High-m Kink/Tearing Modes in Cylindrical Geometry

TL;DR

This paper derives a simplified model for high-m kink/tearing modes in cylindrical geometry, analyzing how current profile features influence tearing stability parameters and discussing implications for tokamak pedestal stability.

Contribution

It introduces a simplified high-m kink equation in cylindrical geometry that relates tearing stability to current profile parameters, extending understanding of current-driven instabilities.

Findings

$ riangle^\prime$ depends on current gradient and magnetic shear parameters.

Current profile shape significantly influences tearing mode stability.

Results relate to gyro-kinetic calculations and tokamak pedestal stability.

Abstract

The global ideal kink equation, for cylindrical geometry and zero beta, is simplified in the high poloidal mode number limit and used to determine the tearing stability parameter, $\Delta^\prime$. In the presence of a steep monotonic current gradient, $\Delta^\prime$ becomes a function of a parameter, $\sigma_0$, characterising the ratio of the maximum current gradient to magnetic shear, and $x_s$, characterising the separation of the resonant surface from the maximum of the current gradient. In equilibria containing a current "spike", so that there is a non-monotonic current profile, $\Delta^\prime$ also depends on two parameters: $\kappa$, related to the ratio of the curvature of the current density at its maximum to the magnetic shear, and $x_s$, which now represents the separation of the resonance from the point of maximum current density. The relation of our results to earlier studies of tearing modes and to recent gyro-kinetic calculations of current driven instabilities, is discussed, together with potential implications for the stability of the tokamak pedestal.