Effect of the Plasma Pressure on Magnetohydrodynamic Kink Instability in a Cylindrical Geometry

A semi-analytical method is introduced to study kink instability in cylindrical plasma with line-tied boundary conditions. The method is based on an expansion for magnetohydrodynamics (MHD) equations in one-dimensional (1D) radial eigenvalue problems by using Fourier transforms. The MHD equations then become an ordinary differential equation. This method is applicable to both ideal and non-ideal MHD problem. The effect of plasma pressure (P0) on kink instability is studied in a cylindrical geometry. Complex discrete spectra are presented. Two-dimensional (2D) eigenfunctions with the line-tied boundary conditions are obtained. The growth rate and radial eigenfunctions are different in the two cases of P0 = 0 and P0 ≠ 0, which indicate that the effect of plasma pressure can not be ignored if it is large enough. This method allows us to understand the role of individual radial eigenfunctions, and is also computationally efficient compared to direct solutions of the MHD equations by the finite difference method.