Nonlinear modeling of the scaling law for the $m/n = 3/2$ error field penetration threshold
Qiming Hu, N.C. Logan, Jong-Kyu Park, C. Paz-Soldan, R. Nazikian, Q. Yu
Abstract
The scaling law for the m/n=3/2 error field (EF) penetration threshold is predicted numerically based on nonlinear <i>single-fluid</i> and <i>two-fluid</i> modeling using the TM1 code. The simulated penetration threshold of radial magnetic field b<sub>r</sub> at the plasma edge is scaled to the electron density n<sub>e</sub>, temperature T<sub>e</sub>, viscous time τ<sub>μ</sub>, toroidal field B<sub>t</sub> and the natural frequency ω in the form of b<sub>r</sub>/B<sub>t</sub>∝n<sub>e</sub> <sup>αn</sup>T<sub>e</sub> <sup>αT</sup>τ<sub>μ</sub> <sup>αμ</sup>B<sub>t</sub> <sup>αB</sup>ω<sup>αω</sup> by scanning these parameters separately. Here, α<sub>n</sub>, α<sub>T</sub>, α<sub>μ</sub>, α<sub>B</sub> and α<sub>ω</sub> are the scaling coefficients on n<sub>e</sub>, T<sub>e</sub>, τ<sub>μ</sub>, B<sub>t</sub> and ω, respectively. Single-fluid modeling shows that the 3/2 EF threshold scales as b<sub>r</sub>/B<sub>t</sub>∝n<sub>e</sub> <sup>0.56</sup>T<sub>e</sub> <sup>0.6</sup>τ<sub>μ</sub> <sup>-0.59</sup>B<sub>t</sub> <sup>-1.15</sup>ω, which is similar with the analytical scaling law in both the <i>Rutherford</i> and <i>visco-resistive</i> regimes. Yet, two-fluid modeling shows that the scaling law differs significantly in particular regarding the dependence on plasma rotation. In detail, the scaling coefficient α<sub>n</sub> on density decreases from 0.67 to 0.56 and α<sub>T</sub> on temperature decreases from 0.67 to 0.32, while α<sub>μ</sub> on viscous time is around -0.45 and α<sub>B</sub> on toroidal field decreases slightly from -1.15 to -1, when the ratio |ω<sub>E</sub>/ω<sub>*e</sub>| between plasma rotation frequency ω<sub>E</sub> and diamagnetic drift frequency ω<sub>*e</sub> varies from 0 to 10. Scans of the plasma rotation reveals that the penetration threshold linearly depends on the perpendicular rotation frequency (or natural frequency) ω<sub>⊥e</sub>=ω<sub>E</sub>+ω<sub>*e</sub>, and there is a minimum in the required field amplitude when ω<sub>⊥e</sub><img src="https://ej.iop.org/icons/Entities/backsim.gif" alt="backsim" align="absmiddle" />0. In addition, the enduring mystery of non-zero penetration threshold at zero plasma natural frequency in EF experiments is resolved by two-fluid simulations. We report that the very small island and smooth bifurcation in EF penetration near zero frequency is hard to detect in the experiment, leading to a finite penetration threshold within the capability of the experimental measurements.