Smoothed particle hydrodynamics method for pinch plasma simulation with non-ideal MHD model

When plasma is compressed by magnetic forces, a pinch phenomenon is observed. Pinch plasma has received significant attention as an efficient source of radiation and a way for high-density plasma physics analysis. In this study, a non-ideal magnetohydrodynamics (MHD) model is applied to a smoothed particle hydrodynamics (SPH) framework to analyze pinch plasmas whose local resistivity varies with temperature and pressure. The proposed SPH model incorporates several numerical treatments, such as a correction term to satisfy the (SIC).B constraint and some artificial dissipation terms to govern the shock wave. Moreover, it includes the evaluation of a novel SPH discretization for non-ideal MHD terms, including current density calculations. Furthermore, the proposed model is validated with three benchmark cases: (1) Brio and Wu shock tube (ideal MHD), (2) resistive MHD shock simulation, and (3) magnetized Noh Z-pinch problem. The simulation results are compared with the results of some reference Eulerian MHD simulations and analytical solutions. The simulations agree well with the reference data, and the introduced numerical treatments are effective. Finally, X-pinch simulations are performed using the proposed model. The simulations well produce the micro Z-pinch and jet shapes, which are important X-pinch features. Overall, the proposed SPH model has extensive potential for studying the complex pinch plasma phenomena.