Curvature of Radial Electric Field Aggravates Edge Magnetohydrodynamics Mode in Toroidally Confined Plasmas

We show that the radial electric field (E-r) plays a dual role in edge magnetohydrodynamics (MHD) activity. While E-r shear (first spatial derivative of E-r) dephases radial velocity and displacement, and so is stabilizing, a new finding here is that E-r curvature (second spatial derivative of E-r) tends to synchronize the radial velocity and displacement, and so destabilizes MHD. As a highlighted result, we analytically demonstrate that Er curvature can destabilize an otherwise stable kink mode, and so form a joint vortex-kink mode. The synergetic effects of E-r shear and E-r curvature in edge MHD extend the familiar E x B shearing paradigm. This theory thus explains the experimental findings that a deeper E x B well may aggravate edge MHD, and so trigger the formation of the edge harmonic oscillation. A simple criterion linking E-r structure and the edge MHD activity is derived.