1. Introduction 4

1.1 Determination of the Magnetic Equilibrium 4

1.2 Criteria of choice 5

2.1 Methods of External Magnetic Field Measurement 6

3.1 Visible & Bolometric Images 17

3.2 Soft X-Ray Images 17

3.3 Hard X-Ray Images 17

4.1 Finding peaks or centroids from discrete data 18

4.2 Balancing Heat Loads 19

4.3 RF Antenna Coupling 19

1. Introduction

The TPX Diagnostics Description Document (TPX DDD:WBS 62) provided high-level descriptions and requirements for diagnostic systems. In particular in the area of Plasma Control:

"Plasma Control An array of magnetic diagnostics shall be provided to measure the plasma and vacuum vessel currents, the radial and vertical plasma position, and the plasma shape with time resolution and accuracy sufficient to satisfy the associated control and operational requirements."

The primary problem addressed in this study is how to achieve the control and operational requirements in true steady-state, not just for 1000 second pulses. Solutions to this problem (for they should be multiple and redundant) will probably have to be engineered into the initial design of TPX. (However, the TPX DDD said "at the present time such steady-state magnetic capability is not included in the baseline diagnostic set for TPX.")

Whether or not magnetic measurements are directly used as the fundamental position sensing technique in steady-state, magnetic probes will be used on TPX for interim control and fluctuating field measurements. With the long (fusion) experience with "fluxmeters" using integrating electrical circuits (both passive, active, and in software) and the accuracy on short times they can achieve, an array of such integrated probes will certainly be used on TPX. The "zero point" of such fluxmeters can then be periodically set in time by comparison to some other DC or steady-state position sensing technique. In between such "set times" the magnetic data can be used in the normal, familiar fashion to provide instantaneous equilibrium information.

The problem of steady-state position control then comes down to finding a technique (or redundant set of techniques) that can periodically determine the equilibrium to sufficient accuracy to "set" the fluxmeters.

1.1 Determination of the Magnetic Equilibrium

For the record, thorough reviews of MHD equilibrium calculations and use of magnetic information are found in Tatsuoki Takeda and Shinji Tokuda, "Computation of MHD Equilibrium of Tokamak Plasma," J. Comp. Physics 93 (1991) 1, and Bastiaan J. Braams, "The Interpretation of Tokamak Magnetic Diagnostics," Plasma Phys. Controlled Fusion 33 (1991) 715 (see Refs. 1 and 2).

1.2 Criteria of choice

What are the design criteria that the technique (or redundant techniques) need to satisfy in the TPX design? The TPX DDD specified for Plasma Position and Shape generally 5 mm accuracy in radius and X-point positioning, and 2.5 mm up-down positioning. In addition the sensors providing this accuracy must be:

These criteria will be applied below in making recommendations.

2. Magnetic Methods

Based on previous experience in the fusion program, the most likely techniques for sensing the position of the plasma equilibrium are to measure the magnetic field. The initial problem is that standard probes or "fluxmeters" measure the change of the flux through the probe and not the absolute value, and require integration in time. While such integration may work out to the initial 1000 second operation of TPX, it cannot be straightforwardly extrapolated to steady-state. A further complication, even under the <1000 second scenario, is that the toroidal field in TPX will be on long before the plasma is initiated, since the TF (indeed, most all coils) in TPX are superconducting.

Nevertheless, there are methods of measuring DC magnetic fields, some of which might be applicable to the conditions of TPX. Methods of measuring the magnetic field both external and internal to the plasma are considered.

2.1 Methods of External Magnetic Field Measurement

2.1.1 Fixed Magnetic pickup coils: Electronic integrators

"A coil subjected to a changing magnetic field ... generates a voltage proportional to the time derivative of the magnetic flux. Integration of this voltage gives a signal proportional to the change in flux. The instrument that performs this integration is called a fluxmeter."

A typical magnetic coil and integrating circuit is shown schematically in Figure 1. Different coil sizes, shapes, and mountings on the tokamak are used in short-pulse machines to accomplish a variety of tasks, including:

2.1.1.1 Rogowski Coils

2.1.1.2 Voltage/Flux Loops

2.1.1.3 Magnetic Probes & Position Coils

2.1.1.4 Diamagnetic Loops

2.1.2 Vibrating or Rotating magnetometer

2.1.3 A Hall probe

Hall probes apply a DC voltage across a conductor and then measure the ExB current perpendicular to the voltage and the magnetic field. A number of commercial vendors are available (including LakeShore, Micro Instruments, etc). Probe heads typical cost a few hundred dollars each, and require a controller to measure the current and/or voltage. Multiplexing of probes from one controller is possible for TPX timescales. Five digit accuracy for DC magnetic fields is typical, and different probe heads work in up to 300 kG fields.

Hall probes have been used by the TRIAM-1M tokamak for discharges of more than one hour duration. Two probes are used for in-out, and two for up-down position control. They are mounted on water-cooled copper fingers which are encased in a thin stainless steel vacuum jackets near the circular plasma cross-section boundary.

2.1.4 Force method (DC gradient)

"The force on a magnetized sample located in a field gradient can be used to determine the magnitude of the magnetic moment of the sample. This is a venerable technique, known sometimes as the Faraday method and sometimes as the Curie method... The relevant equation may be written as:

We don’t need to measure the gradient of the field for the TPX problem. This is thus an unnecessary complication.

2.1.5 Magnetostriction

"Magnetostriction refers to any dimensional changes which take place when a material is subjected to a magnetic field."

Again, sample rotation, as with rotating a fluxmeter, is complicating. Furthermore, the temperature sensitivity of these techniques may be very problematical. One might need yet another primary standard for calibrating these sensors on a given day.

2.1.6 Lorentz Force on Fiber-Optics

2.1.7 Torque magnetometer

"Under equilibrium conditions, when the magnetization in a material does not align with the applied magnetic field vector, a torque on the sample results which is a measure of the magnetic anisotropy energy. The basic function of a torque magnetometer is to measure the magnitude of the torque on a specimen located in a uniform magnetic field as a function of the angle between a particular axis of the sample and field."

Again, moving parts seem to argue against primary use on TPX. Also, long-term changes in the magnetization of a sample could lead to drift in the measurement.

2.1.8 Gas Turbine

Once again, something moving/rotating.

2.1.9 Galvanomagnetic Devices

The following is not from Flanders and Graham: "Agrawal and Swami (1981) have shown that the static I-V characteristics of an unijunction transistor [sic] (UJT) is modified in a magnetic field. If this UJT forms part of a relaxation oscillator, then the magnetic field would change the frequency of the oscillator (which is a function of peak point voltage and valley point voltage)." Such solid-state electronics may suffer dramatically over the lifetime of TPX from neutron damage.

2.1.10 Faraday Rotation External to Plasma

2.1.11 SQUID Magnetometers

2.1.12 Nuclear Magnetic Resonance

The technique of nuclear magnetic resonance can be used in "reverse", to determine the total local magnetic field strength. A frequency-scanned RF pulse which applies a rotating magnetic filed to a known sample (ie, protons in water) is used to determine an unknown (larger) "static" magnetic field. The frequency value of the nuclear magnetic moment is about 76 MHz per Tesla, so for TPX one would need to scan in the range of 200-400 MHz. This could be done rapidly with a short (broadband) RF pulse, in an inverse-Fourier transform type of NMR spectrometer. In contrast to laboratory situations where the magnetic field and temperature are precisely controlled, the environment on TPX would be problematic. It is conceivable that a pair (or more) of sensors (RF pickup coils) could allow determination of the spin axis, and hence field direction. We have not identified a manufacturer of compact (also cheap?) NMR equipment. At first glance, this technique may be robust, and should not be ruled out for eventual reactor applications.

2.2 Measurements of the Internal Magnetic Field

DC measurements of the internal magnetic field could also be used to constrain the magnetic equilibrium and reset the integrators on the fluxmeters. An excellent review can be found in H. Soltwisch, "Current Density Measurements in Tokamak Devices," Plasma Phys. Controlled Fusion 34 (1992) 1669. Many of these techniques suffer from accuracy (in both magnitude and space) as well as possibly precision over months of operation, and they are considered unlikely to meet the detailed requirements of the position for TPX. However, their use can significantly improve the equilibrium reconstructions of limited magnetic data.

2.2.1 Faraday Rotation to measure B(r) and n(r)

Faraday rotation of polarized laser beams passing through the plasma, measures the change in polarization angle which is proportional to along the laser path. This technique has been used on TEXTOR, TFTR, MTX, and other plasma devices (ZT-40M & JET). Even with a 10-chord polarimeter for simple feedback control, it is not widely seen as being high enough resolution for position control. If limited spatial resolution were deemed sufficient, the main difficulty will be one of access, mode quality, and vibration effects associated with TPX’s geometry and long pulse length.

It is conceptually possible to have a multi-fan approach, and use quasi-optical waveguide horns (for 100 micron radiation) near the plasma. However, required retroreflectors would have to be mounted on internal vessel structures (rather than supported by an external "vibration-less" space-frame. The resulting vibrations during a 1000 second to steady-state pulse must be compensated, presumably with a two-color scheme. This is a much more serious complication than encountered in short-pulse machines. In fact, it is qualitatively similar to the integrator drift problem faced by standard magnetic loops......it is a long time before you get to see the post-shot baselevel of the signal.

The spatial resolution of an FIR Polarimeter is typically a few cm in the transverse direction to the laser beam, but has no resolving power along the beam. Time resolution can be in the 100 microsecond to 10 millisecond range. As a diagnostic for standard short-pulse plasmas (0.1 to 20 second duration), there is no question that this approach offers value in determining the internal magnetic field. It is a sophisticated, proven (although not widespread due to it’s complexity and finicky nature of the available FIR sources) diagnostic.

2.2.2 Motional Stark Effect (MSE)

2.2.3 Microwave Emission (ECE)

From TPX DDD: "there has been discussion of current profile determination via use of O and X-mode reflectometry, where the O-mode cutoff depends solely on density and the X-mode cutoff depends on both density and magnetic field."

3. Imaging Techniques

By imaging the edge or core plasma with plasma light emission in the desired wavelength band, usually with a "tangential" view, one can in principle determine the plasma position. If soft x-rays are imaged, then the core plasma position can be determined, while if lower energy photons are observed, the plasma edge can be located. Since positioning accuracy of a few mm is desired, the imaging system must have a correspondingly large number of pixels. Many pixels implies a long readout time. Consequently, an imaging device could be envisioned which would periodically be used to calculate the plasma position during a long period where the plasma is not moved, and "reset" the drift on standard, high time-resolution, magnetics signals every 1- 10 seconds.

In order to deconvolve the plasma shape from the line-integrated image, one must have a model of the plasma. Spurious light which contributes to the image, such as Marfes, ELMs, and divertor light must be averaged out, or taken into account. Particular slices, corresponding to specific vertical and horizontal moments could be analyzed rapidly, and other regions of the image near the X-point position separately fit with the goal of determining the X-point position. It is well-known that visible spectrum film images of the divertor region specifically "show" the shape of magnetic field lines near the X-point (as in ASDEX or Alcator C-Mod ), although a detailed comparison of positions from these images to the magnetics determined position has not been done to our knowledge.

3.1 Visible & Bolometric Images

Visible imagery is planned for TPX. By selecting appropriate line filters, the plasma X-point can be imaged in CIII light (for example) from a tangential view. This could provide a near real-time monitor of the X-point position. An analysis algorithm to deal with ELMs and Marfes would have to be developed. Visible light imagery will by necessity be useful only for locating the plasma edge. Problems associated with chordal measurements and Abel-type inversions are still present. Local asymmetries (tile hot-spots, RF-antennae shields, etc) will also exist in the data.

An imaging bolometer could also provide similar data, but covering a wider spectral band, which should view more deeply into the plasma.

Rather than tangential imaging, tomographic reconstruction from vertical slices could be tried. Efforts to date only achieved 1 cm out of 17 cm minor radius accuracy.

3.2 Soft X-Ray Images

A tangential-view soft x-ray imaging camera has been employed on PBX-M to make low-resolution measurements of the highly-shaped PBX-M plasma. The 128x128 pixel image was reduced to a 32x32 array for image analysis, and for inversion purposes the plasma was assumed to be toroidally symmetric. Then a maximum entropy algorithm was used in combination with external magnetics information to map the internal magnetic structure of the plasma. Spatial resolution was necessarily limited on PBX-M as they were trying for relatively fast time response. Similar pixel resolution was achieved on COMPASS-C. On TPX a longer integration time would allow more pixels to be left in the analysis both because of more signal per pixel and more time to do the computational inversion. Survival of the intensifier due to radiation damage in a close-in position (for a wide field-of-view) is problematic, as is operation of the intensifier electronics in the strong magnetic field near the tokamak. These problems are difficult but not unsolvable.

3.3 Hard X-Ray Images

Hard X-ray imaging is especially relevant to determine core magnetics geometry if lower-hybrid current drive is employed. The resulting high energy electrons produce an easily detectable bremsstrahlung radiation, which has been used on PBX-M for moderate resolution plasma-shape determination.

K. Ida from NIFS in Japan has proposed a high resolution 2D X-ray camera for real time plasma position control in the steady-state tokamak. He suggests using a fiber bundle coupled to a slow-readout 512x512 element cooled-CCD with 12-bit dynamic range, in conjunction with a thin NaI converter for 50-100 keV x-rays. The frame rate is variable from 16 frames/second to 1 frame per hour. For slow feedback (10 Hz) control the plasma position information is provided by the imaging. Three computer CPU’s are suggested: one to acquire the images, one to calculate the horizontal position, and one to calculate the vertical position. This technique should be directly applicable to TPX. A primary concern would be the influence of neutrons on the x-ray converter phosphors, or of neutron fluorescence in the imaging bundle. It is easy to imagine an even higher resolution system for TPX in the next 5-year period, with 1024x1024 or even 2048x2048 pixel elements. The images need only be stored transiently for long enough to process the desired position and shaping moments. Spatial resolution of 1-2 mm should be achievable, especially if readouts every second or so give adequate temporal information to reset standard integrator offsets.

4. Other Techniques

4.1 Finding peaks or centroids from discrete data

There are a variety of diagnostics that measure what are supposed to be flux-surface quantities (like temperature or density; however, certainly in the case of density there is much present controversy about asymmetries in the density on flux surfaces). However, typical tokamak diagnostics tend to have finite spatial resolution, and not particularly great spatial accuracy. Figure 4 shows the analyzed position of the peak of electron and ion temperature, electron density, and neutron emission from several different diagnostics (interferometry (RMIRI), Thomson scattering (RTETV), CHERS (RTI), electron cyclotron emission (RECE), and neutron collimator (RG)) for a common data set of discharges on TFTR plotted versus the position of the magnetic axis determined from magnetic loops. Not only is there typically several centimeter disagreement between diagnostics, but finite resolution of the diagnostics leads to several centimeter variations of a single diagnostic as the plasma moves. This clearly illustrates the difficulty of using most plasma diagnostics to determine plasma position with millimeter accuracy.

Higher accuracy in relative position sensitivity has been achieved by moving the plasma across the field of view of a diagnostic. Such "jogs" could be programmed on TPX every few seconds or so; however, such movement may affect coupling to RF antennas and be difficult considering the constrained geometry of the deep TPX divertors.

4.2 Balancing Heat Loads

As an engineering position control technique in a reactor, it has been suggested to monitor the heat loads on tile surfaces through platinum thermocouples which monitor the coolant temperature from tile sections or belts. While this is a "reactive" technique, and it has a relatively slow (1-10 second) time constant, due to coolant flow issues, it is simple. Certainly tile temperatures will be monitored at key stike-point and inner armor positions, as well as at protective limiters on RF antennaes in TPX. This information could be incorporated into a position control algorithm. However, it is exactly this problem of excess plasma heat hitting components that the position control is trying to avoid.

4.3 RF Antenna Coupling

The outside midplane position may be essentially controlled by adjusting the plasma edge density to optimally couple RF power to the plasma. This can be done in principle by feedback control of the reflected ICRF or LH power, to provide a signal to the plasma vertical field magnet supplies. Some information from antenna (or antenna shields) surface temperature may also be of use in this algorithm. It would also be possible, although maybe not necessary, to perform the same task with a continuous density measurement in the edge (either interferometry or reflectometry).

5. Summary

We have identified a host of truly steady-state magnetic field measurement techniques. All have differing strengths and weaknesses. Common themes running throughout these techniques are questions of reliability, stability, and ruggedness, especially given the fact of relatively difficult mounting constraints. Achieving adequate sensitivity is generally not a problem. In almost every case, the steady-state technique is more complex than a simple pickup coil and passive integrator. We have a bias against techniques with moving parts, although it has been pointed out that a speedometer cable usually works just fine for 10 year periods!

Because we envision the steady-state measurement as providing the capability to "reset" the standard magnetic loop integrator drifts, fast time response is not a requirement for the steady-state techniques (although several techniques are quite fast). In some cases (the Rogowski for example) could be outside the "thick" vacuum vessel. This would presumably make their replacement easier (outside of the nuclear boundary). However, a well-designed set of Hall-probe modules could be envisioned to go in vacuum, but protected from direct plasma exposure by thin stainless shields. Measurements associated with the highly-shaped plasma in the divertor require sensors close-in to the divertor. Issues associated with maintaining alignment accuracy are the same for steady-state techniques, as for the standard magnetic set.

We have not identified a suitable replacement for diamagnetic loops, which effectively perform an "integral measurement". Even assuming that Hall probes can measure all three field components, they are still effectively a point measurement, do not measure the flux excluded from the plasma interior. Similarly, there is no steady-state equivalent of the "loop voltage" monitor, but fortunately it isn’t needed, since in principle, there is no steady-state loop voltage, and the normal B-dot probes work fine for transients!

A collection of the diagnostics discussed in this paper is summarized in Table 2 on the next page. Specific time and space constraints depend in most cases on the desired accuracy of the measurement, and the number of sensors deployed on the machine. This is also related to the minimum size of the sensor, which usually sets the spatial averaging distance (or area).

Finally, the prospects for truly steady-state operation provide a new development direction for so-called "standard" plasma diagnostics. The problems with magnetic sensors in steady-state are only the first wrinkle to appear in the fielding of all diagnostics on TPX.