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Relaxation-time measurement via a time-dependent helicity balance model
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Image of FIG. 1.
FIG. 1.

Cutaway view of a surface magnetic probe, all of which are mounted in the copper wall of the HIT-SI vessel and separated from the vacuum by a stainless steel disc. Each probe is electrostatically isolated and shielded from the experiment and differential leads are brought back to the digitizer. Image adapted from Ref. 16 .

Image of FIG. 2.
FIG. 2.

Panel (a) depicts the locations of the surface magnetic probes on a cross section in the R-Z plane of the HIT-SI device, taken at a toroidal angle that intersects two poloidal arrays (0° and 180°). The surface probe locations are shown in green along the edge of the bowtie cross-section. Panel b) depicts the locations of the four toroidal locations of the Amperian arrays, along with the gap array that consists of 16 probes.

Image of FIG. 3.
FIG. 3.

The curved arrow depicts the integral path, and its approximate subdivision into segments, for accomplishing the discrete closed-path integrals. The geometric lengths are represented by the line segments between the hatch marks, and the actual path is taken directly upon the surface.

Image of FIG. 4.
FIG. 4.

From left to right, field line traces of the: X-injector, spheromak, and Y-injector equilibria at 1 Amp, depicting how each is calculated independently; no field from one injector threads the other, and no field from the spheromak threads either injector. The set of images shows the three equilibria used to form the composite Taylor state, through scaling by measured currents and then superposition of the individual scaled states.

Image of FIG. 5.
FIG. 5.

The toroidal current and injector currents are shown at top for shot 117529, driven the Y injector at 5.8 kHz. The total helicity as calculated from the composite Taylor state, using the injector and spheromak currents, is shown center. The helicity decay time is shown at bottom, with the contributions from each injector summed (green) and then filtered (blue). The green vertical bar marks the formation of plasma and start of the model, and the black vertical bar corresponds to the time at which the constant helicity decay rate is calculated (3.6 ms) where the steady state period begins.

Image of FIG. 6.
FIG. 6.

Delay due to the finite relaxation rate in the measured toroidal current, versus the instantaneous relaxation in the model, for the 5.8 kHz Y-injector-only shot 117529. The top traces show: the total measured helicity as scaled by the composite Taylor state (red), the model helicity as calculated through cumulative helicity injection and decay (blue), and the helicity content of the injector state (green). The middle traces show the absolute value of the toroidal current as measured (red) and as calculated by the model (blue) with vertical lines highlighting the peaks in each. The lower traces show the injector currents, with vertical black lines highlighting the zero crossings.


Generic image for table
Table I.

Table of the fitting coefficients used to calculate the helicity of the composite Taylor state. The cross-coupling coefficients (C4 and C5) between the injectors and the spheromak are five orders of magnitude lower than the other coefficients, allowing the helicity of the spheromak alone to be approximated by using only C1. The coefficients are calculated to produce Krel in SI units of Wb2.

Generic image for table
Table II.

The 5.8 kHz single-injector shots used to calculate an average relaxation time; all shots are with helium plasmas, with an average of 37 zero crossings per shot.

Generic image for table
Table III.

Relevant time scales for comparison to relaxation rates in HIT-SI, as calculated or measured. The spread in the Sweet-Parker time results from whether the empirical resistive decay time for τL/R is used, or if τL/R is calculated using other parameters, respectively.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Relaxation-time measurement via a time-dependent helicity balance model