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

The scaling law for the $m/n=3/2$ 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 ${\tau }_{\mu }$, toroidal field B _t and the natural frequency ω in the form of $b_r/B_t\propto n_e^{{\alpha }_n}{T}_e^{{\alpha }_T}{\tau }_{\mu }^{{\alpha }_{\mu }}{B}_t^{{\alpha }_B}{\omega }^{{\alpha }_{\omega }}$ by scanning these parameters separately. Here, α _n, α _T, ${\alpha }_{\mu }$, α _B and ${\alpha }_{\omega }$ are the scaling coefficients on n _e, T _e, ${\tau }_{\mu }$, B _t and ω, respectively. Single-fluid modeling shows that the 3/2 EF threshold scales as $b_r/B_t\propto n_e^{0.56}{T}_e^{0.6}{\tau }_{\mu }^{-0.59}{B}_t^{-1.15}\omega$, 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 ${\alpha }_{\mu }$ on viscous time is around -0.45 and α _B on toroidal field decreases slightly from -1.15 to -1, when the ratio $|{\omega }_E/{\omega }_{\ast e}|$ 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) ${\omega }_{\perp e}={\omega }_E+{\omega }_{\ast e}$, and there is a minimum in the required field amplitude when ${\omega }_{\perp e}\sim 0$. 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. (paper)