The Evolution of Growth Rate and Eigenfunction in a Cylindrical Plasma column

The evolution of growth rate and eigenfunction of kink instability in a cylindrical plasma column with different plasma pressure is studied by a semi-analytical method. The method can transform magnetohydrodynamics (MHD) equations into a second-order ordinary differential equation. Growth rate can be obtained by solving the second-order ordinary differential equation. 2-D radial eigenfunction can be calculated with a fixed growth rate. The significant change of growth rate and eigenfunction indicates inhomogeneous plasma pressure P-0 is destructive for kink instability. The advantage of our method is that it can divide problem into two parts and then solve them separately.