Visco-resistive MHD study of internal kink(m=1) modes

TL;DR

This study explores how sheared axial and poloidal flows influence the resistive internal kink mode in a cylindrical plasma, revealing flow-dependent changes in growth rates and nonlinear saturation levels affected by viscosity.

Contribution

It provides new insights into the impact of different flow shears and viscosity on the internal kink mode within a reduced MHD framework, highlighting flow-induced stabilization and destabilization effects.

Findings

Axial flows alter the scaling of growth rates with Lundquist number.

Viscosity significantly modifies flow effects on mode growth and saturation.

Flow helicity influences symmetry breaking in mode behavior.

Abstract

We have investigated the effect of sheared equilibrium flows on the $m = 1, n = 1$ resistive internal kink mode in the framework of a reduced magnetohydrodynamic model in a periodic cylindrical geometry. Our numerical studies show that there is a significant change of the scaling dependence of the mode growth rate on the Lundquist number in the presence of axial flows compared to the no flow case. Poloidal flows do not influence the scaling. We have further found that viscosity strongly modifies the effect of flows on the (1,1) mode both in the linear and nonlinear regime. Axial flows increase the linear growth rate for low viscosity values, but they decrease the linear growth rate for higher viscosity values. In the case of poloidal flows the linear growth rate decreases in all cases. Additionally at higher viscosity, we have found strong symmetry breaking in the behaviour of linear growth rates and in the nonlinear saturation levels of the modes as a function of the helicities of the flows. For axial, poloidal and most helical flow cases, there is flow induced stabilisation of the nonlinear saturation level in the high viscosity regime and destabilisation in the low viscosity regime.