toward demonstrating this stability, and new experiments are underway toward developing other aspects along the FRC reactor development path. If successful, these experiments could represent a breakthrough in fusion reactor attractiveness.

Hoffman, A. (1998). “Field-reversed configurations.”

A description is given of a steady-state FRC reactor driven by Rotating Magnetic Fields (RMF), and compared with present FRC status. A new experiment, TCS (Translation, Sustainment, & Confinement) is described which will test the principal of RMF flux build-up and sustainment of FRCs. It is shown that very attractive reactors can be envisioned if this sustainment scheme is successful.

Hoffman, A. (1998). “Flux buildup in field reversed configurations using rotating magnetic fields.”

Rotating magnetic field (RMF) current drive is a very attractive method for both increasing the flux and sustaining the current in field reversed configurations (FRC). It has been demonstrated in low temperature, low field rotamaks, and will now be applied to a new translation, confinement, and sustainment (TCS) experiment attached to the LSX/mod (Large s field-reversed configuration Experiment) facility [Hoffman et al. Fusion Technol. 23, 185 (1993)]. Previous RMF calculations have been concerned primarily with the plasma currents and particle orbits produced in one-dimensional cylinders with the rotating field strength of near equal magnitude to the confining axial field. Both fluid current and particle orbits are calculated here in the more interesting regime appropriate to TCS and reactors where the confinement field far exceeds the rotating field strength. New insight is gained into both the flux buildup requirements for two-dimensional equilibria and into the limits on ion rotation in this high confinement field regime. (C) 1998 American Institute of Physics.

Hoffman, A., P. Gurevich, et al. (1999). “Inductive field-reversed configuration accelerator for Tokamak Fueling.”

Compact toroids can be used for fueling other fusion devices by accelerating them to high enough velocities to penetrate strong magnetic fields. In the simplest analysis, the kinetic energy density of a flux-excluding object 1/2 rho v(2) must exceed the magnetic field energy density B-2/2 mu(0) Of the field to be pushed aside. Field reversed configurations (FRCs) are a type of compact toroid that are particularly efficient for this application due to their high density and thus lower required energy per unit mass. FRCs are also formed and accelerated inductively, thus minimizing possible impurity contamination. The Tokamak Refueling by Accelerated Plasmoids (TRAP) experiment was built to develop the inductive acceleration method and test the ability of high-velocity FRCs to penetrate transverse magnetic fields. Simple models have been 'developed for both the acceleration and penetration processes to determine fueler parameters required for a given tokamak field. Experimental results are given for the acceleration process. Half-milligram FRCs with number densities of 10(22) m(-3) were accelerated to velocities of 200 km/s, sufficient to fuel tokamaks with Tesla magnetic fields. The technology is easily extendable to much higher FRC densities and velocities, sufficient to fuel the largest highest-field tokamaks.

Hoffman, A. (2000). “Rotating magnetic field current drive of FRCs subject to equilibrium constraints.”

The standard analysis for rotating magnetic field (RMF) current production in simple fixed density plasma columns is extended to include the critical interaction between the RMF drive and an elongated field reversed configuration (FRC) equilibrium inside a Aux conserver. The standard analysis involves penetration of the RMF into a highly conducting plasma through production of synchronous rotation of the electron fluid due to Hall terms in Ohm's law. In the present article the RMF analysis is combined with two dimensional equilibrium constraints, which have a defining role in governing the RMF penetration. Very simple analytic models are developed, based on instantaneous RMF penetration into an edge layer, that illuminate the basic parameters necessary for current drive and flux buildup or sustainment to be successful. The model does not account for time dependent RMF penetration or transport consistent density profiles, but it clearly points out the basic conditions that must be satisfied, and how they scale, for RMF sustainment of FRCs to be effective.

Hoffman, A., H. Guo, et al. (2002). “The TCS rotating magnetic field FRC current-drive experiment.”

Field-reversed configurations (FRCs) have extremely attractive reactor attributes because of their singly connected geometry. They have been created in theta-pinch devices, but being compact toroids and lacking a center hole, their toroidal current cannot be sustained by transformer action as in other toroidal configurations. A new device, the Translation, Confinement, and Sustainment (TCS) facility has been constructed to use rotating magnetic fields (RMFs) to build up and sustain the flux of hot FRCs formed by the normal theta-pinch method. RMF formation and sustainment of similar, but cold, pure poloidal field configurations have been demonstrated in devices called rotamaks, and RMF formation, but not sustainment, has been achieved in a smaller FRC facility, called the Star Thrust Experiment (STY). Initial formation and sustainment have now been achieved in TCS, albeit still with cold (T-e similar to 50 eV) plasmas. Both the formation and final steady-state conditions are found to agree with newly developed analytic and numerical models for RMF flux buildup and sustainment inside a standard cylindrical flux conserver. The required plasma conditions (mainly resistivity but also density) can now be determined for the planned hot FRC, RMF flux buildup experiments and for eventual reactor conditions.

HORIUCHI, R. and T. SATO (1989). “FULL MAGNETOHYDRODYNAMIC SIMULATION OF THE TILTING INSTABILITY IN A FIELD-REVERSED CONFIGURATION.”

HORIUCHI, R. and T. SATO (1990). “THE MEANDERING ORBIT EFFECT ON STABILIZATION OF THE TILTING INSTABILITY IN A FIELD-REVERSED CONFIGURATION.”

Horiuchi, R., K. Nishimura, et al. (1999). “Kinetic stabilization of tilt disruption in field reversed configurations.”

The process of kinetic stabilization of the tilt disruption in a field reversed configuration is investigated by means of a three dimensional particle simulation. For the case of no ion beam the growth rate of the tilt instability decreases as the plasma beta value at the magnetic separatrix, beta(sp), increases. This stabilization effect originates from the 'anchoring ions' which exist in the vicinity of the magnetic separatrix and act as an 'anchor' to hold the internal plasma to the external plasma. The tilt mode is also found to be stabilized by injecting an ion beam with about 20% of the ion thermal energy in the vicinity of the null point even for small beta(sp) plasmas.

HOROWITZ, E., D. SHUMAKER, et al. (1989). “QN3D - A 3-DIMENSIONAL QUASI-NEUTRAL HYBRID PARTICLE-IN-CELL CODE WITH APPLICATIONS TO THE TILT MODE-INSTABILITY IN FIELD REVERSED CONFIGURATIONS.”

Horton, W. (1997). “Chaos and structures in the magnetosphere.”

The nonlinear plasma transport mechanisms that control the collisionless heating in the Earth's magnetosphere and the onset of geomagnetic substorms are reviewed. In the high-pressure plasma trapped in the reversed magnetic field loops on the nightside of the magnetosphere, the key issue of the role of the ion orbital chaos as the mechanism for the plasma sheet energization is examined. The energization rate is governed by a collisionless conductance and the solar wind driven dawn-to-dusk electric field. The low-frequency response function is derived and the fluctuation dissipation theorem is given for the system. Returning to the global picture the collisionless energization rate from the transport physics is the basis for a low-dimensional energy-momentum-conserving dynamical model of magnetospheric substorms.

HSIAO, M. and G. MILEY (1984). “VELOCITY-SPACE PARTICLE LOSS IN FIELD-REVERSED CONFIGURATIONS.”

HSIAO, M. and G. MILEY (1985). “VELOCITY-SPACE PARTICLE LOSS IN FIELD-REVERSED CONFIGURATIONS.”

HSIAO, M., K. WERLEY, et al. (1989). “CFRX, A ONE-AND-A-QUARTER-DIMENSIONAL TRANSPORT CODE FOR FIELD-REVERSED CONFIGURATION STUDIES.”

HSIAO, M. and M. OHNISHI (1989). “SUMMARY OF THE UNITED-STATES-JAPAN WORKSHOP ON D-HE-3 FIELD-REVERSED CONFIGURATIONS, NAGOYA, JAPAN, MARCH 20-23, 1989.”

HSIAO, M., J. STAUDENMEIER, et al. (1989). “ELECTRIC-FIELD DUE TO VELOCITY SPACE PARTICLE LOSS IN FIELD-REVERSED CONFIGURATIONS.”

HSIAO, M. and P. CHIANG (1990). “EFFECTS OF VELOCITY-SPACE PARTICLE LOSS IN FIELD-REVERSED CONFIGURATIONS.”

Ichinose, F., F. Kodera, et al. (1997). “Electron temperature distribution measurement of a field-reversed configuration plasma from the attenuation of helium and hydrogen mixed beam.”

For the estimation of the electron temperature of field-reversed configuration plasma, the helium and hydrogren mixed neutral beam attenuation method is proposed. In the first step, a one-chord beam attenuation experiment is presented, in order to confirm the proposed method. For the multichord measurement, a new system is introduced, which employed the bucket ion source, the electric energy analyser, the momentum selector with the permanent magnet and the microchannel plate. (C) 1997 Elsevier Science S.A.

Intrator, T., M. Taccetti, et al. (2002). “Experimental measurements of a converging flux conserver suitable for compressing a field reversed configuration for magnetized target fusion.”

Data are presented that are part of a first step in establishing the scientific basis of magnetized target fusion (MTF) as a cost effective approach to fusion energy. A radially converging flux compressor shell with characteristics suitable for MTF is demonstrated to be feasible. The key scientific and engineering question for this experiment is whether the large radial force density required to uniformly pinch this cylindrical shell would do so without buckling or kinking its shape. The time evolution of the shell has been measured with several independent diagnostic methods. The uniformity, height to diameter ratio and radial convergence are all better than required to compress a high density field reversed configuration to fusion relevant temperature and density.

ISHIDA, A. (1987). “2-FLUID VARIATIONAL FORM FOR PLASMAS IN FIELD-REVERSED CONFIGURATIONS.”

ISHIDA, A., H. MOMOTA, et al. (1988). “VARIATIONAL FORMULATION FOR A MULTIFLUID FLOWING PLASMA WITH APPLICATION TO THE INTERNAL TILT MODE OF A FIELD-REVERSED CONFIGURATION.”

ISHIDA, A., L. STEINHAUER, et al. (1991). “VARIATIONAL FORM FOR A VISCOUS PLASMA.”

The variational formulation for a fluid plasma including the parallel and gyroviscosities is developed using the basic approach of Berk et al. [Phys. Fluids 24, 2245 (1981)]. The equivalence of the variational problem to the original viscous fluid equations of motion is shown. The theory is developed for an axisymmetric plasma with no magnetic field in the azimuthal direction and therefore applies to field-reversed configurations and axisymmetric mirrors. This theory offers the advantage of describing both parallel and transverse ion kinetic effects within the simplicity afforded by a variational fluid model.

ISHIDA, A., R. KANNO, et al. (1992). “TILT STABILITY OF A GYROVISCOUS FIELD-REVERSED CONFIGURATION WITH REALISTIC EQUILIBRIA.”

The gyroviscous fluid theory [L. C. Steinhauer and A. Ishida, Phys. Fluids B 2, 2422 (1990)] is applied to the tilting instability of field-reversed configurations (FRC) using realistic equilibria and a more complete basis set than in the previous treatment. This leads to two important new results. (1) Quantitative agreement is found for the first time between experiment and the theory of FRC tilting stability, i.e., the stability of nearly all FRC's can be explained by the gyroviscous theory. (2) Quantitative agreement (within 30%) is also found between the gyroviscous theory (with modifications to account approximately for parallel kinetics and the Hall effect) and the more complete-but harder to apply-Vlasov-fluid model.

ISHIDA, A., N. SHIBATA, et al. (1994). “LOCAL MODES OF FIELD-REVERSED CONFIGURATIONS.”

Ishida, A., N. Shibata, et al. (1996). “Fast local mode properties in field-reversed configurations.”

Local eigenmodes of field-reversed configurations (FRCs) were previously computed using ideal magnetohydrodynamics, including compressibility and double adiabaticity. Here the eigenmodes are compared with earlier analytic models. In equilibria, as initially generated in theta pinches, the rigid displacements of the analytic models are similar to actual eigenmodes in structure and growth rate; moreover, the growth rates are similar to those of global modes. In equilibria that naturally arise later in the quiescent FRC, the analytic models fail to predict features of the eigenmode behavior: ballooning-like structure, and much faster growth rate than global modes. This suggests explanations for the difficulty of forming large FRCs in theta pinches, and for the appearance of characteristic profiles in quiescent FRCs. (C) 1996 American Institute of Physics.

ITO, Y., M. TANJYO, et al. (1987). “ION ROTATIONAL VELOCITY OF A FIELD-REVERSED CONFIGURATION PLASMA MEASURED BY NEUTRAL BEAM PROBE SPECTROSCOPY.”

ITO, Y., N. ARAI, et al. (1991). “MEASUREMENTS OF ION ANGULAR VELOCITY OF FIELD REVERSED CONFIGURATION WITH SUPPRESSED ROTATIONAL INSTABILITY.”

The angular velocity OMEGA-c of the impurity ions (CV) is measured spectroscopically for the FRC (Field-Reversed-Configuration) plasmas confined in the theta-pinch region and translated into the confinement region with magnetic mirror field. The FRC plasma confined in the theta-pinch region becomes unstable due to the n = 2 rotational instability which can be suppressed by the multipole magnetic field. The ion rotation in the stabilized plasma is almost equal to the velocity in the unstabilized case, suggesting that the multipole field acts on the plasma surface due to the skin effect and suppresses the instability without changing the field configuration within the separatrix radius. The FRC plasma translated in the confinement region is stable without destructive instability. The ion rotation in such a plasma indicates that a suppression mechanism of the n = 2 instability exists, which is excited by the rotation in the confinement region.

Iwasawa, N., A. Ishida, et al. (2000). “Ideal magnetohydrodynamic stability of static field reversed configurations.”

The ideal magnetohydrodynamic (MHD) stability of static field-reversed configurations is investigated. For the first time, the eigenvector fields and eigenvalues for a variety of global modes are found by applying the Rayleigh-Ritz technique to the variational principle using a verifiably complete basis set. This method is applied to a wide range of equilibria and mode types, including kink and sausage-like modes, modes with intermediate azimuthal mode number, and higher-harmonic modes with respect to the minor radius structure. The findings include the following. Modes with intermediate azimuthal mode number are somewhat more unstable than the well-known tilt mode. The tilt is not stabilized by proper current profile and separatrix shape. The inverse scaling of the tilt growth rate with the elongation (found in previous studies) is not valid in general. This suggests that large elongation alone cannot be relied on for stability when non-MHD corrections are added.

Iwasawa, N., A. Ishida, et al. (2000). “Tilt mode stability scaling in field-reversed configurations with finite Larmor radius effect.”

The marginal stability of a static plasma with finite-Larmor-radius (FLR) effects depends on a combination of the FLR effect and the ideal magnetohydrodynamic (MHD) potential energy. For the tilt mode in a field-reversed configuration (FRC) previous computations of these two factors led to a prediction of stability for S-* less than or equal to (3-5)E where S-* is the macroscale parameter (separatrix radius/ion skin depth) and E is the elongation (separatrix half length/separatrix radius). This prediction explained the observed stability of most experiments. However, recent computations of actual MHD eigenfunctions indicate that the MHD growth rate has a much weaker scaling with elongation than previously believed. As a consequence, most of the long-lived, stable FRC experiments lie in the region predicted to be unstable. It appears then that the stability of FRC experiments is not explained by FLR effects in a static equilibrium. (C) 2000 American Institute of Physics. [S1070-664X(00)00803-X].

Iwasawa, N., A. Ishida, et al. (2001). “Linear gyroviscous stability of field-reversed configurations with static equilibrium.”

A discrepancy persists between field-reversed configuration experiments, which are generally stable, and theoretical predictions of instability. The common consensus has been that the stability is the result of finite Larmor radius (FLR) effects. An FLR analysis is presented that finds the self-consistent displacement functions and complex frequency. This is done using the linear gyroviscous model, a fluid-based representation of FLR that allows a wide range of equilibria and modes to be examined with modest computations. The conclusion is that FLR in static FRC fails to explain the observed stability. The cause of stability must lie elsewhere. (C) 2001 American Institute of Physics.

JAIN, K. and P. JOHN (1984). “ROTATING RELATIVISTIC ELECTRON BEAM-PLASMA INTERACTION AND FORMATION OF A FIELD-REVERSED CONFIGURATION.”

JAMIN, C., L. INTRATOR, et al. (1985). “CYPROTERONE-ACETATE IS NOT EFFECTIVE IN THE PROPHYLAXIS OF HEREDITARY ANGIONEUROTIC-EDEMA.”

JARBOE, T. (1994). “REVIEW OF SPHEROMAK RESEARCH.”

Spheromak research from 1979 to the present is reviewed including over 160 references. Emphasis is on understanding and interpretation of results. In addition to summarizing results some new interpretations are presented. An introduction and brief history is followed by a discussion of generalized helicity and its time derivative. Formation and sustainment are discussed including five different methods, flux core, theta-pinch z-pinch, coaxial source, conical theta-pinch, and kinked z-pinch. All methods use helicity injections. Steady-state methods and rules for designing spheromak experiments are covered, followed by equilibrium and stability. Methods of stabilizing the tilt and shift modes are discussed as well as their impact on the reactor designs. Current-driven and pressure-driven instabilities as well as relaxation in general are covered. Energy confinement is discussed in terms of helicity decay time and and betas limits. The confinement in high and low open-flux geometries are compared and the reactor implications discussed.

Ji, H., M. Yamada, et al. (1998). “Studies of global stability of field-reversed configuration plasmas using a rigid body model.”

Global stability of field-reversed configuration (FRC) plasmas has been studied using a simple rigid body model in the parameter space of s (the ratio of the separatrix radius to the average ion gyro-radius) and plasma elongation E (the ratio of the separatrix length to the separatrix diameter). Tilt stability is predicted, independent of s, for FRC's with low E (oblate), while the tilt stability of FRC's with large E (prolate) depends on s/E. It is found that plasma rotation due to ion diamagnetic drift can stabilize the tilt mode when s/E less than or similar to 1.7. The so-called collisionless ion gyro-viscosity also is identified to stabilize tilt when s/E less than or similar to 2.2. Combining these two effects, the stability regime broadens to s/E less than or similar to 2.8, consistent with previously developed theories. A small additional rotation (e.g., a Mach number of 0.2) can improve tilt stability significantly at large E. A similar approach is taken to study the physics of the shift stability. It is found that radial shift is unstable when E<1 while axial shift is unstable when E>1. However, unlike tilt stability, gyro-viscosity has little effect on shift stability. (C) 1998 American Institute of Physics. [S1070-664X(98)03110-3].

Jones, I. (1999). “A review of rotating magnetic field current drive and the operation of the rotamak as a field-reversed configuration (Rotamak-FRC) and a spherical tokamak (Rotamak-ST).”

The physics underlying the rotating magnetic field current drive technique is presented. The rotamak is a compact torus configuration having the unique and distinctive feature that the toroidal plasma current is driven in a steady-state, noninductive fashion by means of the application of a rotating magnetic field. In its basic form, the rotamak is operated as a field-reversed configuration (Rotamak-FRC). However, by means of a simple modification, a steady toroidal magnetic field can be added to the basic rotamak apparatus and the configuration then becomes that of a spherical tokamak (Rotamak-ST). The performance of a 50-liter rotamak device, both as an FRC and as an ST, is described. Toroidal currents of over 10.5 kA have been achieved with input powers of 300 kW (at 0.5 MHz). Hydrogen plasmas with n(e) approximate to 7 x 10(18) m(-3) and T-e approximate to 35 eV have been obtained. The noteworthy reproducibility of the rotamak discharge has enabled the magnetic field lines of an ST to be directly reconstructed from experimental data for the first time. Attention is drawn to the fact that a fair evaluation of the rotamak concept requires experimentation at higher radio-frequency power levels than are presently available. (C) 1999 American Institute of Physics. [S1070-664X(99)94705-5].

JOUAULT, H., C. ANDRE, et al. (1985). “HISTOLOGICAL AND IMMUNOHISTOCHEMICAL ASPECTS OF OF NON-HODGKIN FOLLICULAR LYMPHOMAS (LNHF) - COMPARATIVE-STUDY OF 12 CASES.”

KAKO, M., T. ISHIMURA, et al. (1983). “EQUILIBRIA OF FIELD-REVERSED CONFIGURATION WITH SUBSIDIARY COILS.”

Kanki, T., Y. Suzuki, et al. (1999). “Numerical simulation of magnetic compression on a field-reversed configuration plasma.”

A two-dimensional magnetohydrodynamic (MHD) simulation of an axial magnetic compression on a field-reversed configuration (FRC) plasma is carried out for the parameter range of a corresponding experiment conducted on the FRC Injection Experiment (FIX) [S. Okada , 17th IAEA Fusion Energy Conference 1998 (International Atomic Energy Agency, Vienna) (in press)]. The simulation results show that during the initial stage of the magnetic compression the front part of the FRC plasma is mainly compressed radially, and that after this stage, the compression is primarily axial. Of particular interest is expected that the closed magnetic flux surfaces of the FRC can be retained without any degradation during the magnetic compression process. Further, it is observed in the simulation that the axial magnetic compression enables a transition of the MHD equilibrium from a long and thin to a short and fat FRC. The effects of this magnetic compression on FRC plasmas are discussed. (C) 1999 American Institute of Physics. [S1070-664X(99)01812-1].

Kanki, T. (2002). “Numerical studies of reflection process on a field-reversed configuration plasma.”

A two-dimensional magnetohydrodynamic (MHD) simulation of a reflection on a field-reversed configuration (FRC) plasma is performed in the parameter range of the FRC injection experiment (FIX). The full set of MHD equations are solved on a rezoned Lagrangian mesh which employs an adaptive algorithm to concentrate the grid in regions of sharp plasma pressure gradients. It is shown from the simulation results that the FRC plasma is reflected by downstream magnetic mirror field at the end of the confinement region in the FIX machine without destroying the closed magnetic flux surfaces. The effects of this field on FRC plasma are discussed.

KANNO, R., A. ISHIDA, et al. (1995). “IDEAL-MAGNETOHYDRODYNAMIC-STABLE TILTING IN FIELD-REVERSED CONFIGURATIONS.”

The tilting mode in field-reversed configurations (FRC) is examined using ideal-magnetohydrodynamic stability theory. Tilting, a global mode, is the greatest threat for disruption of FRC confinement. Previous studies uniformly found tilting to be unstable in ideal theory: the objective here is to ascertain if stable equilibria were overlooked in past work. Solving the variational problem with the Rayleigh-Ritz technique, tilting-stable equilibria are found for sufficiently hollow current profile and sufficient racetrackness of the separatrix shape. Although these equilibria were not examined previously, the present conclusion is quite surprising. Consequently checks of the method are offered. Even so it cannot yet be claimed with complete certainty that stability has been proved: absolute confirmation of ideal-stable tilting awaits the application of more complete methods.

KATSURAI, M. (1995). “REVIEW OF EXPERIMENTAL INVESTIGATIONS ON COMPACT TOROIDS AND COMPACT TOKAMAKS USING TS-3 DEVICE.”

The TS-3 device at the University of Tokyo has been used to produce free boundary spheromaks or spheromak-like compact toroids. Plasma production is accomplished either by Z-theta discharges or by means of magnetized coaxial plasma guns installed at both ends of the device. The plasmas produced have a minor approximate to major radius of about 15 to 20 cm with a natural decay time of about 30 to 50 mu s and a toroidal plasma current of about 30 to 60 kA. A unique feature of TS-3 device is the possession of production regions at both ends of the device, and concequently the ability of producing two adjacent compact toroids which can be merged through magnetic reconnection. Another feature of TS-3 device is the possibility of external application of a toroidal field with the aid of an optional center conductor assembly that can carry an axial current ranging from 0 to +/-80 kA. This construction enables us to produce compact toroidal plasmas of various types from reversed field pinch(RFP) to tokamak in terms of the difference in q profile. The variation of both poloidal plasma current and external toroidal field current permits the change in magnetic configuration of merging plasmas, enabling the reconnection angle to continuously vary from about 20 degrees (tokamak merging) through 90 degrees (cohelicity spheromak merging) to 180 degrees (counter-helicity spheromak merging to produce field reversed configurations(FRC)). When the coaxial guns are installed at both ends of the device in place of the center conductor, a center plasma current can be injected to form flux-core spheromaks (or bumpy z-pinches). Novel research subjects that have emerged from TS-3 experiments are; (1) the investigation of three dimensional effects of magnetic reconnection in laboratory plasmas, (2) the formation of FRC plasmas by a counter-helicity spheromak merging, (3) non-OH production and merging of tight aspect ratio tokamaks, (4) the stabilization of tilt motions of tight aspect ratio tokamaks, and (5) the formation and compression (flux amplification) of free-boundary tilt stabilized flux-core spheromaks.

KATZIR, G. and N. INTRATOR (1987). “THE STRIKING OF UNDERWATER PREY BY A REEF HERON, EGRETTA-GULARIS.”

KATZIR, G. and N. INTRATOR (1987). “STRIKING OF UNDERWATER PREY BY A REEF HERON, EGRETTA-GULARIS-SCHISTACEA.”

KATZIR, G., A. LOTEM, et al. (1989). “STATIONARY UNDERWATER PREY MISSED BY REEF HERONS, EGRETTA-GULARIS - HEAD POSITION AND LIGHT REFRACTION AT THE MOMENT OF STRIKE.”

KERNBICHLER, W. (1992). “OPERATIONAL PARAMETERS FOR D-HE-3 IN FIELD-REVERSED CONFIGURATIONS.”

The intrinsic potential of a field-reversed configuration (FRC) for high-beta operation (beta values in the range of 50 to 100%) stimulates much interest in this device as an attractive candidate for a compact fusion reactor with high power density. Several additional benefits, e.g., the cylindrical geometry of the concept, the simplicity of the magnetic system, the simply connected plasma, the low synchrotron radiation, the divertor action of the open field lines, and the possibility for direct energy conversion of the charged-particle flow, justify a closer look at the benefits and problems of FRCs. The emphasis here is on operation with D-He-3 fuel under reactor-relevant conditions, whereas deuterium-tritium (D-T) is taken as a reference case. The reasons for that choice are that (a) D-He-3 offers intrinsic advantages over D-T in neutron production and radioactive inventory and (b) the high-beta regime of an FrC matches ideally some of the requirements for D-He-3 operation. A steady-state version of an FRC is considered to be more attractive than its pulsed counterpart. Frequent startup to high temperatures would be particularly detrimental for D-He-3, where startup scenarios seem to rely either on the transition from D-T to D-He-3, with unavoidable strong tritium contamination, or on high-power neutral beam injection.

Khvesyuk, V., A. Khvesyuk, et al. (1997). “Global stochastic particles in a field-reversed configuration.”

This paper discusses the dynamics of the fusion products of the D-He-3 reaction in a field-reversed configuration, with application to a reactor regime with a large value of the plasma beta. It shows that, under the conditions in the Artemis-L design [H. Momota and Y. Tomita, J. plasma Fusion Res. 69, 801 (1993)], the motion of protons with an initial energy of 14.1 MeV is strongly stochasticized. The confinement time of these particles and the energy transfer from the fusion products to the plasma are very small. (C) 1997 American Institute of Physics.

Kitano, K., K. Yamanaka, et al. (2000). “Axial length and separatrix radius behavior of field-reversed configuration plasma in dynamic compression of mirror distance.”

The axial magnetic compression experiment of the field-reversed configuration (FRC) plasma is reported. The FRC produced in the theta-pinch system is translated into the confinement region. The separatrix length of the translated FRC is decided by the mirror distance. The compression is done in a manner as shortening the distance in time. The compression coil is installed inside the chamber to raise the strength of the confinement field at the neighborhood of the mirror. The mirror distance is compressed to be 70% of the original one. The increment of the separatrix radius is observed to be 14%. This is nearly consistent with the adiabatic calculation. The decay rate of the radius has a constant value. From the line integrated density signal measured by the interferometer, no n = 2 rotational instability is observed even in the case of the compression. (C) 2000 American Institute of Physics. [S1070-664X(00)00104-X].

Kitano, K., S. Maeshima, et al. (2001). “Dynamic process during axial magnetic compression of field-reversed configuration for equilibrium shape control.”

Adiabatic magnetic compression experiments on a field-reversed configuration (FRC) plasma are reported. The compression is performed on a long FRC held in a straight mirror field. The separatrix length of the FRC is limited by the distance between the magnetic mirrors. The mirror distance is compressed in time to 35% of the original one by the compression coil installed inside the chamber, and the separatrix length is shortened to 38%. The separatrix radius of the compressed FRC increases by 56% and the aspect ratio (separatrix length/separatrix diameter) changes from 12.6 to 4.1. Magnetic probes with the compensation circuit are utilized to investigate the dynamic transition phase during the compression. The transition process is found from these measurements to be divided into three stages, where a new equilibrium state is achieved in the final stage. (C) 2001 American Institute of Physics.

KNIGHT, A. and I. JONES (1990). “A QUANTITATIVE INVESTIGATION OF ROTATING MAGNETIC-FIELD CURRENT DRIVE IN A FIELD-REVERSED CONFIGURATION.”

Kodera, F., M. Kojima, et al. (1999). “Development of a multichord beam-attenuation probe of hydrogen and helium for plasma diagnostics.”

In order to estimate the density and the electron temperature profiles of a medium temperature plasma, a multichord beam probing system has been developed. The ion density can be estimated by hydrogen neutrals attenuation via charge exchange. The electron temperature could be inferred from the electron impact ionization attenuation of a helium atom beam under some assumption. Our beam system includes a large bucket ion source which can simultaneously emit both hydrogen and helium ions, a neutralization drift tube, a beam energy and momentum analyzer corresponding to six chords and a data acquisition system. The completed device is applied for the measurement of a field-reversed configuration plasma which has a typical electron temperature of 50 eV and a line density of 2.0X10(15) cm(-2). (C) 1999 American Institute of Physics. [S0034-6748(99)58601-2].

KONIG, R., K. KOLK, et al. (1987). “INFLUENCE OF IMPURITIES ON THE PLASMA PARAMETERS AND STABILITY OF A FIELD-REVERSED CONFIGURATION.”

KRALL, N. (1987). “LOW-FREQUENCY STABILITY FOR FIELD REVERSED CONFIGURATION PARAMETERS.”

KRALL, N. (1989). “THE EFFECT OF LOW-FREQUENCY TURBULENCE ON FLUX, PARTICLE, AND ENERGY CONFINEMENT IN A FIELD-REVERSED CONFIGURATION.”

KRALL, J., C. SEYLER, et al. (1991). “KINETIC STABILIZATION OF INTERCHANGE MODES IN AN AXISYMMETRICAL MIRROR BY LARGE ORBIT RADIUS THERMAL IONS.”

A dispersion functional analysis that includes the full kinetic effects of large Larmor radius thermal ions is applied to the problem of stability of an axisymmetric mirror to finite azimuthal mode number (m) interchange modes. Vlasov theory is used to describe the ions, which are imbedded in a background of fluid electrons. The dispersion functional is solved numerically, both for a trial function displacement, where only the growth rate is determined, and the general case, where both the displacement and the growth rate are determined. In the trial function case, it is found that finite Larmor radius (FLR) effects are recovered, with a significant reduction in the growth rate when (rho-i/L)2 greater-than-or-similar-to gamma-MHD/OMEGA-i. In a general case, the growth rate is reduced, but not so strongly as in the trial function case. It is shown heuristically that FLR effects may be recovered from the analysis and that these effects increase with the phase-space decorrelation time of the thermal ion distribution.

KRIVOSHEEV, M. and V. LITUNOVSKY (1995). “COMPACT D-HE-3 FUELED FUSION-REACTOR BASED ON AN FRC.”

The possibility to minimize in principle the weight overall and output characteristics of D-He-3 fueled Fusion Reactor (FR) on the base of plasma Field Reversed Configuration (FRC) is analyzed. It is shown, that with the optimistic outlook on an FRC plasma confinement improvement prospects, the FR specific mass of about 5 kg/kW at electric power of P-e congruent to 300 MW can be achieved.

KUMASHIRO, S., T. TAKAHASHI, et al. (1993). “SOURCES OF FLUCTUATING FIELD ON FIELD-REVERSED CONFIGURATION PLASMA.”

Fluctuating azimuthal fields, B(theta), are detected during a lifetime of a Field-Reversed Configuration plasma. The maximum strength reaches to 70 G which corresponds to about 1.5% of a confining field. Sources of the fields are discussed with relation to such plasma motions as radial shifting and tilting motions, and elliptical deformation of the plasma column triggered by a rotational instability. Analytic formulas of the B(theta), are derived from disturbance of the confining field due to these motions. Estimated values from the formulas agree well with field profiles obtained from a magnetic probe array.

LAGRUE, G., C. BRUNEAU, et al. (1985). “IGA NEPHROPATHY ASSOCIATED WITH SERONEGATIVE SPONDYLARTHROPATHIES - EFFICACY OF NON STEROIDAL ANTI-INFLAMMATORY DRUGS (NSAIDS).”

LAGRUE, G., J. LAURENT, et al. (1986). “LONG-TERM-PROPHYLACTIC TREATMENT OF HEREDITARY ANGIONEUROTIC-EDEMA WITH ANDROGENIC-ANABOLIC STEROIDS.”

LAURENT, J., A. BRANELLEC, et al. (1987). “AN INCREASE IN CIRCULATING IGA ANTIBODIES TO GLIADIN IN IGA MESANGIAL GLOMERULONEPHRITIS.”

LAURENT, J., L. INTRATOR, et al. (1987). “NEONATAL DIAGNOSIS OF HEREDITARY ANGIONEUROTIC-EDEMA (HANE).”

LAURENT, J., L. INTRATOR, et al. (1987). “HEREDITARY ANGIONEUROTIC-EDEMA - TREATMENT OF A PSEUDO-SURGICAL ABDOMINAL ATTACK WITH THE C1-INHIBITOR CONCENTRATE.”

Lifschitz, A., R. Farengo, et al. (2002). “Monte Carlo simulation of neutral beam injection into a field reversed configuration.”

A Monte Carlo code is employed to study the interaction of neutral beams with a field reversed configuration (FRC). The code follows the exact particle trajectories in the self-consistent equilibrium calculated including the beam and plasma currents. For high enough beam currents, a self-consistent confining effect is observed which prevents expansion of the beam along the FRC axis. The beam current drive and the power and momentum transferred are calculated for a variety of beam parameters. The results are slightly affected by the details of the injection geometry. The dependence on the neutral current IN and beam energy EN is influenced by several factors, such as particle losses through the ends, the density increase around the injection region and the finite Larmor radius effect.

Lifschitz, A., R. Farengo, et al. (2002). “Numerical calculations of neutral beam injection in spheromaks.”

A numerical study of neutral beam injection into spheromaks is presented. The beam evolution is calculated through a Monte-Carlo simulation and the plasma MHD equilibrium is determined self-consistently with the current produced by the beam. The exact equations of motion are used for the beam particles instead of the usual guiding-centre approximation. The guiding-centre trajectories are clearly different from the actual particle trajectories and this difference produces discrepancies in the total driven current and in the current profiles. A reduction of the plasma effective charge, Z(eff), does not result in an improvement in the current drive efficiency because the reduction of the stopping cross section is compensated by an increase in the electron cancelling current. The safety factor profile of the self-consistent equilibria shows a clear sensitivity to the driven current profile. The value at the magnetic axis (q(0)) diminishes when the beam is injected at the magnetic axis and increases for injection above the axis. Power deposition profiles for simple injection configurations are also shown.

MAJESKI, R., J. BROWNING, et al. (1987). “EFFECT OF VARIABLE EIGENMODE EXCITATION ON RF STABILIZATION OF A MIRROR PLASMA.”

MAQUEDA, R., G. WURDEN, et al. (1992). “WIDE-BAND SILICON BOLOMETERS ON THE LSX FIELD REVERSED CONFIGURATION EXPERIMENT.”

Silicon photodiode detectors, which have nearly flat energy response from 1 eV to 6 keV [R. Korde and L. Randall Canfield, Proc. SPIE 1140, 126 (1989)], were used as bolometers in the field reversed theta pinch experiment LSX. Plasma escaping from the field reversed configuration is naturally diverted to the ends of the vacuum enclosure. There it affects the bolometer measurements either by direct energy deposition or by emission of low energy photons. These two particle effects can be avoided by optimizing the location of the bolometers and restricting their field of view. Good agreement is observed between the silicon bolometers and a gold foil calorimeter.

MATSUURA, H., Y. NAKAO, et al. (1993). “EFFECTIVE ION TAIL FORMATION DURING STARTUP NEUTRAL BEAM HEATING IN D-HE-3 PLASMAS.”

Formation of an effective ion tail due to neutral beam injection heating during startup in D-He-3 plasmas is investigated. The main idea is to reduce the energy input required for startup heating as well as the 14-Me V neutron yield by creating an effective tail. The optimal beam injection energy and beam species are first estimated by solving the steady-state Fokker-Planck equations for the injected species and for tritons. The startup of D-He-3 plasma is simulated by simultaneously solving the time-dependent power balance and particle conservation equations together with the Fokker-Planck equations. As a result of tail formation in the fuel ion distribution, both the total input energy and the 14-Me V neutron yield during the startup phase are reduced by approximately 20 % from the values for Maxwellian plasma.

MATSUURA, H., Y. TANAKA, et al. (1995). “TAIL EFFECTS ON D-HE-3/FRC STARTUP HEATING.”

An intense neutral beam injected into a plasma creates a tail (i.e. non-Maxwellian component) in velocity distribution function of the same species as the one injected with enhancing (or reducing) fusion reactivities from the values for Maxwellian plasmas. In a typical D-He-3 startup operation with field reversed configuration (FRC), tail effect on reduction in neutral beam injection (NBI) power required for plasma heating is investigated. It is shown that as a result of effective tail control, the required NBI power can be reduced by about 60% from the value for Maxwellian plasma.

Matsuura, H., Y. Nakao, et al. (2000). “Triton distribution function and 14 MeV neutron generation rate in D-He-3 field reversed configuration plasmas.”

The effect of magnetic field oil the velocity distribution function of tritons in D-He-3 fuelled/field reversed configuration (FRC) plasmas is investigated. Some of the tritons produced by D(d,p)T reactions in the FRC are immediately and asymmetrically lost from the device without any interaction with background charged particles, and then non-symmetric loss causes a distortion of the velocity distribution function as well as a decrease in the number of trapped tritons. Using the distorted triton distribution, the 14 MeV neutron generation rate is estimated and compared with the values for Maxwellian plasmas (the effect of the magnetic field is neglected). It is found that in a typical ignited D-He-3/FRC plasma, for example, T-i = T-e = 80 keV, n(D) = 2ns(He) = 05n(e) = 3 x 10(20) m(-3) T-E = 0.5 tau(P) = 3 S, r(s) = 1.6 m and B-W = 6 T, the reduction in 14 MeV neutron generation is about 20%.

McCollam, K. and T. Jarboe (2002). “Magnetic relaxation in coaxial helicity injection.”

The Helicity Injected Torus (HIT-II) (Jarboe T R 1998 Phys. Plasmas 5 1807) is operated with either cathode or anode central column (CC) during coaxial helicity injection (CHI). The CC polarity has a strong effect on tokamak behaviour. For cathode CC operation, the magnetic profile is inferred from surface data to be more relaxed, and then = 1 mode is stronger and more slowly rotating than for anode CC operation. Mode toroidal rotation follows the applied E x B direction. Ion toroidal spin-up in the core is consistent with electromotive action. Apparently, some type of mode asymmetry, effected by the plasma flow and mode rotation, is integral to the current drive observed. This is discussed in terms of electromotive effects, and the picture is shown to be consistent with observations. Some possible implications are outlined, including those concerning parallel fluid velocity shear and other magnetic confinement configurations.

MCKENNA, K., D. REJ, et al. (1983). “EQUILIBRIUM AND POWER BALANCE CONSTRAINTS ON A QUASI-STATIC OHMICALLY HEATED FIELD-REVERSED CONFIGURATION (FRC).”

MCKENNA, K., W. ARMSTRONG, et al. (1983). “PARTICLE CONFINEMENT SCALING IN FIELD-REVERSED CONFIGURATIONS.”

MCKENNA, K., W. ARMSTRONG, et al. (1985). “FIELD-REVERSED CONFIGURATION RESEARCH AT LOS-ALAMOS.”

MEASSICK, S., T. INTRATOR, et al. (1989). “MEASUREMENTS OF THE PONDEROMOTIVE FORCE INCLUDING SIDEBAND MODE-COUPLING EFFECTS AND DAMPING RATES.”

MILEY, G. (1989). “SUMMARY OF THE UNITED-STATES-JAPAN WORKSHOP ON D-3HE FIELD-REVERSED CONFIGURATIONS, URBANA-CHAMPAIGN, ILLINOIS, OCTOBER 5-8, 1988.”

MILEY, G. (1995). “COMPACT TORI AS EXTENSIONS OF THE SPHERICAL TOKAMAK.”

The need for a flexible experimental facility, capable of studying several alternate confinement concepts simultaneously, is discussed. A facility suitable for both spherical tokamak (ST) and Field Reversed Configuration (FRC) studies is examined. Such a facility could advance the physics database of both concepts at a minimum cost. An International Center for Alternate Confinement Studies is proposed to develop such facilities and to provide opportunities for international collaboration in this critical area.

Miley, G., J. Santarius, et al. (2000). “On design and development issues for the FRC and related alternate confinement concepts.”

Two prior D-He-3 field-reversed configuration (FRC) reactor designs, ARTEMIS and SAFFIRE are reviewed to identify key physics, technology, and design issues for FRC development. It is concluded that the D-He-3 FRC can potentially offer a cost competitive and environmentally compatible power plant if the technology issues can be suitably resolved. The D-He-3 FRC also appears to be particularly attractive for non-electrical application such as He-3 breeding or hydrogen production. An important developmental issue becomes whether or not a D-T version should be employed as the first-generation unit. If so, emphasis must be placed on methods to handle high neutron and heat first-wall loadings, e.g. by use of a liquid first wall. Also, the development of improved thermal energy conversion cycles such as the use of liquid metal MHD becomes an important goal. (C) 2000 Elsevier Science S.A. All rights reserved.

MILROY, R., J. SLOUGH, et al. (1984). “PLASMA WALL SHEATH CONTRIBUTIONS TO FLUX RETENTION DURING THE FORMATION OF FIELD-REVERSED CONFIGURATIONS.”

MILROY, R. and J. SLOUGH (1987). “POLOIDAL FLUX LOSS AND AXIAL DYNAMICS DURING THE FORMATION OF A FIELD-REVERSED CONFIGURATION.”

MILROY, R., D. BARNES, et al. (1989). “NONLINEAR MAGNETOHYDRODYNAMIC STUDIES OF THE TILT MODE IN FIELD-REVERSED CONFIGURATIONS.”

Milroy, R. (1999). “A numerical study of rotating magnetic fields as a current drive for field reversed configurations.”

A fixed ion model has been developed to study the use of a Rotating Magnetic Field (RMF) as a current drive mechanism in a Field Reversed Configuration (FRC). This model is used to investigate the physics of RMF current drive in a parameter range of interest to two experiments at the University of Washington. Empirical expressions are found to characterize the critical RMF magnitude required for full penetration and the rate of RMF penetration. It is shown that in the presence of a strong anisotropic plasma resistivity, the direction and magnitude of the axial bias field can have a strong influence on the penetration of an RMF. Calculations that include the effects of realistic RMF antennae at finite radius are used to find the effects of coil spacing and positioning. (C) 1999 American Institute of Physics. [S1070-664X(99)01507-4].

Milroy, R. (2000). “A magnetohydrodynamic model of rotating magnetic field current drive in a field-reversed configuration.”

A numerical model has been developed to study the use of a Rotating Magnetic Field (RMF) as an electron current drive mechanism for the formation and sustainment of a field-reversed configuration (FRC). Previous models assumed a fixed ion model, but here a full two-dimensional (r-theta) magnetohydrodynamic model has been developed. The model has been applied to two classes of problems: (1) For the sustainment problem, a RMF is applied to a preexisting FRC. (2) For the formation problem, a RMF is applied to a plasma column with an initially uniform axial magnetic field and background plasma density. The RMF-induced current reverses this bias field, forming a FRC. The code employs an option to include some three-dimensional effects to satisfy the average beta condition and equalize pressure and density between inner and outer field lines, when it is applied to sustainment simulations. (C) 2000 American Institute of Physics. [S1070-664X(00)03610-7].

Milroy, R. (2001). “Effects of open field line plasma on rotating magnetic field current drive in a field-reversed configuration.”

A numerical model has been used to study the effects that open field line plasma may have on the rotating magnetic field (RMF), when it is applied to a field-reversed configuration (FRC) for current drive. The model is a two-dimensional (r-theta) magnetohydrodynamic computer simulation. The RMF is found to be an extremely good particle pump, continuously sweeping plasma into the FRC from the outer region, and thus evacuating the space near the containment vessel wall. This effect can lead to a very low density near the wall, providing good thermal insulation. However, if there is a plasma source in the open field line region (such as outgassing from the containment vessel wall) capable of maintaining relatively low-density plasma, the RMF may be amplified in this region. While this effect may speed the rate of penetration, it also has a deleterious effect where excessive penetration leads to predictions of an internal structure that rotates slower than the RMF, and chaotic equilibrium. (C) 2001 American Institute of Physics.

Mogahed, E., H. Khater, et al. (2001). “A helium cooled Li2O straight tube blanket design for cylindrical geometry.”

A tritium-breeding blanket design is investigated for a D-T Field-Reversed Configuration (FRC) scoping study. The thrust of our initial effort on the blanket has been to seek solutions as close to present-day technology as possible, and we have therefore focused on steel structure with helium coolant. The simple FRC cylindrical geometry has allowed us reasonable success due to the low FRC magnetic field and relatively easy maintenance. In this design the breeder is Li2O tubes. The design is modular with 10 modules each 2.5 m long. The inner radius of the first wall is 2.0 m and the FW/blanket/shield thickness is about 2 m. The surface heat flux will be radiation dominated, fairly uniform, and relatively low, because most of the charged particles follow the magnetic flux tubes to the end walls. The neutron wall loading is 5 MW/m(2) In this design the surface heat flux equals 0.19 MW/m(2). The maximum Li2O tube temperature is 1003 degreesC. The helium exit temperature from the heat exchanger is about 800 degreesC which allows a thermal efficiency of about 52%. The local tritium breeding ratio (TBR) equals 1.1 and is sufficient because in the FRC geometry the plasma has nearly full coverage. The helium pumping power is I MW. The coolant routing is optimized to limit the steel maximum temperature to 635 degreesC. The same concept would be applicable to a spherical torus and spheromak.

Moir, R. (1997). “Liquid first walls for magnetic fusion energy configurations.”

Liquids (similar to 7 neutron mean free paths thick), with certain restrictions, can probably be used in magnetic fusion designs between the burning plasma and the structural materials of the fusion power core. If this works there would be a number of profound advantages: a cost of electricity lower by as much as a factor of 2; removal of the need to develop new first wall materials, saving over 4 billion US dollars in development costs; a reduction of the amount and kinds of wastes generated in the plant; and the wider choice of materials permitted. The amount of material that evaporates from the liquid which can be allowed to enter the burning plasma is estimated to be less than 0.7% for lithium, 1.9% for Flibe (Li2BeF4 or LiBeF3) and 0.01% for Li17Pb83. The ability of the edge plasma to attenuate the vapour by ionization appears to exceed this requirement. This ionized vapour would be swept along open field lines into a remote burial chamber. The most practical systems would be those with topological open field lines on the outer surface, as is the case with a field reversed configuration (FRC), a spheromak, a Z pinch or a mirror machine. In a tokamak, including a spherical tokamak, the field lines outside the separatrix are restricted to a small volume inside the toroidal coil making for difficulties in introducing the liquid and removing the ionized vapour, i.e., the configuration is not open ended.

Moir, R., R. Bulmer, et al. (2001). “Thick liquid-walled, field-reversed configuration-magnetic fusion power plant.”

A thick flowing layer of liquid (e.g., flibe-a molten salt, Sn80Li20 or Li-liquid metals) protects the structural walls of the field-reversed configuration (FRC) so that they can last the life of the plant even with intense 14 MeV neutron bombardment from the D-T fusion reaction. The surface temperature of the liquid rises as it passes from the inlet nozzles to the exit nozzles due to absorption of line and bremsstrahlung radiation, and neutrons. The surface temperature can be reduced by enhancement of convection near the surface to transport hot surface liquid into the cooler interior. The resulting temperature for evaporation estimates called, T,m is 660, 714 and 460 degreesC for flibe, SnLi and Li, where thermal conductivity was assumed enhanced by a factor of ten for flibe. The corresponding evaporative flux from the wall must result in an acceptable impurity level in the core plasma. The shielding of the core by the edge plasma is modeled with a 2D transport code for the resulting impurity ions; these ions are either swept out to the distant end tanks, or diffuse to the hot plasma core. The calculations show core impurity levels adequately low for Li and Sn80Li20 but is about ten times too large for flibe. An auxiliary plasma between the edge plasma and the liquid wall can further attenuate evaporating flux of atoms and molecules by ionization. The current in this auxiliary plasma might serve as the antenna for the current drive method, which produces a rotating magnetic field.

MOMOTA, H., M. OKAMOTO, et al. (1987). “ADVANCED FUELS IN A FIELD-REVERSED CONFIGURATION.”

MOMOTA, H., M. OKAMATO, et al. (1988). “D HE-3 FUELS IN A FIELD-REVERSED CONFIGURATION.”

MOMOTA, H., A. ISHIDA, et al. (1992). “CONCEPTUAL DESIGN OF THE D-HE-3 REACTOR ARTEMIS.”

A comprehensive design study of the D-He-3 fueled field-reversed configuration (FRC) reactor Artemis is carried out for the purpose of proving its attractive characteristics and clarifying the critical issues for a commercial fusion reactor. The FRC burning plasma is stabilized and sustained in a steady equilibrium by means of preferential trapping of D-He-3 fusion-produced energetic protons. A novel direct energy converter for 15-MeV protons is also presented. On the bases of consistent fusion plasma production and simple engineering, a compact and simple reactor concept is presented. The D-He-3 FRC power plant offers a most attractive prospect for energy development. It is environmentally acceptable in terms of radioactivity and fuel resources, and the estimated cost of electricity is low compared with a light water reactor. Critical physics and engineering issues in the development of the D-He-3 FRC reactor are clarified.

MYNICK, H. (1980). “GUIDING-CENTER HAMILTONIAN FOR FIGURE-8 PARTICLES IN AXISYMMETRIC FIELD-REVERSED CONFIGURATIONS.”

NAKATA, S., T. SEKIGUCHI, et al. (1985). “FORMATION OF A NEARLY SPHERICAL FIELD-REVERSED CONFIGURATION.”

NAKATA, S., T. SEKIGUCHI, et al. (1986). “PLASMA STABILITY OF A NEARLY SPHERICAL FIELD-REVERSED CONFIGURATION.”

NAM, C., N. HERSHKOWITZ, et al. (1988). “MULTIPLE VALUED FLOATING POTENTIALS OF LANGMUIR PROBES.”

NEWTON, A. (1986). “ELECTRON-TEMPERATURE IN FIELD REVERSED CONFIGURATIONS AND THETA-PINCHES WITH CLOSED MAGNETIC-FIELD LINES.”

NGUYEN, K. and T. KAMMASH (1982). “CLASSICAL TRANSPORT-COEFFICIENTS IN A FIELD-REVERSED CONFIGURATION.”

Nishimura, K., R. Horiuchi, et al. (1997). “Tilt stabilization by cycling ions crossing magnetic separatrix in a field-reversed configuration.”

The stabilization of the tilt disruption in a held-reversed configuration is investigated by means of a three-dimensional particle simulation. The growth rate of tilting instability decreases as the plasma beta value at magnetic separatrix beta(sp) increases, while it is slightly affected by the finite ion Larmor radius parameter (s) over bar and the hollowness parameter of an equilibrium current profile D for low beta(sp) and moderately kinetic (2 less than or equal to (s) over bar less than or equal to 5) plasmas. It is found that the number flux of ions crossing the separatrix repeatedly increases with increasing beta(sp) and the crossing motion of ions plays a role in leading to the tilt stabilization by disturbing the unstable tilting motion. (C) 1997 American Institute of Physics. [S1070-664X(97)02911-X].

Nishimura, K., R. Horiuchi, et al. (1999). “Drift-kink instability induced by beam ions in field-reversed configurations.”

The drift-kink instability in field-reversed configurations with a beam component is investigated by means of a three-dimensional particle simulation. The unstable mode with the toroidal mode number n=4 grows with the rate gamma similar to 0.1-1.0 omega(ci) for a strong beam current and deforms the plasma profile along the beam orbit in the vicinity of the field-null line. This mode is nonlinearly saturated as a result of the relaxation of current profile. Both the saturation level and the growth rate tend to increase as the ratio of the beam current to the plasma current I-b/I-p increases. It is also found that there is a threshold value of the beam velocity v(b)similar to v(Ti) (ion thermal velocity) for the excitation of the instability. (C) 1999 American Institute of Physics. [S1070-664X(99)00609-6].

OHI, S. (1995). “CONFINEMENT AND HEATING OF FRC PLASMA.”

Confinement times of particle and trapped magnetic flux in FRC plasmas were simulated using a one dimensional transport model and classical (Spitzer's) resistivity. Comparing the simulation results and experimental results indicated that a transport in the plasmas was basically classical and deviations of experimental results from classical values (so-called anomaly) might attribute to a plasma geometry effect, by which the deviation was larger for fat plasmas and smaller for prolate ones. In order to verify this indication, a plasma electron heating with an axial injection of pulsed and intense ion beams was proposed for the plasmas in current FRC experiments. Possibility of this heating were examined by estimating an energy deposit rate of a beam ion in the plasmas. The energy deposit rate is a few%similar to about 100% for a plasma of 12cm in diameter and 80cm in length with a plasma parameter range of current experiments.

OHKUMA, Y., T. TAKAHASHI, et al. (1994). “EFFECT OF MULTIPOLE FIELDS ON FIELD-REVERSED-CONFIGURATION PLASMA.”

Even when rotational instability observed in a field-reversed-configuration plasma is suppressed by a multipole field, the confinement property of the plasma is not always improved. Plasma stabilized by a quadrupole field shrinks axially with time and its particle confinement time tau(N) becomes shorter than that of nonstabilized plasma. The reduction of tau(N) is large for the quadrupole field (m=2) and slight for the hexapole (m=3) and octupole (m=4) fields. A simple model reveals that the pertubation of the magnetic field on the separatrix by the multipole field takes a finite value for m=2 and approaches zero for m>2. This suggests that the distortion of the magnetic field at the ends of the separatrix is responsible for the degradation of confinement.

OHKUMA, Y., K. SUZUKI, et al. (1995). “BEHAVIOR OF AN FRC PLASMA WITH A MULTIPOLE FIELD.”

A rotational instability is observed in a field-reversed configuration plasma. Onset time, growth rate and modal frequency of the instability are measured in connection with the ion diamagnetic drift frequency over a wide range of plasma parameters. When the plasma is stabilized by a quadrupole field, it shrinks axially with time and its particle confinement time becomes shorter than that of a nonstabilized plasma. A numerical calculation of the field profile reveals that the distortion of the confinement field by the quadrupole field at the ends of the separatrix is responsible for the degradation of particle confinement. However, the multipole field with a higher pole number than the quadrupole can stabilize the plasma without degradation of the particle confinement.

Ohkuma, Y., M. Urano, et al. (1998). “Production of a low density field reversed configuration plasma.”

The plasma density of a field reversed configuration (FRC) needs to be decreased below the present experimental regime in order to heat the plasma and sustain the configuration by a high energy neutral beam in an FRC reactor. However, as the plasma is produced in a linear vacuum vessel, there exists a severe breakdown limit at a low fill pressure as compared with a toroidal system. A method to form FRCs beyond the breakdown limit is proposed here. The preionized plasma is compressed by a strong bias field to enhance the plasma flow from the confinement region to the outside region and is then diluted before the start of the confinement field on the NUCTE device. The use of a diluted plasma enables the critical density of the FRC to be lowered from 1.1 x 10(21) to 5.6 x 10(20) m(-3) and the sum of the electron and ion temperatures to be increased from 0.35 to 0.81 keV.

OHNISHI, M., S. OHI, et al. (1987). “SELF-IGNITION OF AN ADVANCED FUEL FIELD-REVERSED CONFIGURATION REACTOR BY FUSION PRODUCT HEATING.”

OHNISHI, M., H. KURANAGA, et al. (1988). “SUPPRESSION, BY ION-BEAMS, OF THE M=2 ROTATIONAL INSTABILITY IN A FIELD REVERSED CONFIGURATION.”

OHNISHI, M., A. ISHIDA, et al. (1993). “ION-BEAM STABILIZATION OF ROTATIONAL INSTABILITY IN A FIELD-REVERSED CONFIGURATION WITH RIGID ROTATION.”

The rotational instability of a field-reversed configuration (FRC) can be suppressed by applying a multipole magnetic field. The multipole field, however, breaks the axisymmetry and may compromise configuration. An alternative method using injected ''beam'' ions would preserve the symmetry. This method is studied here within the framework of a multifluid model for which a variational principle has been developed and solved using the Rayleigh-Ritz technique. This approach leads to an analytic solution for a rigid-rotor equilibrium and allows the straightforward derivation of marginal stability conditions. This was not possible with a previous hybrid simulation which, though more complete, was cumbersome to apply. It is found that if the ratio of the rotational frequency of beam ions to that of the background ions exceeds a critical value, the radial displacement of the plasma and beam ions are opposite, and the rotational instability can be suppressed. The effect of compressibility of beam ions on the stability is also examined. The stability analysis is applied to present or near-term experimental devices and a future reactor. The beam energy and current need only be a small fraction of those of the background plasma in order to stabilize the rotational instability. These results are in qualitative agreement with previous results from a hybrid particle simulation.

OHNISHI, M., A. ISHIDA, et al. (1995). “CURRENT SUSTAINMENT OF A FIELD-REVERSED CONFIGURATION BY ROTATING MAGNETIC-FIELD.”

The sustainment of a field-reversed configuration by means of a rotating magnetic field (RMF) is studied by the numerical simulation. It has been shown that the RMF applied externally on an FRC immediately after the production by a field-reversed theta pinch is penetrated into the plasma to drive a steady current, before the FRC fades out. There is a threshold value of the RMF which can maintain the FRC by the method. Since the RMF used in the present study is fairly large, we should optimize the parameters of the RMF to reduce the magnitude of the RMF required for sustaining the FRC. The method of applying the RMF to the FRC, however, may be effective for sustaining the hot and dense FRC in a steady state.

Ohnishi, M. and A. Ishida (1996). “Effects of radial flow on current drive in a field reversed configuration by a rotating magnetic field.”

The equilibrium of a field reversed configuration (FRC) with a rotating magnetic field (RMF) applied externally for maintaining steady state is studied theoretically. The momentum balance equations of ions and electrons as well as the mass balance equations have been solved analytically and a solution of a steady equilibrium of the FRC with the RMF, in which the ions and electrons rotate at different velocities, has been found. It has been revealed that the particle source and the radial flow neglected in previous studies plays an important role in the equilibrium.

Ohnishi, M. and A. Ishida (2002). “Stability of equilibrium in rotating magnetic field current drive for sustaining field-reversed configuration.”

The stability of the rotation of the ion and electron fluids is studied in regards to the balance of the forces exerted on the electrons by the resistive friction and the rotating magnetic field (RMF) applied for the sake of maintaining a field reversed configuration (FRC) in steady state. A simple analytical model with infinite-long plasma, rigidly rotating ions, and electrons and uniform plasma density is used. The linear stability analysis of the equilibrium rotation is carried out in the reduced zero-dimensional model, which includes the effects of ion rotation, radial plasma flow and separatrix radius change due to the flux conservation within the flux conserver. The analytical expression that gives the stability criterion is derived from the eigenvalues of the linearized equations. Based upon the stability criterion, an interpretation of the present experimental results and comments on future experiments are given for the penetration of the RMF into the FRC. (C) 2002 American Institute of Physics.

Ohtani, H., R. Horiuchi, et al. (2003). “Self-generation of hollow current profile and tilt instability in field-reversed configuration.”

Two-dimensional electromagnetic particle simulation is performed to investigate the profile relaxation from a magnetohydrodynamic (MHD) equilibrium to a kinetic one and the physical property of the kinetic equilibrium in the field-reversed configuration. The radial oscillation is excited in order to relax an excess energy in the MHD equilibrium. After this profile oscillation, the system spontaneously relaxes toward a kinetic equilibrium, in which the electron current profile becomes hollow as a result of the combined effects of the gradient-B drift near the field-null line and the E X B drift generated by the ion finite Larmor radius effect near the magnetic separatrix. On the other hand, the ion current profile becomes peaked due to the effect of the ion meandering orbit near the field-null line. The stability of the obtained kinetic equilibrium against the tilt mode is also studied by means of three-dimensional full electromagnetic particle simulation. It is found that the growth rate of the tilt instability in the case of the hollow current profile and high separatrix beta value is smaller than that in the case of the peaked current profile. (C) 2003 American Institute of Physics.

Ohtsuka, T., M. Okubo, et al. (1998). “Particle end loss in the edge plasma of a field-reversed configuration.”

Plasma parameters, particle end loss flux, flow velocity, and pressure are measured using a radial array of magnetic probes and directional electrostatic probes, in order to investigate particle loss processes in the edge layer of a field-reversed configuration (FRC). A plasma flow toward the end region is detected outside the separatrix between the axial midplane and the end region. The exhaust flow is also found in the end region. These results imply that particles are lost radially across the separatrix and then axially to the end. Measured flow velocity in the end region agrees within an error of 20% with the fluid-theory prediction, in which isentropy and axial momentum balance along magnetic flux tubes are assumed. The existence of the sonic condition in the end region is also suggested, analogous to ordinary fluid flow in a nozzle. The magnetic flux embedded in the edge layer of the confinement region and in the end region agrees within an error of 30%. These results indicate the applicability of the magnetohydrodynamics (MHD) theory for particle end loss. The end loss time along the open field agrees with the MHD prediction within an error of 20%. The measured particle loss flux from the end region is explained by the MHD theory within an error of 20%. The plasma outside the separatrix is considered to behave as hydrodynamic flow through the magnetic loss channel, contrary to the previous work [L. C. Steinhaur, Phys. Fluids 29, 3379 (1986)]. It seems that the magnetic mirror field improves the particle confinement in the edge plasma of the FRC and thus assist the FRC confinement as previously predicted [Slough et al., Nucl. Fusion 24, 1537 (1984)]. (C) 1998 American Institute of Physics. [S1070-664X(98)01710-8].

OKADA, S., Y. KISO, et al. (1989). “REDUCTION OF THE DENSITY PROFILE OF A FIELD-REVERSED CONFIGURATION PLASMA FROM DETAILED INTERFEROMETRIC MEASUREMENTS.”

OKADA, S., Y. KISO, et al. (1989). “ESTIMATION OF THE ELECTRICAL-RESISTIVITY IN FIELD-REVERSED CONFIGURATION PLASMAS FROM DETAILED INTERFEROMETRIC MEASUREMENTS.”

OKADA, S., S. UEKI, et al. (1995). “MEASUREMENT OF MAGNETIC-FIELD FLUCTUATION IN A FIELD-REVERSED-CONFIGURATION PLASMA.”

Confinement magnetic field of a field-reversed-configuration (FRC) plasma is reduced by a factor of about 10 and plasma density is decreased by a factor of about 100 without lowering the temperature seriously by translating a theta-pinch produced FRC plasma axially into a large bore metal vessel. Reduced magnetic field brings the lower-hybrid frequency into a range easily detected by magnetic probes. Search for wave activities in the FRC plasma for a wide frequency range disclosed magnetic field fluctuations in the lower-hybrid-drift frequency range for the first time in the FRC plasma. The identification of the mode is not done yet but the fluctuation level is close to the values predicted by theories on the LHD instability. This fluctuation level is not large enough to account for the transport rate of the particles from the FRC plasma.

Okada, S., K. Kitano, et al. (1999). “Axial compression of a field reversed configuration plasma.”

A new concept for plasma heating using axial magnetic compression of a field reversed configuration (FRC) plasma is proposed. In this concept, the FRC plasma is compressed only axially, keeping the magnetic flux between the separatrix and the confining chamber (flux conserver) wall unchanged: while allowing the plasma to expand radially. A simple model based on an empirical scaling law of FRC confinement and on the assumption that the compression is done adiabatically predicts that, in addition to heating the plasma, improved confinement will also be accomplished with this concept. This compression is done by energizing segmented mirror coils successively in such a way as to decrease the length of the confinement region between the coils. The apparatus for this axial compression was developed and an experiment was carried out. In this experiment the plasma was compressed by about 30% and the plasma lifetime of about 500 mu s was increased by about 50 mu s.

Okada, S., T. Asai, et al. (2001). “Experiments on additional heating of FRC plasmas.”

Experiments on additional heating by neutral beam injection and application of a law frequency wave to a plasma with an extremely high averaged beta value of about 90% - a field reversed configuration (FRC) plasma are carried out using the FRC Injection Experiment (FIX) apparatus. These experiments are made possible by translating the FRC plasma produced in a formation region of a theta pinch to a confinement region in order to secure better accessibility to heating facilities and to control plasma density. By determining the appropriate injection geometry and the mirror ratio of the confinement region. it became possible to inject a neutral beam with an energy of 14 keV and a current of 23 A into the FRC in a solenoidal confining field of only 0.04-0.05 T. Plasma confinement is improved in this experiment. Ion heating is observed to result from the application of a low frequency (80 kHz, about 1/4 of the ion gyrofrequency) compressional wave. A shear wave, probably mode converted from the compressional wave, is observed to propagate axially.

Okada, S., F. Kodera, et al. (2003). “Additional control experiments on field reversed configuration plasma.”

Plasmas with field reversed configuration (FRC) are confined in open systems and have extremely high beta value of about 100% and they are one of candidates for an attractive reactor But, in many cases they are produced in theta pinch apparatus and accessibility of additional heating facilities is poor In order to solve this problem and to realize density appropriate for neutral beam injection, technology of translation is useful. By the translation, an FRC plasma is ejected out from theta pinch formation region and is translocated into a confinement region. With this translation, experiments related to sustain and control the FRC plasma become to be accomplished. Actually, axial magnetic compression, neutral beam heating and low frequency RF wave heating experiments are carried out on the FRC Injection Experiment (FIX) apparatus.

OKAMOTO, M. (1987). “A STEADY-STATE SOLUTION TO A FIELD REVERSED CONFIGURATION.”

OKAMOTO, M. (1987). “A STEADY-STATE FIELD-REVERSED CONFIGURATION.”

OKAMOTO, M., H. BERK, et al. (1989). “RELATION BETWEEN BEAM DRIVEN SEED CURRENT AND ROTATION IN A STEADY-STATE FIELD REVERSED CONFIGURATION.”

Okubo, M., S. Sugimoto, et al. (1997). “Development of a novel ion energy analyser to measure the energy distribution function f(upsilon(perpendicular to)upsilon)(parallel to) of end-loss ions from FRC plasmas.”

A novel ion energy analyser is developed to measure the energy distribution function f(v(perpendicular to), v(parallel to)) of ions lost from both ends of FRC (field-reversed configuration) plasmas. Simultaneous measurement of both parallel and perpendicular velocity components is carried out in a straight and static magnetic field. The parallel velocity component of the end-loss ions is analysed by a retarding potential parallel to the magnetic held. Selection of perpendicular energy is made by the difference in particular gyroradius in a given magnetic field. A trial to confirm the applicability has been performed on the end-loss flow from the field-reversed configuration plasma produced by the FIX (FRC injection experiment) machine. (C) 1997 Elsevier Science S.A.

Omelchenko, Y. and R. Sudan (1997). “A 3-D Darwin-EM hybrid PIC code for ion ring studies.”

A new, 3-D electromagnetic (EM), hybrid, particle-in-cell (PIC) code, FLAME has been constructed to study low-frequency, large orbit plasmas in realistic cylindrical configurations. The stability and equilibrium of strong ion rings in magnetized plasmas are the first issues suitable for its application. In FLAME the EM-field is governed by Maxwell's equations in the quasi-neutral Darwin approximation (with displacement current neglected), the ion components are represented by discrete macro-particles, and the plasma electrons are modeled as a massless cold fluid. All physical quantities are expanded into finite Fourier series in the azimuthal (theta) direction. The discretization in the poloidal (r, z) plane is done by a finite-difference staggered grid method. The electron fluid equations include a finite scalar resistivity and macro-particles experience slowing-down collisions. A substantial reduction of computation time is achieved by enabling separate time advances of background and beam particle species in the time-averaged fields. FLAME has been optimized to run on parallel, MIMD systems, and has an object-oriented (C++) structure. The results of normal mode tests intended to verify the code ability to correctly model plasma phenomena are presented. We also investigate in 3-D the injection of a powerful annular ion beam into a plasma immersed in a magnetic cusp followed by an axially ramped applied magnetic field. A nonaxisymmetric perturbation is applied to the magnetic field and its effect on ion ring formation is analysed. (C) 1997 Academic Press.

Omelchenko, Y. (2000). “Kinetic simulations of the formation and stability of the field-reversed configuration.”

The Field-Reversed Configuration (FRC) is a high-beta compact toroidal plasma confined primarily by poloidal fields. In the FRC the external field is reversed on axis by the diamagnetic current carried by thermal plasma particles. A three-dimensional, hybrid, particle-in-cell (zero-inertia fluid electrons, and kinetic ions), code FLAME, previously used to study ion rings [Yu. A. Omelchenko and R. N. Sudan, J. Comp. Phys. 133, 146 (1997)], is applied to investigate FRC formation and tilt instability. Axisymmetric FRC equilibria are obtained by simulating the standard experimental reversed theta-pinch technique. These are used to study the nonlinear tilt mode in the "kinetic" and "fluid-like" cases characterized by "small" (similar to 3) and "large" (similar to 12) ratios of the characteristic radial plasma size to the mean ion gyro-radius, respectively. The formation simulations have revealed the presence of a substantial toroidal (azimuthal) magnetic field inside the separatrix, generated due to the stretching of the poloidal field by a sheared toroidal electron flow. This is shown to be an important tilt-stabilizing effect in both cases. On the other hand, the tilt mode stabilization by finite Larmor radius effects has been found relatively insignificant for the chosen equilibria. (C) 2000 American Institute of Physics. [S1070-664X(00)01505-6].

Omelchenko, Y., M. Schaffer, et al. (2001). “Nonlinear stability of field-reversed configurations with self-generated toroidal field.”

The field-reversed configuration (FRC) is a high-beta compact toroidal plasma confinement scheme in which the external poloidal field is reversed on the geometric axis by azimuthal (toroidal) plasma current. A quasineutral, hybrid, particle-in-cell (PIC) approach [Y. A. Omelchenko and R. N. Sudan, Phys. Plasmas 2, 2773 (1995)] is applied to study long-term nonlinear stability of computational FRC equilibria to a number of toroidal modes, including the most disruptive tilt mode. In particular, a self-generated toroidal magnetic field is found to be an important factor in mitigating the instability and preventing the confinement disruption. This is shown to be a unique FRC property resulting from the Hall effect in the regions of vanishing poloidal magnetic field. The instability-driven toroidal field stabilizes kink formation by increasing the magnetic field energy without destabilizing curvature-driven plasma motion. Finally, the tilt instability saturates due to nonlinear, finite Larmor radius (FLR) effects and plasma relaxation to a quasisteady kinetic state. During this transition the FRC is shown to dissipate a substantial amount of initially trapped flux and plasma energy. These effects are demonstrated for kinetic and fluid-like, spherical and prolate FRCs. (C) 2001 American Institute of Physics.

ONO, Y. (1995). “SLOW FORMATION OF FIELD-REVERSED CONFIGURATION BY USE OF 2 MERGING SPHEROMAKS.”

A novel slow formation method of field-reversed configuration (FRC) has been developed by magnetic reconnection of two force-free spheromaks with opposite toroidal magnetic field. The merging process cancels their opposite magnetic helicities, realizing a non-Taylor relaxation from the force-free state to the high-beta FRC state with zero helicity. A significant increase in the ion temperature has been documented up to 180eV during this fully anti-parallel reconnection. The dissipated toroidal ,magnetic energy of the merging toroids is transformed mostly to the ion thermal energy, revealing a unique relaxation mechanism to the high-beta equilibrium, The merging toroids are found to relax either to an FRC or to a new spheromak, depending on whether their total helicity is larger or smaller than a critical value.

Ono, Y., M. Inomoto, et al. (1999). “New relaxation of merging spheromaks to a field reversed configuration.”

A novel high beta relaxation to a field reversed configuration (FRC) has been investigated by axially colliding two spheromaks with opposing toroidal magnetic fields. The beta value of the merging toroids increases from 0.1 to 0.7-1.0 within 15 mu s: indicating an equilibrium transition from the low beta spheromak to the high beta FRC. An important finding is that the merging spheromaks relax either to a high beta FRC or to another low beta spheromak; depending on whether the initial normalized magnetic helicity given to these spheromaks is smaller or larger than a threshold value. This fact suggests that the FRCs are equipped with some global stability as robust as the Taylor magnetic energy minimum state.

Ono, Y. and M. Inomoto (2000). “Ultra-high-beta spherical tokamak formation by use of an oblate field-reversed configuration.”

A new slow formation of oblate field-reversed configuration (FRC) has been developed in the Tokyo University Spherical Torus No. 3 (TS-3) merging experiment using two merging spheromaks with opposing toroidal field. This unique technique was extended to a novel formation of ultra-high-beta (50%-70%) spherical tokamak (ST) by applying an external toroidal field B-t,B-ext to the FRC so produced. The high-beta ST was found to have a diamagnetic toroidal field in sharp contrast with low-beta STs with strong paramagnetic toroidal fields. High-beta properties of FRCs including their hollow current profile were maintained during the equilibrium transition, suggesting a close relationship between FRCs and high-beta STs in the second stability regime. (C) 2000 American Institute of Physics. [S1070-664X(00)92405-4].

Parks, P. (1999). “Self-similar adiabatic compression of highly elongated field reversed configurations.”

A theoretical model of an elongated field reversed configuration (FRC) adiabatically compressed to high density by an imploding liner is presented. Compression is assumed to be self-similar, equal along length and radius, and is accomplished by means of a shaped liner. In particular; the model here takes into account the special magnetic topology of the FRC and the non-uniformity of the radial plasma profiles in order to quantify final to initial compression ratios of the fluid quantities.

PEARLSTEIN, L. (1978). “FINITE ORBIT EFFECTS ON ROTATIONAL INSTABILITY IN FIELD REVERSED CONFIGURATIONS.”

PIERCE, W., R. MAQUEDA, et al. (1993). “INITIAL RESULTS FROM PARALLEL COIL OPERATION OF THE COAXIAL SLOW SOURCE FIELD REVERSED CONFIGURATION DEVICE.”

The Coaxial Slow Source (CSS) is a device in which 'annular' field reversed configurations (FRCs) (small aspect ratio, elongated, toroidal plasmas with poloidal field only) are formed in the space between coaxial coils carrying toroidal currents. The device is constructed so that the plasma can be translated into a simple cylindrical chamber and re-formed as a conventional FRC. Formation of FRCs on slow time-scales (50-250 mus) at low loop voltage (87.5-700 V) has been demonstrated. The paper presents initial results from the new parallel configuration device CSSP in which the inner and outer coils are connected in parallel to the capacitor banks. The parallel coil arrangement has significantly reduced the contact of the plasma with the walls and thus the impurity content. Configurations with confinement times of 10-30 mus, densities of 3 x 10(21) m-3 and temperatures of 3-20 eV are typical. Results are presented on formation, energy balance, a non-destructive tilt instability and dynamics associated with magnetic tearing.

PIERCE, W., T. JARBOE, et al. (1995). “STABILIZATION AND SATURATION OF THE IDEAL TILT MODE IN A DRIVEN ANNULAR FIELD-REVERSED CONFIGURATION.”

Prasad, R. (1998). “Temperature aspect of plasma jet flow in field reversal configuration.”

A qualitative description of the plasma jet flow in field reversal configuration confinement scheme has been presented taking into account the conductivity and anisotropic temperature effects which were not included previously following the ''free-streaming fluid model''.

Qerushi, A. and N. Rostoker (2002). “Equilibrium of field reversed configurations with rotation. III. Two space dimensions and one type of ion.”

A two-dimensional equilibrium model for field reversed configurations (FRCs) with rotation is presented. In a previous paper [N. Rostoker and A. Qerushi, Phys. Plasmas 9, 3057 (2002)] it was shown that a complete description of equilibria for FRCs with rotation is provided by a generalized Grad-Shafranov equation for the plasma flux function. In this paper it is shown how to solve that fundamental equation for the case of two space dimensions and one type of ion. Periodic boundary conditions and a Green's function are used to convert the original differential equation to an equivalent integral equation. The integral equation is solved by iteration. An iteration algorithm is described which converges to a solution of the generalized Grad-Shafranov equation starting with a one-dimensional trial function. Analytic one-dimensional solutions are shown to be a limiting case of two-dimensional solutions when the applied magnetic field is constant. In addition to rapid convergence for a complex nonlinear problem, the Green's function method guarantees that the boundary conditions are satisfied in every iteration. (C) 2002 American Institute of Physics.

Qerushi, A. and N. Rostoker (2002). “Equilibrium of field reversed configurations with rotation. II. One space dimension and many ion species.”

In a previous paper [N. Rostoker and A. Qerushi, Phys. Plasmas 9, 3057 (2002)] it was shown that a complete description of equilibria of field reversed configurations with rotation can be obtained by solving a generalized Grad-Shafranov equation for the flux function. In this paper we show how to solve this equation in the case of one space dimension and many ion species. The following fusion fuels are considered: D-T, D-He-3, and p-B-11. Using a Green's function the generalized Grad-Shafranov equation is converted to an equivalent integral equation. The integral equation can be solved by iteration. Approximate analytic solutions for a plasma with many ion species are found. They are used as starting trial functions of the iterations. They turn out to be so close to the true solutions that only a few iterations are needed. (C) 2002 American Institute of Physics.

Qerushi, A. and N. Rostoker (2003). “Equilibrium of field reversed configurations with rotation. IV. Two space dimensions and many ion species.”

In a previous paper [N. Rostoker and A. Qerushi, Phys. Plasmas 9, 3057 (2002)] a generalized Grad-Shafranov equation for the plasma flux function was derived which provides a complete description of equilibria of field reversed configurations with rotation. In this paper this fundamental equation is solved for two space dimensions and many ion species. The following fusion fuels are considered: D-T, D-He-3, and p-B-11. Using periodic boundary conditions the original differential equation is converted to an equivalent integral equation which involves a Green's function. The integral equation is solved by iteration. Approximate solutions are found for all the fusion fuels considered using a two-dimensional equilibrium model for one type of ion [A. Qerushi and N. Rostoker, Phys. Plasmas 9, 5001 (2002)]. They are used as starting trial functions of the iterations. They turn out to be so close to the real solutions that only a few iterations are needed. (C) 2003 American Institute of Physics.

QUINN, W. (1982). “STABILITY AND CONFINEMENT OF SPHEROMAKS AND FIELD REVERSED CONFIGURATIONS.”

QUINN, W. (1983). “COMPACT TOROID EXPERIMENTS - SPHEROMAKS AND FIELD-REVERSED CONFIGURATIONS.”

RABIE, A., A. BREHIER, et al. (1986). “THYROID STATE AND CHOLECALCIN (CALCIUM-BINDING PROTEIN) IN CEREBELLUM OF THE DEVELOPING RAT.”

RADO, R., N. LEVI, et al. (1987). “SEISMIC SIGNALING AS A MEANS OF COMMUNICATION IN A SUBTERRANEAN MAMMAL.”

RAMAN, R., G. VLASES, et al. (1993). “ENERGY-BALANCE IN THE CSSU DEVICE.”

An analysis of the energy balance in the Coaxial Slow Source Upgrade (CSSU) device is reported. The CSSU consists of two concentric coils carrying pulsed azimuthal currents only, which form an elongated plasma (an 'annular field reversed configuration (FRC)') in the space between the coils. The plasma contains no toroidal field, and is confined by poloidal fields only, resulting in a very high average beta. The CSSU, which operates at loop voltages of 2 kV or less and with risetimes of the order of 70 mu s, was developed to provide a low voltage, slow formation alternative to conventional FRC generation techniques that are based on fast theta pinch technology. It is found that the CSSU device does form annular FRCs, which persist for the duration of the inductive current drive, apparently free of MHD instability. Temperatures are low, however, and the transport is correspondingly poor. To analyse the energy balance, the power input to the plasma is calculated directly from external and internal magnetic field measurements. No assumptions about the resistivity profile have been made. A triple Langmuir probe located at the device end region was used to calculate the energy lost due to escaping particles. Electron temperature measurements from Thomson scattering and impurity estimates from doping studies are used in a time dependent corona model calculation to show that the CSSU plasma is impurity line radiation dominated. Time dependent coronal calculations imply that, with operation over much longer formation times (> 100 to 200 mu s) at lower density (10(14) cm(-3)), it may be possible to burn through the carbon and oxygen impurity radiation barriers and attain plasma conditions closer to those produced in conventional FRCs.

REJ, D. and W. ARMSTRONG (1984). “ELECTRON-TEMPERATURE MEASUREMENTS IN THE FIELD-REVERSED CONFIGURATION EXPERIMENT FRX-C.”

REJ, D. and M. TUSZEWSKI (1984). “A ZERO-DIMENSIONAL TRANSPORT MODEL FOR FIELD-REVERSED CONFIGURATIONS.”

REJ, D., W. ARMSTRONG, et al. (1986). “EXPERIMENTAL STUDIES OF FIELD-REVERSED CONFIGURATION TRANSLATION.”

REJ, D., W. ARMSTRONG, et al. (1986). “HELICAL AND STRAIGHT QUADRUPOLE STABILIZATION OF THE NORMAL = 2 ROTATIONAL INSTABILITY IN TRANSLATED FIELD-REVERSED CONFIGURATIONS.”

REJ, D., G. BARNES, et al. (1990). “ELECTRON-ENERGY CONFINEMENT IN FIELD REVERSED CONFIGURATION PLASMAS.”

REJ, D., G. BARNES, et al. (1990). “FLUX CONFINEMENT MEASUREMENTS IN LARGE FIELD-REVERSED CONFIGURATION EQUILIBRIA.”

REJ, D., D. TAGGART, et al. (1992). “HIGH-POWER MAGNETIC-COMPRESSION HEATING OF FIELD-REVERSED CONFIGURATIONS.”

Magnetic compression heating experiments at the 1 GW level on field-reversed configuration (FRC) compact toroid plasmas are reported. FRC's formed in a tapered theta-pinch coil have been translated into a single-turn compression coil, where the external magnetic field is slowly raised up to seven times its initial value. Significant electron and ion heating consistent with the expected B4/5 adiabatic scaling is observed, despite significant particle diffusion, which is enhanced during compression. The n = 2 rotational instability is enhanced during compression, but has been controlled to an extent by the application of an external quadrupole field. The particle and flux confinement times, tau(N) and tau(phi), remain approximately equal and decrease roughly with the square of the plasma radius R during compression, implying a constant nonclassical field-null resistivity. The observed tau(N) and tau(phi) magnitudes and scalings are compared with classical and anomalous transport theories, and existing empirical models. Particle diffusion dominates the energy confinement, accounting for three-fourths of the total losses. Upper bounds on the electron thermal diffusivities are estimated.

Rostoker, N., M. Binderbauer, et al. (1996). “Fusion reactors based on colliding beams in a field reversed configuration plasma.”

A plasma consisting of large orbit non-adiabatic ions and adiabatic electrons is considered. For such a plasma it is possible that the anomalous transport characteristic of Tokamaks can be avoided. Experimental evidence in support of this possibility has been obtained with energetic beams injected into Tokamaks for healing in DIII-D and TFTR and with energetic fusion products in JET. Energetic particles were observed to slow down and diffuse classically in the presence of anomalous transport of thermal particles. Assuming that classical transport theory is applicable we have elected to investigate magnetic confinement for field reversed configurations (FRC's). This configuration was chosen because there are some 20 years of experimental investigation, about 600 published papers and current programs in Japan to provide background information for a case where a substantial fraction of the ions are non-adiabatic and contribute to the current. The investigation begins with self-consistent equilibrium solutions of the Vlasov-Maxwell equations. The classical Fokker-Planck equation is employed to evaluate Coulomb collisions and transport. Reactor configurations based on D - T, D - He-3 and H-B-11 reactions are considered. Energy balance is investigated considering the only losses to be Bremsstrahlung.

Rostoker, N., M. Binderbauer, et al. (1997). “Colliding beam fusion reactor.”

Recent results with Tokamak experiments provide insights into the problem of magnetic confinement. They demonstrate how to avoid anomalous transport and thus solve the major problems of Tokamak reactors: size, the production of 14-megaelectron volt neutrons, and maintenance. An alternate confinement system, the field-reversed configuration, confines beams of protons and boron-11. For the proton-boron-11 fusion reaction, the fusion products are all charged particles for which direct conversion is feasible and neutron flux is negligible.

Rostoker, N. and A. Qerushi (2002). “Equilibrium of field reversed configurations with rotation. I. One space dimension and one type of ion.”

Self-consistent solutions of the Vlasov-Maxwell equations are obtained. They involve rigid rotor distributions. This selection is justified on physical grounds. For this selection the Vlasov equation can be replaced by moment equations which terminate without any additional assumptions. For one-dimensional equilibria with one type of ion these equations have exact solutions. A complete equilibrium solution appropriate to a field reversed configuration with rotation can be obtained by solving a generalized Grad-Shafranov equation for the flux function. From this solution all other physical quantities can be determined. A Green's function method is developed to solve this equation, which provides a basis for an iterative solution. This method has the advantage that at every iteration the boundary conditions are satisfied. In this paper cylindrical geometry with one space dimension and one type of ion is considered, where analytic solutions are available. The convergence of the Green's function method is established. For this nonlinear problem there is usually more than one solution for completely specified boundary conditions (bifurcation). The present method selects one solution. It is applicable to equilibria with many ion species and to two dimensions. (C) 2002 American Institute of Physics.

ROUGHTON, N., T. INTRATOR, et al. (1983). “THICK-TARGET MEASUREMENTS AND ASTROPHYSICAL THERMONUCLEAR REACTION-RATES - ALPHA-INDUCED REACTIONS.”

Ryutov, D. and R. Siemon (2001). “Magnetized plasma configurations for fast liner implosions: A variety of possibilities.”

A variety of plasma configurations suitable for adiabatic compression by fast liners has been identified. Among them there are field-reversed configurations, spheromaks, diffuse Z pinches, spherical tokamaks, and others. The initial plasma is assumed to have density in the range of 10(17)-10(18) cm(-3) and the temperature of the order of 100 eV. Relative advantages and disadvantages of various plasma configurations are discussed. The very fact of the existing broad spectrum of plasma configurations compatible with the liner compression increases the probability of a success in this branch of fusion research.

Ryzhkov, S., V. Khvesyuk, et al. (2003). “Progress in an alternate confinement system called a FRC.”

The high fusion power density resulting from high beta (the ratio of the plasma to magnetic energy density) and natural divertor make the field-reversed configuration (FRC) a prime candidate for fusion reactor other than tokamak, the so-called alternate concept. Brief review of the simple compact system with natural advantages and reactor potential is given. Theoretical and experimental results over the last seven years are discussed.

Santiago, M., A. Assis, et al. (1998). “Non resistive analysis of rotational instabilities in FRC and the Unicamp TC-1 m=4 results.”

Ideal one dimensional MHD (non-resistive) equations are used to study the rotational instability in field reversed configuration plasmas. Instead of using resistive boundary layer analysis, the eigenmode non hermitian equations are solved on the complex omega-plane using a numerical code constructed using ''Mathematica'' We take into account the plasma compressibility and compare our results with the Compact Torus (TC-1) experiment of the Universidade Estadual de Campinas (UNICAMP), which is presented here. The m = 4 rotational mode observed in TC-1 is used to verify the consistency of our model.

Santiago, M., A. deAssis, et al. (1998). “The viscous MHD spectra application to coronal loop heating and stability.”

We have derived the viscous MHD equilibrium and perturbed equations for current carrying cylindrical plasmas. We have considered compressible plasmas and, when the viscosity is introduced in the equation of motion it leads to a linearized vector second order perturbed equation for the fluid displacement, showing the appearance of non Hermitian operators. The Lagrangian representation is used to investigate the stability and we used the normal mode analysis to study the linearized equation. We applied our model for the problem of the coronal loop heating and solved the eigenmode equation, which is nonlinear in the eigenvalue, using a numerical code based on the software ''Mathematica'', with appropriate boundary conditions. We have confirmed that viscosity is relevant as the dominant mechanism for the coronal loop heating in our self-consistent calculation as indicated by previous non self-consistent work of De Azevedo et al. Solar Phys 136, 295 (1991). In the limit of zero viscosity, we obtain the discrete and the continuous spectra and some unstable points.

SAWAI, S., M. TSUCHIMOTO, et al. (1990). “BOUNDARY ELEMENT ANALYSIS OF FREE-BOUNDARY FIELD-REVERSED CONFIGURATIONS.”

SCHAMILOGLU, E., J. GREENLY, et al. (1993). “ION RING PROPAGATION IN A MAGNETIZED PLASMA.”

The propagation of an ion ring in a 2.5 m long, 0.30 m diam magnetized plasma column was studied using an axial array of magnetic probes and fast proton detectors, a microwave interferometer, and a grating spectrometer. The ring propagated with an initial axial velocity 3X10(6) m/sec, about four times the Alfven speed in the plasma, and excited damped magnetosonic waves whose peak amplitude depended on the plasma return current. The plasma electrons were heated by about 1 eV in response to the ring, as measured by the H(gamma) line-to-continuum intensity ratio. This heating is primarily attributed to classical Coulomb collisions, although about 1%-10% can be attributed to the collective ring-plasma interaction. The collective interaction had no measurable effect on the dynamics of the ion ring, consistent with theoretical models, given the beam, plasma, and magnetic-field parameters in the experiment.

SCHELLER, G., R. GOTTSCHO, et al. (1988). “QUENCHING RATES OF AR METASTABLES IN RADIO-FREQUENCY GLOW-DISCHARGES.”

SCHELLER, G., R. GOTTSCHO, et al. (1988). “NONLINEAR EXCITATION AND DISSOCIATION KINETICS IN DISCHARGES THROUGH MIXTURES OF RARE AND ATTACHING GASES.”

SCHWARZMEIER, J., D. BARNES, et al. (1983). “MAGNETOHYDRODYNAMIC EQUILIBRIUM AND STABILITY OF FIELD-REVERSED CONFIGURATIONS.”

SCHWARZMEIER, J. and C. SEYLER (1984). “INADEQUACIES OF FINITE LARMOR RADIUS TREATMENTS OF THE INTERNAL TILTING INSTABILITY IN FIELD-REVERSED CONFIGURATIONS.”

SETHIAN, J., K. GERBER, et al. (1979). “FIELD REVERSED CONFIGURATION MAINTAINED WITH PLASMA CURRENTS INDUCED BY A ROTATING RELATIVISTIC ELECTRON-BEAM.”

SEVILLANO, E. and F. RIBE (1985). “RECONNECTION STUDIES IN FIELD-REVERSED CONFIGURATIONS.”

SGRO, A., W. ARMSTRONG, et al. (1982). “FLUX LOSS AND HEATING DURING THE FORMATION OF A FIELD-REVERSED CONFIGURATION.”

SHEFFIELD, J. (1994). “THE PHYSICS OF MAGNETIC FUSION-REACTORS.”

During the past two decades there have been substantial advances in magnetic fusion research. On the experimental front, progress has been led by the mainline tokamaks, which have achieved reactor-level values of temperature and plasma pressure. Comparable progress, when allowance is made for their smaller programs, has been made in complementary configurations such as the stellarator, reversed-field pinch and field-reversed configuration. In this paper, the status of understanding of the physics of toroidal plasmas is reviewed. It is shown how the physics performance, constrained by technological and economic realities, determines the form of reference toroidal reactors. A comparative study of example reactors is not made, because the level of confidence in projections of their performance varies widely, reflecting the vastly different levels of support which each has received. Success with the tokamak has led to the initiation of the International Thermonuclear Experimental Reactor project. It is designed to produce 1500 MW of fusion power from a deuterium-tritium plasma for pulses of 1000 s or longer and to demonstrate the integration of the plasma and nuclear technologies needed for a demonstration reactor.

SHEFFIELD, J. (1994). “MAGNETIC FUSION COMMERCIAL POWER-PLANTS.”

Toroidal magnetic systems offer the best opportunity to make a commercial fusion power plant. They have, between them, all the features needed; however, no one system yet meets the ideal requirements. The tokamak is the most advanced system, and the proposed International Thermonuclear Experimental Reactor (ITER) and Tokamak Physics Experiment (TPX) will build upon the existing program to prepare for an advanced tokamak demonstration plant. Complementary toroidal systems such as the spherical torus, stellarator, reversed-field pinch, field-reversed configuration, and spheromak offer, between them, potential advantages in each area and should be studied in a balanced fusion development program.

SHEFFIELD, J. and J. GALAMBOS (1994). “PROSPECTS FOR TOROIDAL FUSION-REACTORS.”

Work on the International Thermonuclear Experimental Reactor (ITER) tokamak has refined understanding of the realities of a deuterium-tritium (D-T) burning magnetic fusion reactor. An ITER-like tokamak reactor using ITER costs and performance would lead to a cost of electricity (COE) of about 13O mills/kWh. Advanced tokamak physics to be tested in the Toroidal Physics Experiment (TPX), coupled with moderate extrapolation in engineering, technology, and unit costs (i.e., based on the ITER design), should lead to a COE comparable with best existing fission systems around 60 mills/kWh. However, a larger unit size, similar to 2000 MW((e)), is favored for the fusion system. Alternative toroidal configurations to the conventional tokamak, such as the stellarator, reversed-field pinch, and field-reversed configuration, offer some potential advantage, but are less well developed, and have their own challenges.

SHIBATA, N. and A. ISHIDA (1995). “MAGNETIC-FIELD COORDINATE AND EQUILIBRIUM STRUCTURE OF FIELD-REVERSED CONFIGURATIONS.”

According to the recent study of the magnetohydrodynamic stability for both the global and local modes of field-reversed configurations (FRCs), it is required to develop a theory including the ion's finite orbit effect which is valid in FRCs. This means that the two dimensional analysis on the poloidal surface is inevitably necessary. As the first step toward the two dimensional stability analysis, the magnetic field coordinate is obtained numerically in FRCs for the first time. Using the co-ordinate, the equilibrium properties of FRCs are examined for the preparation of stability analysis.

SHIMAMURA, S. and Y. NOGI (1986). “HELICAL QUADRUPOLE FIELD STABILIZATION OF FIELD-REVERSED CONFIGURATION PLASMA.”

SHIOKAWA, A., S. OKADA, et al. (1991). “SPONTANEOUS APPEARANCE OF TOROIDAL FIELD IN FIELD REVERSED CONFIGURATION PLASMA.”

The field reversed configuration (FRC) plasma had been thought to have poloidal field only, but in this experiment, toroidal field was observed. We report magnetic probe measurements on our FIX machine, and the existence of toroidal field in the FRC plasma during its translation. The magnitude of the toroidal field is 100 approximately 150 G at the peak, and the direction of the toroidal field is counterclockwise looking toward the theta-pinch region, irrespective of the direction of the external axial field. The obtained toroidal field has a direction opposite to the toroidal field in FRX-C/LSM.

SHIOKAWA, A. and S. GOTO (1993). “DYNAMIC PROPERTY OF SPONTANEOUS TOROIDAL FIELD IN FIELD-REVERSED CONFIGURATION PLASMAS.”

The toroidal field in the translated field-reversed configuration (FRC) plasma has been measured, although the FRC plasma has sometimes been described as having only the poloidal field. Measurements of the toroidal field distribution during the plasma translation clarify the location where the toroidal field originates. The experimental results show that the flux of poloidal and toroidal components decays monotonically in time after the beginning of the translation. This indicates that the toroidal field occurs just after the FRC formation without further production during the translation.

SHUMAKER, D. (1986). “NUMERICAL-CALCULATION OF EQUILIBRIA FOR THE FIELD-REVERSED CONFIGURATION.”

SHUMAKER, D. (1988). “TRANSPORT SIMULATION OF A FIELD-REVERSED CONFIGURATION PLASMA.”

SLOUGH, J., A. HOFFMAN, et al. (1984). “FLUX AND PARTICLE LIFETIME MEASUREMENTS IN FIELD-REVERSED CONFIGURATIONS.”

SLOUGH, J. and A. HOFFMAN (1988). “OBSERVATION OF TILT STABILITY OF FIELD REVERSED CONFIGURATIONS AT LARGE-S.”

SLOUGH, J., A. HOFFMAN, et al. (1989). “FORMATION STUDIES OF FIELD-REVERSED CONFIGURATIONS IN A SLOW FIELD-REVERSED THETA-PINCH.”

SLOUGH, J. and R. MILROY (1990). “DIAGNOSTIC SYSTEM FOR DETERMINING THE INTERNAL STRUCTURE OF A FIELD REVERSED CONFIGURATION.”

SLOUGH, J. and A. HOFFMAN (1990). “EXPERIMENTAL-STUDY OF THE FORMATION OF FIELD-REVERSED CONFIGURATIONS EMPLOYING HIGH-ORDER MULTIPOLE FIELDS.”

SLOUGH, J., A. HOFFMAN, et al. (1992). “CONFINEMENT AND STABILITY OF PLASMAS IN A FIELD-REVERSED CONFIGURATION.”

Experiments have been conducted on the LSX device where plasmas confined in a field-reversed magnetic geometry have exhibited record energy, particle, and configuration lifetimes. The scaling from previous smaller devices showed a very positive confinement scaling with s, the number of ion gyroradii inside the field-reversed configuration. These plasmas were observed to have gross stability to global low-order modes such as the internal tilt. The growth of tilt instabilities was not observed during the equilibrium decay of plasmas up to s is similar to 8.

SLOUGH, J. and A. HOFFMAN (1993). “STABILITY OF FIELD-REVERSED CONFIGURATIONS IN THE LARGE S-EXPERIMENT (LSX).”

Data from several diagnostics employed on the Large s Experiment (LSX) field-reversed theta pinch were analyzed to seek correlation between plasma distortions and the confinement properties of the field-reversed configurations (FRC's) formed. In particular, an array of B-theta probes was used to determine separatrix movement, which might indicate the existence of low-order modes, such as a tilt instability. No correlation between the quality of confinement and signal was observed. The parameter s, equal to the average number of ion gyroradii inside the separatrix, has been postulated as a measure of FRC stability with values above 2, leading to instability and loss of confinement. However, the confinement observed in experiments conducted over a large range of a (1<s<8) appeared to correlate more with the shape of the equilibrium radial density profile produced during formation rather than s. Flatter profiles correlated with poorer confinement.

SLOUGH, J., A. HOFFMAN, et al. (1995). “TRANSPORT, ENERGY-BALANCE, AND STABILITY OF A LARGE FIELD-REVERSED CONFIGURATION.”

Slough, J. and A. Hoffman (1999). “Penetration of a transverse magnetic field by an accelerated field-reversed configuration.”

The field-reversed configuration (FRC) is a compact toroid with near unity beta that is an ideal candidate to provide central fueling for large tokamaks. The study of the acceleration and penetration physics of the FRC into a transverse magnetic field gradient is necessary in order to evaluate the fueling efficiency of the FRC. To this end, experiments were conducted on the LSX/mod facility [J. T. Slough and A. L. Hoffman, 16th IAEA Fusion Energy Conference 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. II, p. 237], where large mass (0.8 mg) FRCs were accelerated to high velocity (2 X 10(5) m/s), and then guided into a transverse magnetic field. Various diagnostics were employed to characterize the penetration process. These included thermocouple probes, magnetic probes, and emission arrays. A simple analytical model is developed that explains the basic features of the penetration process. Further modeling with two-dimensional numerical calculations provided for scaling laws to reach the conditions necessary to penetrate a large fusion tokamak. (C) 1999 American Institute of Physics. [S1070-664X(99)04701-1].

Slough, J. and K. Miller (2000). “Enhanced confinement and stability of a field-reversed configuration with rotating magnetic field current drive.”

A new experiment has been constructed to study the sustainment of a field-reversed configuration (FRC) with a rotating magnetic field (RMF). FRCs were formed with cold, unmagnetized ions and thus without a kinetic ion component that was believed to provide stability to internal tilt modes. No destructive instabilities were observed for the RMF FRC. Only peripheral radial penetration of the RMF was observed. The radially inward flow arising from axial screening currents at the FRC edge reduced convective and conductive losses to the measurement limit of the diagnostics.

Slough, J. and K. Miller (2000). “Flux generation and sustainment of a field reversed configuration with rotating magnetic field current drive.”

A new experimental device has been constructed to study the flux build-up and sustainment of a field reversed configuration (FRC) with a rotating magnetic field (RMF). Even though complete penetration was expected from RMF theory, the RMF field was observed to penetrate only a few centimeters inside the FRC separatrix. Despite the limited penetration, significantly larger toroidal currents (40 kA) were driven than in previous experiments (similar to 2 kA) with the same RMF field. The high currents and lack of deep penetration allowed the axial field to be the dominant field throughout the FRC. The radially inward pondermotive force arising from axial screening currents at the FRC edge had a significant influence on energy and particle confinement, reducing convective losses to the limit of observability. With only ohmic heating, the measured low ion temperatures (2 eV) left the ions unmagnetized while the electrons (similar to 40 eV) were well magnetized. No destructive instability was observed for the RMF driven FRC despite the lack of a strong kinetic ion component. (C) 2000 American Institute of Physics. [S1070-664X(00)96305-5].

Slough, J. and K. Miller (2001). “Small, high frequency probe for internal magnetic field measurements in high temperature plasmas.”

In previous experiments on high temperature (> 50 eV), high density (> 10(20) m(-3)) plasmas such as the field-reversed configuration (FRC), it has not been possible to obtain direct information of the internal field structure in a nondestructive way. The probe surface would vaporize due to high electron thermal transport as well as ablate due to high energy ion bombardment. To minimize these processes, the smallest possible probes made from materials with the longest thermal time to melting were constructed and tested. In order to measure fast magnetic field changes (similar to several MHz), as well as not influence the FRC internal electric fields, the probe wall material was constructed from a nonconducting material. Of several insulating materials tested, beryllia was the only material that was found to be suitable. The probe wall consisted of a 0.3-m-long 2-mm-diam beryllia tube bored out to 1.5 mm. Inside the small bore, a "chain" probe of 24 loops was constructed out of 50-mum-diam magnet wire. The two axis probe measured axial and azimuthal FRC magnetic fields as small as a few gauss with centimeter resolution and a frequency response of 1 MHz or better. With the probe inserted, no changes in FRC confinement or behavior were observed over the entire 1 ms lifetime of the discharge. (C) 2001 American Institute of Physics.

SOBEHART, J. (1989). “ANALYTIC, 2 FLUID, FIELD REVERSED CONFIGURATION EQUILIBRIUM WITH SHEARED ROTATION.”

SOBEHART, J. and R. FARENGO (1990). “LOW-FREQUENCY DRIFT DISSIPATIVE MODES IN FIELD-REVERSED CONFIGURATIONS.”

SOBEHART, J. (1990). “FLUX TRAPPING EFFICIENCY DURING THE EARLY FORMATION PHASE OF A FIELD REVERSED CONFIGURATION.”

SPARKS, L., R. SUDAN, et al. (1982). “OPTIMAL PLASMA-BETA IN AN MHD-STABLE FIELD-REVERSED CONFIGURATION WITH ENERGETIC, LARGE-ORBIT IONS.”

SPENCER, R. and D. HEWETT (1982). “FREE-BOUNDARY FIELD-REVERSED CONFIGURATION (FRC) EQUILIBRIA IN A CONDUCTING CYLINDER.”

SPENCER, R., M. TUSZEWSKI, et al. (1983). “ADIABATIC-COMPRESSION OF ELONGATED FIELD-REVERSED CONFIGURATIONS.”

SPENCER, R. and M. TUSZEWSKI (1985). “EXPERIMENTAL AND COMPUTATIONAL EQUILIBRIA OF FIELD-REVERSED CONFIGURATIONS.”

SPENCER, R. and M. TUSZEWSKI (1985). “MAGNETOHYDRODYNAMIC EQUILIBRIUM AND STABILITY OF ROTATING FIELD-REVERSED CONFIGURATIONS WITH EXCLUDED MULTIPOLE FIELDS.”

Srinivasan, R., K. Avinash, et al. (2001). “High beta compact toroidal equilibria.”

The relationship of the recently proposed tokamak with spheromak shell (STSS) with other compact equilibria in the low aspect ratio A regime, e.g., spherical tokamaks, field reversed configurations, is studied. It is shown that these equilibria are complementary to equilibria with a magnetic hole studied earlier by Cowley [S. C. Cowley, P. K. Kaw, R. S. Kelly, and R. M. Kulsrud, Phys. Fluids B 3, 2066 (1991)] in the large A regime. The former is perfectly paramagnetic while the latter is perfectly diamagnetic. Relevance of these results to the study of compact equilibria conducted recently on Tokyo University Spherical Torus(TS)-3 and TS-4 [M. Inomoto, Y. Ueda, Y. Ono, T. Murakami, M. Tsurda, M. Yamada, and M. Katsurai, Proceedings of the 17th Conference on Fusion Energy, Yokohama, 1998 (International Atomic Energy Agency, Vienna, 1998), Vol. 3, p. 927] is briefly discussed. (C) 2001 American Institute of Physics.

STEINHAUER, L. (1985). “MAGNETIC-FLUX TRAPPING DURING FIELD REVERSAL IN THE FORMATION OF A FIELD-REVERSED CONFIGURATION.”

STEINHAUER, L., R. MILROY, et al. (1985). “A MODEL FOR INFERRING TRANSPORT RATES FROM OBSERVED CONFINEMENT TIMES IN FIELD-REVERSED CONFIGURATIONS.”

STEINHAUER, L. (1986). “ELECTROSTATIC CONFINEMENT IN THE EDGE LAYER OF FIELD-REVERSED CONFIGURATIONS.”

STEINHAUER, L. (1990). “SUMMARY OF THE UNITED-STATES JAPAN WORKSHOP ON D-3HE FIELD-REVERSED CONFIGURATIONS, BERKELEY, CALIFORNIA, NOVEMBER 20-21, 1989.”

STEINHAUER, L. and A. ISHIDA (1990). “GYROVISCOUS STABILITY THEORY WITH APPLICATION TO THE INTERNAL TILT MODE OF A FIELD-REVERSED CONFIGURATION.”

STEINHAUER, L. (1990). “A NEARLY ONE-AND-ONE-HALF-DIMENSIONAL CONFINEMENT MODEL FOR FIELD-REVERSED CONFIGURATIONS.”

STEINHAUER, L. (1990). “IMPROVED ANALYTIC EQUILIBRIUM FOR A FIELD-REVERSED CONFIGURATION.”

STEINHAUER, L. (1991). “SUMMARY OF THE UNITED-STATES-JAPAN WORKSHOP ON D-HE-3 FUELS IN FIELD-REVERSED CONFIGURATIONS, FUKUOKA, JAPAN, NOVEMBER 28-30, 1990.”

STEINHAUER, L. and J. SANTARIUS (1992). “SPECIAL ISSUES ON D-HE-3 FUSION - PREFACE.”

STEINHAUER, L. (1992). “ELECTRON THERMAL CONFINEMENT IN THE EDGE PLASMA OF A FIELD-REVERSED CONFIGURATION.”

The electron energy loss rate along the open field lines in the edge layer of field-reversed configurations (FRC's) can be inferred from experiments using a simple model. Since FRC edge layers resemble theta pinches a similar model can be applied to theta pinches. Collecting results from a large number of FRC and theta-pinch experiments, it is shown that the electron energy loss is convective, with 3-7kT(e) lost per electron escaping from the plasma. This stands in marked contradiction to the conclusions of two previous papers, which claimed that the electron energy loss could be explained by thermal conduction. Convective electron thermal loss is well established as the loss mechanism in low-collisionality plasmas such as mirrors. However, thermal conduction (a diffusive mechanism) was expected in the dense, collisional plasmas of typical FRC's and theta pinches. The thermal conduction mechanism (which applies for sufficiently high collisionality) is shown here to fail at a higher level of collisionality than expected. Consequently, in collisionality ranges where thermal conduction applies, its rate is comparable to or less than the convective loss rate.

STEINHAUER, L. and A. ISHIDA (1992). “PROFILE CONSISTENCY IN EQUILIBRIA OF FIELD-REVERSED CONFIGURATIONS.”

Experimental evidence is presented for a regulatory principle governing field-reversed configuration (FRC) equilibria. This leads to a form of "profile consistency" with which the current profile exhibits a remarkable correlation with x(s) (the ratio of the separatrix radius to the coil radius). The proposed explanation is that these equilibria are regulated by an instability which maintains the profile at a marginally stable condition.

STEINHAUER, L., A. ISHIDA, et al. (1994). “IDEAL STABILITY OF A TOROIDAL CONFINEMENT SYSTEM WITHOUT A TOROIDAL MAGNETIC-FIELD.”

New results show that a toroidal plasma can be ideally stable to gross modes without a toroidal magnetic field. Previous ideal-magnetohydrodynamic (MHD) studies for such systems [commonly called field-reversed configurations (FRC)] have consistently predicted instability to the tilting mode (lowest-order kink mode). However, a new range of equilibria not previously considered are found, which are stable to tilting in ideal-MHD theory. The equilibrium properties that promote stability are hollow current profile, and racetrack separatrix shape. Stable equilibria may not be possible in a theta-pinch system, but could be achieved with a properly designed vertical field coil set. The stability of FRC's in past theta-pinch experiments arises partly from nonideal effects, but benefits considerably from hollow current profile and racetrack separatrix shape.

Steinhauer, L. (1996). “FRC 2001: A white paper on FRC development in the next five years.”

This document expresses the consensus of a worldwide community effusion energy researchers on directions for research on the field-reversed configuration (FRC) over the next 5 yr. The FRC, a variety of compact torus, occupies a unique position in the parameter space of magnetically confined plasmas. it differs markedly from other toroidal systems: no mechanical structure in the center of the torus, no appreciable toroidal field, engineering beta near unity no rotational transform, and scrape-off layer exhausting outside the coil system. FRCs range from small gyroradius to large-orbit ion-ring-dominated plasmas. Because of these peculiar features, FRC research adds unique insight into the physics of tokamaks and similar fusion systems. Moreover FRC research offers a means of exploring fundamental plasma physics questions unrelated to fusion. Review panels have repeatedly called for fusion system improvements in order to project economical fusion energy However, even improved tokamaks may not overcome the shortcomings of low power density, high complexity large unit size, and high development cost. Among alternative concepts based on low-density magnetic confinement, the FRC offers arguably the best reactor potential because of high power density simple structural and magnetic topology, simple heat exhaust handling, and potential for advanced fuels. Projected FRC reactors are much smaller than those based on the tokamak. Small size leads to lo,ver costs. The enormous potential payoff as a reactor justifies a broad and sustained program art FRC stability and confinement. Several FRC-related facilities are in operation around the world as well as other small theory efforts. Favorable results from theory and experiments have raised hopes for ultimate development into a practical fusion system Parameters achieved include densities ranging from 5 x 10(13) to 5 x 10(15) cm(-3) temperatures up to 3 keV (ions) and 500 eV (electrons), and beta similar to 0.75 to 0.95. Noteworthy achievements include formation by theta pinch and by counterhelicity merging, simulation of large-orbit ion-ring injection and trapping, stabilization of rotational instability, detection of global internal modes, tilting mode theory, global translation along a guide field, identification of transport anomalies, and demonstration of the convective nature of energy loss. In view of the foregoing, five action items are recommended. First, FRC research should be continued and expanded both as an adjunct to mainline fusion research and as a stand-alone alternative fusion concept. Second, existing FRC-related resources should be exploited in an expanded program, including both facilities and the intellectual capital established in institutions and individuals with a long commitment to FRCs. Third, new FRC facilities or upgrades of existing facilities should be considered on the merits of how they address the directions offered bl this document. This should include consideration of a jointly operated international FRC research facility. Fourth, researchers and institutions with a history of activity on the tokamak should be encouraged to broaden their research to include FRC theory, diagnostic development, and systems studies. Fifth, vigorous international collaboration on FRC research should be encouraged, including at least annual workshops and long-term exchange visits.

Steinhauer, L. and A. Ishida (1998). “Relaxation of a two-species magnetofluid and application to finite-beta flowing plasmas.”

The relaxation theory of a two-species magnetofluid is presented. This generalizes the familiar magnetohydrodynamic (single-fluid) theory. The two-fluid invariants are the self-helicities, one for each species. Their ''local'' invariance follows from the helicity transport equations, which are derived. The global forms of the self-helicities are examined in a weakly dissipative system. They are shown to pass three tests of ruggedness (''relative'' invariance compared with the magnetofluid energy): the cascade test; the selective decay test; and the stability to resistive modes test. Once ruggedness is established, relaxed states can be found by minimizing the magnetofluid energy subject to constrained self-helicities. The Euler equations are found by a variational procedure. Example equilibria are presented that resemble field-reversed configurations (FRC) and tokamaks. These states are characterized by finite pressure and significant sheared flows. Throughout the analysis it is shown how this more general theory reduces to the magnetohydrodynamic (single-fluid) theory for suitable reducing assumptions. (C) 1998 American Institute of Physics. [S1070-664X(98)00407-8]

Steinhauer, L., H. Yamada, et al. (2001). “Two-fluid flowing equilibria of compact plasmas.”

The properties of two-fluid flowing equilibria are explored. This is facilitated by limiting attention to compact toroids in a "stationary-energy" state with uniform density. Flowing equilibria are found to fall into two classes, force-free and non-force-free, referring to the absence or presence of a jxB force. The force-free class may have significant flows. Spheromaks are in this class. The non-force-free class is diamagnetic and has Alfvenic poloidal flows. Field reversed configurations (FRCs) are in this class. Both classes admit arbitrarily large equilibria. Both classes occupy certain "allowed" regions in "helicity space," a two-dimensional parameter map with the electron and ion helicities as coordinates. Allowed regions for the two classes overlap; in the overlap region the non-force-free class is energetically favorable. This sheds light on the FRC-spheromak bifurcation observed in experiments. Two-dimensional analytic equilibria are also found that span both classes. These may play a role similar to the familiar Hill's vortex and Bessel function models in static, magnetohydrodynamic equilibria. (C) 2001 American Institute of Physics.

Steinhauer, L. (2002). “End-shorting and electric field in edge plasmas with application to field-reversed configurations.”

The shorting of open field lines where they intersect external boundaries strongly modifies the transverse electric field all along the field lines. The modified electric field is found by an extension of the familiar Boltzmann relation for the electric potential. This leads to a prediction of the electric drift. Flow generation by electrical shorting is applied here to three aspects of elongated field-reversed configurations: plasma rotation rate; the particle-loss spin-up mechanism; and the sustainability of the rotating magnetic field current drive method. (C) 2002 American Institute of Physics.

Stenzel, R., M. Griskey, et al. (2002). “Precession of an electron-magnetohydrodynamic field-reversed configuration - art. no. 185004.”

A field-reversed configuration is generated in a large laboratory plasma in the parameter regime of electron magnetohydrodynamics. During its free relaxation, the magnetic moment is observed to precess when tilted from its original axis. The precession velocity is the electron drift velocity in the toroidal current layer. The precession is a manifestation of frozen-in field lines in a moving electron fluid.

SUDAN, R. (1993). “INERTIAL CONFINEMENT FUSION WITH MAGNETICALLY COMPRESSED ION RINGS.”

Ballistic propagation and focusing of intense light-ion beams requires (1) close limits on allowable beam divergence (approximately 5 mrad) and (2) gas-filled magnetic lenses that must function effectively even if deleterious self-fields are generated during the passage of the beam through the lens. An alternative to ballistic focusing was suggested some years ago in which magnetically compressed light-ion rings capable of delivering 3-4 MJ in a pulse of approximately 1 ns are transported to the target in a tube. This concept is reexamined in light of recent work on the creation of ion rings and magnetic compression of stabilized liners. The physics issues of (1) magnetic compression, (2) transport of ion rings in a tube, and (3) the interaction of the ring with the target will be explored to evaluate the feasibility of this scheme.

SUGIMOTO, S., T. NIINA, et al. (1989). “SPECTROSCOPIC PLASMA TOMOGRAPHY ON FIELD-REVERSED CONFIGURATION.”

SUGIMOTO, S. and S. GOTO (1991). “SPECTROSCOPIC PLASMA TOMOGRAPHY WITH MULTIPLE PHOTOCOLLECTOR ARRAYS.”

A spectroscopic plasma tomography measurement system has been developed and operated on a field-reversed configuration (FRC) plasma machine with the use of five photocollector arrays. Each photocollector array that is located azimuthally around the plasma column consists of ten optical fibers and a pinhole. Two-dimensional (2D) and time-resolved visible emission profiles can be reconstructed numerically from the fifty-channel projection data. The use of five multichannel visible monochromators makes it possible to obtain a result that has explicit physical meanings. A computer simulation has been performed to demonstrate the potential to reconstruct the 2D profile without the assumptions about plasma rotation or symmetry. The first experimental result for visible bremsstrahlung emission profiles of the FRC plasma is presented.

SUZUKI, K. and S. HAMADA (1984). “MIRROR EFFECT ON RADIUS OF SEPARATRIX IN FIELD REVERSED CONFIGURATION.”

SUZUKI, K. and S. HAMADA (1986). “NUMERICAL CONFIRMATION OF CLOSED SEPARATRIX IN EXPERIMENTAL FIELD REVERSED CONFIGURATIONS.”

SUZUKI, K. (1991). “EFFECT OF THE MIRROR FIELD ON THE AVERAGED BETA-VALUE IN FIELD REVERSED CONFIGURATION.”

Suzuki, Y., S. Okada, et al. (2000). “Two-dimensional numerical equilibria of field-reversed configuration in the strong mirror field.”

Two-dimensional numerical equilibria of field-reversed configuration (FRC) plasmas in the strong mirror field applied externally are studied by means of the Grad-Shafranov equation. Appropriate choice of the pressure function is necessary to obtain a thin and elongated equilibrium, as observed in the FRC Injection Experiment (FIX) [H. Himura , Phys. Plasmas 2, 191 (1995)]. To solve the Grad-Shafranov equation, the finite difference method is used, applying the boundary-fitted curvilinear coordinates and the attracted grids near the separatrix. The outstanding feature of the equilibria is the presence of a narrow and sharp spike in the toroidal current profile near the separatrix. (C) 2000 American Institute of Physics. [S1070- 664X(00)02110-8].

TAKAHASHI, T., K. YAMADA, et al. (1995). “CONTROL OF EQUILIBRIUM SEPARATRIX SHAPE ON FIELD-REVERSED-CONFIGURATION PLASMAS.”

Equilibrium shape of a field-reversed-configuration plasma is controlled to maximize its poloidal flux. Plasma elongation is changed from 7.5 to 4.5 by adding a local field to the plasma due to the introduction of a control coil. The control field strength is about 10% of the confinement field. The plasma shape modifies while keeping its volume and the product of its poloidal flux and elongation constant. The poloidal flux is twice that of the uncontrolled plasma. Its flux confinement time also improved.

Takahashi, T., Y. Tomita, et al. (1997). “Collisionless pitch angle scattering of plasma ions at the edge region of a field-reversed configuration.”

The motion of a plasma ion gyrating around the separatrix of. field-reversed configuration is studied. Numerical studies showed that the action integral of a particle changes abruptly when a particle passes through the vicinity of a held null x point. This phenomena is understood as collisionless stochastic scattering of the pitch angle. In the case of a particle with positive canonical; angular momentum P-theta, the resultant correlation coefficients of the action integral between before and after the scattering appear to be stochastic in some cases. As the action integral increases for a particle with negative P-theta, its motion tends to be adiabatic. If the negative P-theta of a particle approaches zero, a stochastic motion is observed. (C) 1997 American Institute of Physics.

Takaku, Y. and S. Hamada (1996). “Rebound coefficient of collisionless gas in a rigid vessel: A model of reflection of field-reversed configuration.”

A system of collisionless neutral gas contained in a rigid vessel is considered as a simple model of reflection of field-reversed configuration (FRC) plasma by a magnetic minor. The rebound coefficient of the system is calculated as a function of the incident speed of the vessel normalized by the thermal velocity of the gas before reflection. The coefficient is compared with experimental data of FIX (Osaka U.) and FRX-C/T(Los Alamos N.L.). Agreement is good for this simple model. Interesting is that the rebound coefficient takes the smallest value (similar to 0.365) as the incident speed tends to zero and approaches unity as it tends to infinity. This behavior is reverse to that expected for a system with collision dominated fluid instead of collisionless gas. By examining the rebound coefficient, therefore, it could be successfully infered whether the ion mean free path in each expeiment was longer or shorter than the plasma length.

TCHOBROUTSKY, C., J. CLAUVEL, et al. (1988). “SUCCESSFUL PREGNANCIES IN THE ANTIPHOSPHOLIPID SYNDROME WITHOUT PREDNISONE.”

Tomita, Y., T. Takahashi, et al. (1998). “Use of polarized helium-3 for the energy production.”

After the discovery of plentiful of minable helium-3 on the lunar surface, fusion scientists have tried to find out the methods for utilizing this attractive fuel for fusion reactors. Among various approaches, a field-reversed configuration (FRC) for confinement of fusion plasma appears the most promising candidate for a D-He-3 fueled fusion reactor. A conceptual design of D-He-3 fueled FRC reactor ''ARTEMIS'' (Momota et al., in: Proc. 7th Int. Conf. on Emerging Nuclear Energy Systems, Chiba, Japan, 1993) has been carried out showing that bases of engineering needed for achieving a commercial reactor are conventional and the cost of electricity from ''ARTEMIS'' is estimated as cheap as approximately 30 mills/(kWh). A low neutron yield allows us large freedom of reactor materials and reduces the problem of disposal of radioactive waste. In this paper, we will examine the use of polarized D-He-3 fuels. A favorable characteristic of polarized fuels lies on the reduction of neutron yield and the compactness of the fusion core. Because of the enhancement of reactivity of D-He-3 reaction by applying polarization, the neutron fraction in the total fusion power decreases to 1.3% with the same volume of ''ARTEMIS'' and consequently neutron wall loading is 72 kW/m(2). The wall loading should be compared with 180 kW/m(2) from ''ARTEMIS'' or 10000 kW/m(2) from a D-T fueled reactor. Consequently, this low neutron mode gives us large freedom in choosing reactor materials. The fusion reactor using polarized fuels with the same neutron yields as ''ARTEMIS'' decreases its size from 196 to 33 m(3). This operation mode gives us the possibility of developing an economic fusion reactor.

TUSZEWSKI, M., W. ARMSTRONG, et al. (1982). “FLUX LOSS DURING THE EQUILIBRIUM PHASE OF FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M. and R. LINFORD (1982). “PARTICLE-TRANSPORT IN FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M. (1984). “EXPERIMENTAL-STUDY OF THE EQUILIBRIUM OF FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M. and K. MCKENNA (1984). “INTERPRETATION OF END-ON INTERFEROMETRY IN FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M. and R. SPENCER (1986). “EQUILIBRIUM PROPERTIES OF SHORT FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M., W. ARMSTRONG, et al. (1986). “CONFINEMENT OF TRANSLATED FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M. (1988). “FIELD REVERSED CONFIGURATIONS.”

TUSZEWSKI, M. (1988). “A SEMIEMPIRICAL FORMATION MODEL FOR FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M., G. BARNES, et al. (1988). “THE ORIGIN OF THE ROTATION IN FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M. and B. WRIGHT (1989). “OBSERVATION OF FIELD-REVERSED CONFIGURATIONS WITH SPHEROMAK MAGNETIC-FIELD PROFILES.”

TUSZEWSKI, M. (1989). “STATUS OF THE FIELD-REVERSED CONFIGURATION AS AN ALTERNATE CONFINEMENT CONCEPT.”

TUSZEWSKI, M. (1990). “MIRNOV LOOP ARRAY FOR FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M., G. BARNES, et al. (1990). “THE N=1 ROTATIONAL INSTABILITY IN FIELD-REVERSED CONFIGURATIONS.”

TUSZEWSKI, M., D. BARNES, et al. (1991). “OBSERVATIONS OF TILT INSTABILITIES IN FIELD-REVERSED CONFIGURATIONS OF A CONFINED PLASMA.”

We report the first consistent observations of internal tilt instabilities in field-reversed configurations. Detailed comparisons with numerical calculations establish that data from an array of external magnetic probes are signatures of these destructive plasma instabilities. As suggested by finite-Larmor-radius theory, field-reversed configurations appear grossly stable when s/e [(average number of ion gyroradii)/(separatrix elongation)] is less than 0.2-0.3 and show MHD-like tilt instabilities when s/e approximately 1.

TUSZEWSKI, M., W. ARMSTRONG, et al. (1991). “AXIAL DYNAMICS IN FIELD-REVERSED THETA PINCHES .1. FORMATION.”

Bias field scans are performed at various fill pressures in the FRX-C [Fusion Technol. 9, 13 (1986)] and FRX-C/LSM [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1989), Vol. II, p. 517] field-reversed theta pinches. These data show a systematic degradation of the confinement properties of field-reversed configurations whenever strong axial implosions occur during plasma formation. This limitation prevents access to the desired regime of large-size and long-lived field-reversed configurations. The cause of the confinement degradation must be due to some formation or gross stability problem. Here many studies are reported that attempt to correlate confinement degradation with some formation characteristic. These investigations remain inconclusive and suggest further stability studies presented in a companion paper.

TUSZEWSKI, M., D. TAGGART, et al. (1991). “AXIAL DYNAMICS IN FIELD-REVERSED THETA PINCHES .2. STABILITY.”

Detailed stability studies are made with new diagnostics in the FRX-C/LSM field-reversed theta pinch [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1989), Vol. II, p. 517]. These studies seek the origin of a degradation of the confinement properties of field-reversed configurations (FRC's) that appears associated with strong axial dynamics during plasma formation. Several instabilities are observed, including rotational modes, interchanges, and tilt instabilities. Only the latter are strongly correlated with FRC confinement. Tilt instabilities are observed for FRC's with larger average number of ion gyroradii (s approximately 3-5) and smaller separatrix elongations (e approximately 3-4). Coincidently, strong axial dynamics occurs for cases with larger s and smaller e values, through increases in either reversed bias field or fill pressure. These data provide some understanding of FRC stability. In agreement with finite Larmor radius theory, there is a regime of gross stability for the very kinetic and elongated FRC's with s/e < 0.2-0.3. This is the regime that has been studied in most FRC experiments. However, tilt and other instabilities are observed for FRC's with s/e approximately 1. Additional stabilization techniques will be required for future large-size FRC's.

TUSZEWSKI, M., D. BARNES, et al. (1991). “STABILITY AND COMPRESSIONAL HEATING OF LARGE FIELD-REVERSED CONFIGURATIONS IN THE FRX-C LSM DEVICE.”

Recent data from the FRX-C/LSM device [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1989), Vol. II, p. 517] concerning the stability, translation, and compression heating of field-reversed configurations (FRC's) are reported. FRC tilt instabilities are clearly observed for the first time, a major step toward reconciling theory and experiments. Grossly stable FRC's appear to be restricted to very kinetic and elongated plasmas. Internal probing of translated FRC's reveals substantial toroidal field and nearly force-free magnetic field profiles in the central region of the compact toroid. High-power magnetic compression of translated FRC's is demonstrated. Substantial heating is observed, while the FRC confinement properties remain mostly unchanged.

URANO, M., Y. OHKUMA, et al. (1995). “SEPARATRIX SHAPE OF FIELD-REVERSED CONFIGURATIONS.”

Near-infrared radiation from a field-reversed-configuration (FRC) plasma is observed during the stable phase using optical fiber tubes. Internal structure of the FRC is estimated from an Abel inversion of the radiation intensities which are obtained from the vertical array of the fibers. It is confirmed that the structure has a concave form at the core region of the plasma column, as expected from previous FRC studies. The axial array of the fibers shows that the separatrix boundary is similar in shape to a racetrack when the FRC is long, extending to mirror regions of the confining held, and elliptical for a short FRC. The equilibrium shape of the separatrix which is calculated using a two-dimensional code also changes from elliptical to racetrack-like with increase of the length in the mirror field, as observed in the experiment.

Uritsky, V., A. Klimas, et al. (2001). “Stable critical behavior and fast field annihilation in a magnetic field reversal model.”

We show that the Lu (Phys. Rev. Lett. 74(13) (1995) 2511) model, which is known to exhibit some properties of a system in self-organized criticality (SOC) [Lu, 1995; Klimas et al. (J. Geophys. Res. 105 (2000) (A8),18,765-18,780.)], can be obtained through a reduction of the resistive MHD system to an idealized one-dimensional limit. Resistivity in this model is anomalous and localized and is due to the excitation of an idealized current-driven instability at positions where large spatial gradients appear in the magnetic field distribution, We note that, by reversing the reduction to the idealized one-dimensional limit, the Lu model presents an opportunity to construct a true MHD system that incorporates kinetic phenomena when small spatial scales are generated which may evolve into SOC under some conditions. We study the evolution of this model in a driven magnetic field reversal configuration on a high-resolution spatial grid. It has been shown earlier that the behavior of several parameters that are global measures of the state of the field reversal suggests that the reversal can evolve into SOC (Klimas et al., 2000). Here, we study the internal dynamics of the field reversal during the unloading phase of a loading-unloading cycle. Unloading is due to internal, localized, dynamic field annihilation; no flux is lost by the system through its boundaries. For this continuum model, we define an "avalanche' as a group of unstable grid points that are contiguous in position and time. We demonstrate scale-free power-law size and duration distributions for these avalanches during the unloading phase of a loading-unloading cycle. We further demonstrate the stability of these distributions; they do not evolve significantly as the unloading progresses. Box counting statistics on the position-time plane show that the avalanches can be characterized as intermittent one-dimensional structures; gaps in these otherwise one-dimensional structures lower their dimension to below one. The stable scale-free avalanche size and duration distributions, plus the fractal structure of the avalanches at small scales, provide further evidence that solutions of the continuum Lu model in a field reversal configuration can evolve into SOC. (C) 2001 Elsevier Science Ltd. All rights reserved.

VLASES, G. and D. ROWE (1986). “DESIGN OF A TRANSLATING FIELD-REVERSED CONFIGURATION REACTOR.”

WANG, G., S. WANG, et al. (1984). “EXPERIMENTS OF A FIELD-REVERSED CONFIGURATION.”

WANG, E., N. HERSHKOWITZ, et al. (1986). “TECHNIQUES FOR USING EMITTING PROBES FOR POTENTIAL MEASUREMENT IN RF PLASMAS.”

WANG, E., N. HERSHKOWITZ, et al. (1986). “DIRECT INDICATION PLASMA POTENTIAL DIAGNOSTIC BASED ON SECONDARY-ELECTRON EMISSION.”

WANG, E., N. HERSHKOWITZ, et al. (1987). “SECONDARY-ELECTRON EMISSION-CAPACITIVE PROBES FOR PLASMA POTENTIAL MEASUREMENTS IN PLASMAS WITH HOT-ELECTRONS.”

WANG, A., X. SONG, et al. (1995). “FLUCTUATION-INDUCED CURRENT AND ENERGETIC ELECTRONS IN REVERSED-FIELD PINCH PLASMAS.”

In this paper, two sets of equation are derived from a set of fundamental MHD equations with a dynamo field. The first set of equations, which governs the evolution of the energies of the mean magnetic field and the mean plasma velocity with time, couples not only the mean motions with turbulent motion but also the mean motions with each other. It is pointed out that the reversed field pinch (RFP) plasma described by this set of equations can spontaneously relax to the Taylor state. The second set of equations, which governs the evolution of the helicity of the mean field and the mean helicity of the fluctuating field, depicts the helicity transfer between the mean and fluctuating field. It is shown that in the RFP plasma there exists a fluctuation-induced mean current consisting of energetic electrons, the generation of which is dominated by the dynamo field and completely determined by the dynamo field at the edge, and the energetic electron flow sustains the field-reversal configuration and reduces the anomaly in the loop voltage.

Watanabe, T., T. Sato, et al. (1997). “Magnetohydrodynamic simulation on co- and counter-helicity merging of spheromaks and driven magnetic reconnection.”

A magnetohydrodynamic relaxation process of spheromak merging is studied by means of an axisymmetric numerical simulation. As a result of counter-helicity merging, a field-reversed configuration is obtained in the final state, while a larger spheromak is formed after co-helicity merging. In the counter-helicity case, a clear pressure profile of which iso-surfaces coincide with flux surfaces is generated by thermal transport of a poloidal flow induced by driven reconnection. It is also found that a sharp pressure gradient formed in the vicinity of a reconnection point causes a bouncing motion of spheromaks. According to the bounce motion, the reconnection rate changes repeatedly. As shown by the Tokyo University Spherical Torus No. 3 (TS-3) experiments [M. Yamada, et al., Phys. Rev. Lett. 65, 721 (1990)], furthermore, strong acceleration of a toroidal flow and reversal of a toroidal field in the counter-heIicity merging were observed. (C) 1997 American Institute of Physics.

WEBSTER, R., J. SCHWARZMEIER, et al. (1991). “2-DIMENSIONAL KINETIC FIELD-REVERSED EQUILIBRIA.”

A two-dimensional kinetic description of field-reversed equilibria has been developed. Three equilibrium models are presented: a kinetic model, a rigidly rotating model, and a magnetohydrodynamics (MHD) model. The kinetic model of equilibrium provides spatial distributions of the macroscopic moments, including velocity shear, that are in good agreement with experimental observations. The rigidly rotating and MHD models allow more general pressure profiles than previous studies. These models, which allow the computation of a wide range of equilibria, suggest that for parameters typical of the current experiments kinetic modifications of the equilibrium are small; however, they may be important if the field-reversed configuration is interacting strongly with a magnetic mirror. Also, the ability to compute kinetic equilibria makes possible a self-consistent examination of the stability of field-reversed configurations, which is believed to be strongly influenced by kinetic effects.

WERLEY, K. (1987). “1-1/4-DIMENSIONAL TRANSPORT MODELING OF THE FIELD-REVERSED CONFIGURATION.”

Wessel, F. and N. Rostoker (1998). “D-T beam fusion reactor.”

The Beam Fusion Reactor (BFR) is based on a field-reversed configuration and confined ion energies in the range of hundreds of keV. Repetitively pulsed, intense ion beams sustain the ion distributions and provide current drive. In the BFR the ion orbit size is comparable to the dimensions of the confined plasma and the expectation is for classical transport of the particles and energy. Based on technologies that readily exist, or nearly so, a D-T fueled BFR could be assembled in a compact configuration that is scaleable in terms of its output energy as well as to the advanced fuel regime. In the simplest case the mean azimuthal velocities and temperatures of the two ion (fuel) species are equal and the plasma current is unneutralized by electrons; the resulting distribution functions are thermal in a moving frame of reference. Reactor kinetic calculations are based on the Vlasov-Maxwell equation, including a Fokker Planck collision operator and all sources and sinks for energy and particle flow. The quality factor for this system is projected to be: Q = P-fusion/P-bremsstrahlung = 104.

WOLLBERG, Z., R. SHABOSHINA, et al. (1988). “A NOVEL CARDIOTOXIC POLYPEPTIDE FROM THE VENOM OF ATRACTASPIS-ENGADDENSIS (BURROWING ASP) - CARDIAC EFFECTS IN MICE AND ISOLATED RAT AND HUMAN-HEART PREPARATIONS.”

WRIGHT, B. (1990). “FIELD REVERSED CONFIGURATIONS AND SPHEROMAKS.”

Wurden, G., T. Intrator, et al. (2001). “Diagnostics for a magnetized target fusion experiment.”

We are planning experiments using a field reversed configuration plasma injected into a metal cylinder, which is subsequently electrically imploded to achieve a fusing plasma. Diagnosing this plasma is quite challenging due to the short timescales, high energy densities, high magnetic fields, and difficult access. We outline our diagnostic sets in both a phase I study (where the plasma will be formed and translated), and phase II study (where the plasma will be imploded). The precompression plasma (diameter of only 8-10 cm, length of 30-40 cm) is expected to have n similar to 10(17) cm(-3), T similar to 100-300 eV, B similar to 5 T, and a lifetime of 10-20 mus. We will use visible laser interferometry across the plasma, along with a series of fiber-optically coupled visible light monitors to determine the plasma density and position. Excluded flux loops will be placed outside the quartz tube of the formation region, but inside of the diameter of the theta -pinch formation coils. Impurity emission in the visible and extreme ultraviolet range will be monitored spectroscopically, and fast bolometers will measure the total radiated power. A 20 J Thomson scattering laser beam will be introduced in the axial direction, and scattered light (from multiple spatial points) will be collected from the sides. Neutron diagnostics (activation and time-resolved scintillation detectors) will be fielded during both phases of the DD experiments. (C) 2001 American Institute of Physics.

Yamada, H., T. Katano, et al. (2002). “Equilibrium analysis of a flowing two-fluid plasma.”

An improved formalism for a flowing two-fluid equilibrium with constant density is developed. This extends the usual single-fluid model. In this generalization, the magnetic field is replaced by two quantities, the generalized vorticities of each species. Criteria are found for when the single-fluid model is adequate and when the more general two-fluid model is necessary. The two-dimensional equilibria with purely azimuthal ion flow are studied analytically and numerically. Spherical torus and compact toroid equilibria are found that are relevant to the current experiment. The ion flow and plasma beta as well as the size parameter are found to play a major role in the question of whether two-fluid corrections are needed. (C) 2002 American Institute of Physics.

Yamada, H., T. Katano, et al. (2003). “Stability formalism of a flowing two-fluid plasma.”

An improved formalism for a stability analysis of flowing two-fluid equilibria with constant density is developed. The two-fluid formalism, in which the generalized vorticity of each species is introduced as characteristic quantity, extends the usual single-fluid formalism. A new relation between the perturbed generalized vorticity and the displacement is found for each species. The spectral formalism is developed for stability of axisymmetric equilibrium. The missing elements in the single-fluid analysis of Frieman and Rotenberg [Rev. Mod. Phys. 32, 898 (1960)] are identified. (C) 2003 American Institute of Physics.

Yamanaka, K., Y. Suzuki, et al. (1999). “Estimation method of a separatrix profile of field-reduced configuration plasma with the deconvolution concept.”

A method to analyze the separatrix profile of a field-reversed configuration is presented that is based on a multichannel excluded flux measurement. In the method, the plasma current is represented by current filaments. This current code includes all the magnetic sources (e. g., a vacuum conducting vessel, coils for the confinement field, search coils, and coils for additional fields) as inputs to estimate the separatrix profile. With the aid of a numerically calculated function, experimental data are deconvolved to determine the current filament. The influence of measurement error included in the raw data of the calculated profiles is also discussed. (C) 1999 American Institute of Physics. [S0034-6748(99)61201- 1].

Yamanaka, K., S. Yoshimura, et al. (2000). “Heating experiment of field-reversed configuration plasma by low-frequency magnetic pulse.”

An effective heating method and experimental verification for a field-reversed configuration (FRC) plasma by applying the low-frequency magnetic pulse is presented. The low-frequency magnetic field is applied by an antenna that consists of two single-turn coils, and the frequency of the magnetic field is lower than the ion cyclotron frequency at the separatrix. An increase of the plasma energy and a fluctuation of the internal magnetic field are simultaneously observed. The comparison of the total temperature and the ion temperature shows that the increase of the plasma energy is mostly due to the ion heating. The fluctuation is directly observed by the internal magnetic probe arrays. The analysis of the phase velocity along the equilibrium magnetic field implies that the Alfven wave is excited and propagates. (C) 2000 American Institute of Physics. [S1070- 664X(00)03307-3].

YAO, W., T. INTRATOR, et al. (1985). “DIRECT INDICATION TECHNIQUE OF PLASMA POTENTIAL WITH DIFFERENTIAL EMISSIVE PROBE.”

Ye, M. and D. Jiang (1999). “Multiframing Mach-Zehnder interferometer for spatiotemporal electron density measurement in a field-reversed configuration plasma.”

Interferometric measurement is used to establish the spatially and temporally resolved electron density distribution in high beta plasma experiments. However, a series of interferograms are recorded separately on different shots. In order to avoid shot-to-shot data variation, we have developed a multiframing Mach-Zehnder interferometer system to produce multiframe interferograms on a single field-reversed configuration (FRC) plasma shot. In this interferometer system, a continuous wave He-Ne laser is used to illuminate the interferometer and the interferograms at various instances are recorded photographically by a rotating mirror framing camera at framing rates of 0.7-2.9 MHz. A simple electromechanically operated optical shutter with opening time of 300 ms was developed in our lab to gate the laser light to prevent both the considerable attenuation of laser light intensity and multiple exposure of the interferograms. The precise timing of the interferograms relative to FRC plasma discharge is determined with two optical fiber glasses pointed separately towards the first and the last microlenses in the framing camera to pick up their laser light pulse signals. Twenty-eight consecutive FRC plasma interferograms were recorded successfully on Kodak T-MAX 400 film in the first half discharge period of 10 ms with this system. From these interferograms, the spatiotemporal evolution of plasma density can be evaluated. (C) 1999 American Institute of Physics. [S0034-46748(99)63501-8].

YOSHIKAWA, K. (1987). “EFFICIENCY OF THE DIRECT ENERGY CONVERTER FOR ADVANCED FUELS IN A FIELD-REVERSED CONFIGURATION.”

Yoshimura, S., K. Shinagawa, et al. (2002). “Computer tomography of axially compressed field reversed configuration plasma on the FIX device.”

A computer tomography system for the axial compression experiment of field reversed configuration (FRC) plasma is completed on the FIX device. This system is composed of three arrays of detectors sensitive to the near-infrared radiation. Two-dimensional distributions of the fight emissivity of FRC plasmas are reconstructed using the Fourier-Bessel expansion technique. It is found that after the axial compression, the intensity of the light emissivity of the FRC plasma increases as well as the separatrix radius increases.

Yumi, H., T. Toshiki, et al. (2002). “Classification of particle orbits and related stochasticity of plasma ion motion in a field-reversed configuration with D-(3) He advanced fuel.”

Properties of regular (integrable) and stochastic (non-integrable) orbits of the deuterium-helium-3 (D-He-3) fusion plasma particles in a field-reversed configuration (FRC) are studied with the aid of the particle tracing routine. A chaotic behaviour of the ion motion is examined with the Lyapunov exponents as well as the radial action integral as a third adiabatic invariant, and by the Poincare's surface of section plot. It appears that a large majority of high energetic fusion protons tend to have regular motion. On the other hand, bulk ions in the D-He-3 advanced fusion plasma are almost stochastic because of a randomization of gyro-phase due to the orbit shape transition between off-axis gyration and encircling betatron or figure-8.

ZUBRIN, R. (1986). “A DEUTERIUM-TRITIUM IGNITION RAMP FOR AN ADVANCED FUEL FIELD-REVERSED CONFIGURATION REACTOR.”

ZWI, H., A. KUTHI, et al. (1991). “OBSERVATION OF A STEADY-STATE FIELD-REVERSED EQUILIBRIUM.”

Steady-state quiescent field-reversed configurations are produced in the toroidal UCLA RACETRACK [Rev. Sci. Instrum. 57, 2720 (1986)] by rotating magnetic fields. Observed pressure and magnetic field profiles agree with high beta, rigid electron rotor theory. Full penetration of the right-hand component of the rotating field and slight ion drag by the electrons were observed for the first time.