Two-way coupling of magnetohydrodynamic simulations with embedded particle-in-cell simulations

TL;DR

This paper presents a novel two-way coupling method integrating magnetohydrodynamic (MHD) and particle-in-cell (PIC) simulations, enabling localized kinetic effects to influence large-scale plasma dynamics.

Contribution

It introduces a new numerical implementation and parallelization strategy for coupled MHD-PIC simulations, demonstrating stability, conservation, and applicability to plasma wave and reconnection studies.

Findings

Coupling with MHD is stable for fast magnetosonic waves.

Coupling with Hall-MHD accurately captures whistler wave dynamics.

Method successfully simulates kinetic reconnection signatures.

Abstract

We describe a method for coupling an embedded domain in a magnetohydrodynamic (MHD) simulation with a particle-in-cell (PIC) method. In this two-way coupling we follow the work of Daldorff et al. in which the PIC domain receives its initial and boundary conditions from MHD variables (MHD to PIC coupling) while the MHD simulation is updated based on the PIC variables (PIC to MHD coupling). This method can be useful for simulating large plasma systems, where kinetic effects captured by particle-in-cell simulations are localized but affect global dynamics. We describe the numerical implementation of this coupling, its time-stepping algorithm, and its parallelization strategy, emphasizing the novel aspects of it. We test the stability and energy/momentum conservation of this method by simulating a steady-state plasma. We test the dynamics of this coupling by propagating plasma waves through the embedded PIC domain. Coupling with MHD shows satisfactory results for the fast magnetosonic wave, but significant distortion for the circularly polarized Alfv\'en wave. Coupling with Hall-MHD shows excellent coupling for the whistler wave. We also apply this methodology to simulate a Geospace Environmental Modeling (GEM) challenge type of reconnection with the diffusion region simulated by PIC coupled to larger scales with MHD and Hall-MHD. In both these cases we see the expected signatures of kinetic reconnection in the PIC domain, implying that this method can be used for reconnection studies.