Developing an MHD simulator for tokamaks

Abstract

We are on a long journey to develop an MHD (Magnetohydrodynamic) simulation code for tokamak plasma. We are making an ideal MHD simulation code using WENO (Weighted Essentially Non-Oscillatory) method, which is newest numerical scheme suitable to one fluid non-linear ideal MHD equation. This scheme easily and well describe the conservation law of ideal plasma and is especially suitable for fast flow and shock wave in plasma, hence the numerical code can easily analyze MHD phenomena in tokamak related to fast plasma flow like sawtooth mode or disruption after expansion. This ideal MHD simulator is a backbone of full MHD simulator which will be expanded to include terms presenting non-ideal and 2-fluid effects. And we will introduce AMR or parallelization methods to this code for more efficient calculation. This code adopts finite difference method in both of cartesian and cylindrical coordinates and WENO method in hybrid type for spatial discretization and Runge-Kutta method for time advance. Positivity preserving scheme is used, which guarantees positive density, pressure, and energy during numerical simulation. Divergence free characteristic of magnetic field is realized using flux constrained transport method, which is based on the staggered grid idea. The spatial accuracy of this code is 5th order and accuracy for time is 3rd order. This code adopts ghost cell method for boundary condition of real tokamak geometry. This code can be used to analyze the experimental results, to understand the physical characteristics, and to estimate experimental phenomena of tokamak plasma. And also this code can be used to simulate astronomic plasmas because of its ability to simulate fast flow. Finally it can be one of the core parts of a virtual tokamak, which should be developed in future.