Poloidal Mirnov toroidal array
A toroidal array of 10 poloidal field oriented 1-D Mirnov coils. These local sensors will be useful for detecting any changes in n=1+ external mode (e.g. external kink) activity, as well as equilibrium helical perturbations. Mirnov coils will be mounted radially inside TF magnets A, D, E, F, H, I, L, M, N, and P.
Design
The toroidal array uses surplus 1-D Mirnov sensors from NSTX, made from bare copper wire wound on macor sensor forms.
Coil Parameters:
- Width (W): 0.90" (2.29cm)
- Depth (D): 0.075" (0.191cm)
- Flux Area (A=WxD): 0.0675 sq. in. (0.437cm2)
- Number of windings (N): 50
- Sensitivity:
- Predicted: 2.187 mVs/T
- Measured: 2.354 ± 0.024 mVs/T
The toroidal array Mirnov sensors are mounted to the vacuum vessel (green rectangles in Fig. 1).
Originally designed for use in NSTX, these coils are rated to much higher temperatures than those reached in LTX, and rated safe for vacuum use, but still require protection from liquid lithium which can infiltrate the insulation and short the copper windings. Mounting brackets are affixed to the vessel wall at the midplane by spot-welded shim stock straps. Each Mirnov coil is connected by #0-80 screws to a mounting plate, which in turn is attached to a mounting bracket by #2-56 screws. A shield of 0.003" 316 stainless shim stock is spot-welded to the mounting plate over the Mirnov coil to provide electrostatic shielding. For protection from poorly-confined hot ions, a 0.125" thick 316 stainless outer shield/heat shield is fastened to the mounting plate over---and electrically insulated by a sheet of 0.004" mica from---the electrostatic shield. The outer shield is attached to the mounting plate by recessed countersunk #2-56 screws, and also captivates the mounting screws, with access holes.
To prevent conducting paths enclosing the Mirnov coil, the electrostatic shield has only four faces, and there is a ~1/16" gap between the outer shield and the mounting plate on one side; to ensure protection from molten/vaporized lithium, the open face of the electrostatic shield faces away from the outer shield gap. Since the entire Mirnov coil mounting assembly will be mounted to the vessel wall, the back plate should be kept relatively cool, so deposited lithium should not remain liquid, minimizing lithium creep.
The most up-to-date schematics can be found here.
Including fiberglass cladding, the Mirnov leads are just under 0.090", and is run down a 0.120" OD 316 tube with an 0.007" wall (0.106" ID), spot-welded with shim stock straps to the Mirnov mounting plate and to the vessel wall, protecting the leads from line-of-sight lithium exposure. Most tubes are 8" long, but those at either side of the shell gaps (A, H, I, and P) are 12" long to ensure the end of the tube is behind the shell. 316 stainless steel braid is spot-welded to the end of the tube, providing mechanical and lithium protection and electrostatic shielding along the length of the cable run. The tube extends downward from the Mirnov so that any liquid lithium evaporated onto it should run down, away from the sensor, where it will have good thermal contact to the outer vessel wall before it reaches the shield braid and leads.
Field Pickup
Since the Mirnov is a B-dot sensor, it has to be integrated to get B, which means any saturation of the digitizers or amplifiers will give incorrect results. To gauge whether this will be a concern, the expected voltage across the Mirnov from equilibrium fields is calculated.
Local coupling (i.e. field picked up at the proposed TA sensor location per unit current) for each equilibrium coil was found using the MATLAB script /p/ltxdata/MATLAB/LTX_BiotSavart/Examples/text_calc_b_LTX_2.m, which uses and requires pre-loading /p/ltxdata/MATLAB/LTX_BiotSavart/calc_b_LTX/calc_b_LTX.m to run.
- TF: ~10^-20 T/A
- OH: ~2.3x10^-9 T/A
- Red VF: ~4.6x10^-6 T/A
- Green VF: ~3.18x10^-8 T/A
- Orange VF: ~1.44x0^-6 T/A
- Yellow VF: ~5.2x10^-7 T/A
- Blue VF: ~1x10^-5 T/A
- Internal VF: ~1.8x10^-6 T/A
The coupling for plasma current is estimated to first order as that of a cylinder at R = 40cm.
Coil current-monitor tree nodes and calibration values were found in the script /p/ltxdata/idl_analysis/general/plot_shot_data3.pro near line 500. Coil current data from shots 1405051414 and 1504291255 was differentiated, multiplied by each coil's local coupling, and the Mirnov's sensitivity to find the voltage peaks expected prior to disruption.
A 10,000 gain integrator should suffice for purposes of the TA Mirnovs; typical signals modeled on shot 1504291255 would peak at around 1.5V, well within the ±10V input range of the digitizer. Raw Mirnov voltage at the integrator input would peak at +1/-2V shortly after plasma ramp-up and at disruption, well within the ±15V supply limit of the integrator.
Error Tolerance
Modeling the effects of random orientation and position errors on n=1 discrimination by least squares (using the 8 symmetric sensors for n=1 subtraction) shows that, including the influence of equilibrium vertical field, the dominant error source by a large margin is coil tilt. A nearly 2cm standard deviation on toroidal position vanishes next to even a modest alignment error. A random tilt error with a standard deviation of 6 degrees, which produces 15% RMS error in amplitude discrimination and 9 degree RMS error in phase discrimination. Reducing tilt error standard deviation to 2 degrees drops RMS amplitude and phase error to 2% and and 1 degree, respectively.
| TA positioning | Mode Resolution (95% conf.) | ||
| Tilt err stdv (deg) |
φ err stdv (deg (cm)) |
Amp. err (%) |
Phase err (deg) |
| 0 |
0 (0) |
<0.05 |
<0.05 |
| 1 |
0 (0) |
±1 |
±0.5 |
| 0 |
1 (1.2) |
±2 |
±1.5 |
| 2 |
0.5 (0.6) |
±4 |
±2.5 |
| 2 |
1.5 (1.8) |
±5 |
±2.5 |
| 2 |
3 (3.7) |
±6 |
±3.0 |
| 6 |
1.5 (1.8) |
±30 |
±15 |
Calibration
As of July 7th, the TA Mirnov coils have been calibrated after shield assembly, demonstrating stable sensitivity from 100Hz to 10kHz. The first day of calibration showed an unexplained apparent rise in sensitivity at low frequency (red), although this disappeared on subsequent test days (green and blue), and may have been a fault in the signal amplifier. Typical coil sensitivities were found to be 2.354±0.024mVs/T; typical calibration error for an individual Mirnov coil is <0.7%. Comparing a spare coil without shielding ("XB") and with shielding ("XS") indicates a loss of sensitivity comparable to the measurement error. NB: absolute calibration is limited by the ~2.5% error in the calibration of the Helmholtz coil. Individual coil calibration results and LEMO breakout polarities can be found in this Google spreadsheet.
Acquisition
The toroidal array uses 10 channels. Sensors 01-05 (A, D, E, F, and H) exit from a 19-pin Mil-C feedthrough on a T off of the left lower outboard feedthrough port at section C-D (shared with one half of the poloidal flux loops). Sensors 06-10 (I, L, M, N, and P) exit from a 19-pin Mil-C feedthrough on the lower outboard port at section O-P. Twisted-pair for each set terminates in a 15-pin female D-sub, which mates to a D-sub/differential-LEMO breakout adapter. Each LEMO connector is individually labelled with its TA channel. The breakout adapter shell is tied to the magnetics rack ground bus.
Sensors 01-05 (A, D, E, F, and H) are connect to ~10,000x-gain integrator 1 channels 1-5 (previously used by the deprecated "gap Mirnovs") and Helios channels 65-69. Sensors 06-10 (I, L, M, N, and P) are planned to go to ~10,000x-gain integrator 1 channels 17-21 and Helios channels 81-85.
Cross-reference at the following links for integrators and digitizers.
Related Pages
Toroidal array photo documentation galleries: Assembly | In vessel
Diagnostics
Magnetics (Local): Reentrant array | Toroidal array | Saddle coils | Shell eddy sensors
Magnetics (Areal): Poloidal flux loops | Loop voltage | Diamagnetic loop | IP Rogowski
Spectroscopy: Thomson scattering | ChERS | X-ray spectroscopy | Spectrometry | Vacuum UV spectroscopy
Microwaves: Reflectometry | Interferometry
Physical Probes: HFS edge probes | LFS SOL probes | RFEA
Operational Diagnostics: Ion gauges | Coil current monitors | Thermocouples | RTDs
