Long-wavelength kink instabilities in low-pressure, uniform axial current, cylindrical plasmas with elliptic cross sections

Abstract

The magnetohydrodynamic stability of a straight plasma column with elliptic cross section, carrying a uniform axial current, is investigated by extremizing the Lagrangian of the system using a natural coordinate system based on the magnetic field lines. Stability criteria are derived and growth rates are obtained analytically for systems with a uniform mass density inside the plasma. It is shown that the coupling between kink modes and Alfvén waves produced by noncircularity is a destabilizing effect. A technique for solving the problem numerically is also discussed and used to demonstrate the effect of a spatially varying plasma density on the growth rate.