Dephasing and Phase-Pinning: Dual Role of Radial Electric Field in Edge MHD Dynamics of Toroidally Confined Plasmas*

We propose a new understanding of how the radial electric field ($E_r$) impacts the edge magnetohydrodynamic (MHD) instabilities. The analysis uncovered that $E_r$-shear stabilizes the Peeling-Ballooning modes, while $E_r$-curvature destabilizes the low-n kink/peeling modes. The underlying physical mechanism is that the perturbed radial velocity and displacement become stronger dephasing or phase pinning. More specifically, the ratio of $E_r$-curvature to $E_r$-shear could be measured to quantify their relative competition strength.