Nonlinear modeling of the scaling law for the m/n = 3/2 error field penetration threshold

The scaling law for the error field (EF) penetration threshold is predicted numerically based on non-linear single-fluid and two-fluid modeling using the TM1 code. The simulated penetration threshold of radial magnetic field b _r at the plasma edge is scaled to the electron density n _e, temperature T _e, viscous time τμ toroidal field B _t and the natural frequency ω in the form of by scanning these parameters separately. Here, α _n, α _T, αμ, α _B and αω are the scaling coefficients on n _e, T _e, τμ, B _t and ω, respectively. Single-fluid modeling shows that the 3/2 EF threshold scales as, which is similar with the analytical scaling law in both the Rutherford and visco-resistive regimes. However, two-fluid modeling shows that the scaling law differs significantly in particular regarding the dependence on plasma rotation. In detail, the scaling coefficient α _n on density decreases from 0.67 to 0.56 and α _T on temperature decreases from 0.67 to 0.32, while αμ on viscous time is around-0.45 and α _B on toroidal field decreases slightly from-1.15 to-1, when the ratio between plasma rotation frequency ω _E and diamagnetic drift frequency ω _*e varies from 0 to 10. Scans of the plasma rotation reveals that the penetration threshold linearly depends on the perpendicular electron flow frequency (or natural frequency) ω⊥ e = ωE+ω*e, and there is a minimum in the required field amplitude when ω⊥e∼ 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 find 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.