Development of a 2D code framework for high-energy-density plasmas of X-pinch

Abstract

X-pinch is one of the efficient sources of radiation due to its capability to generate high-energy-density plasmas. While existing 3D magneto-hydrodynamics (MHD) codes could be utilized to model such plasma, conducting full 3D numerical simulations is often expensive and time-consuming. In this study, we present a numerical framework capable of flexible adoption of models, based on the concept of the fractional step method where we separated the solution methods for different parts of the system. Numerical schemes were chosen primarily for their generality and flexibility, independent of specific characteristics of the target system, such as strict hyperbolicity. Specifically, we adopt the explicit relaxation scheme of the advection part and the implicit TR-BDF2 method of the source part. The developed framework is applied up to the 2D (r, z) cylindrical coordinate system and validated against representative benchmark problems for the MHD system, including (1) the Brio and Wu shock tube in both ideal and resistive settings, (2) the Orszag–Tang vortex, and (3) the magnetized Noh problem. Finally, we present a preliminary simulation of X-pinch.