Numerical simulation of magnetohydrodynamic instability with variational principle in the tokamak

A computer code of variational principle for the plasma potential energy was written and used to analyze magnetohydrodynamic instability in D-shaped tokamak. Paths of steepest descent are defined by solving an initial value problem for a system of partial differential equations which are expressed in terms of artificial time parameter. Pressure of plasma, flux surfaces, plasma energy and safety factor are calculated by applying the method of steepest descent to the variational principle. Pressure of plasma descent monotonously and reach to zero at last. Safety factor denote the MHD system is linear unstable. All results are similar to the results by calculating MHD equations directly. So variational principle is effective in deal with magnetohydrodynamic instability.