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 (E-r) impacts the edge magnetohydrodynamic (MHD) instabilities. The analyses reveal that E-r-shear (E-r', 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 (nu(r)) and displacement (xi(r)). However, E-r-curvature (E-r ") tends to destabilize the kink/peeling modes by inducing a phase lock between nu(r) and xi(r). More specifically, the ratio between them could be measured to quantify their relative competition strength. Consequently, the shape of E-r is crucial to the shape of linear growth rate spectrum gamma(n) (here n is the toroidal mode number), which further determines the nonlinear dynamics. On the one hand, relatively larger Er-curvature causes narrower gamma(n), leading to larger nonlinear energy loss fraction. On the other hand, relatively larger Er-shear has the opposite effect.