Dephasing and phase-locking: Dual role of radial electric field in edge MHD dynamics of toroidally confined plasmas

We carry out several numerical simulations to illustrate how the radial electric field (Er) impacts the edge magnetohydrodynamic (MHD) instabilities. The analyses reveal that Er-shear (Er′, here the prime denotes the derivative with respect to the radial direction) tends to stabilize the kink/Peeling–Ballooning modes by dephasing the perturbed radial velocity (ṽr) and displacement (ξ̃r). However, Er-curvature (Er″) tends to destabilize the kink/peeling modes by inducing a phase lock between ṽr and ξ̃r. More specifically, the ratio between them could be measured to quantify their relative competition strength. Consequently, the shape of Er is crucial to the shape of linear growth rate spectrum γ(n) (here n is the toroidal mode number), which further determines the nonlinear dynamics. On the one hand, relatively larger Er-curvature causes narrower γ(n), leading to larger nonlinear energy loss fraction. On the other hand, relatively larger Er-shear has the opposite effect