Hybrid simulation of energetic particles interacting with magnetohydrodynamics using a slow manifold algorithm and GPU acceleration

TL;DR

This paper introduces M3D-C1-K, a hybrid simulation code combining particle-in-cell and magnetohydrodynamics, utilizing a slow manifold algorithm and GPU acceleration to accurately and efficiently model energetic particle interactions with plasma modes.

Contribution

The paper presents a novel hybrid simulation code that integrates a slow manifold particle algorithm with GPU acceleration within an MHD framework, enabling accurate long-term simulations of energetic particles.

Findings

Successfully simulated MHD modes driven by energetic particles.

Achieved good agreement with existing eigenvalue and hybrid codes.

Demonstrated significant speedup using GPU acceleration.

Abstract

The hybrid method combining particle-in-cell and magnetohydrodynamics can be used to study the interaction between energetic particles and global plasma modes. In this paper we introduce the M3D-C1-K code, which is developed based on the M3D-C1 finite element code solving the magnetohydrodynamics equations, with a newly developed kinetic module simulating energetic particles. The particle pushing is done using a new algorithm by applying the Boris pusher to the classical Pauli particles to simulate the slow-manifold of particle orbits, with long-term accuracy and fidelity. The particle pushing can be accelerated using GPUs with a significant speedup. The moments of the particles are calculated using the $\delta f$ method, and are coupled into the magnetohydrodynamics simulation through pressure or current coupling schemes. Several linear simulations of magnetohydrodynamics modes driven by energetic particles have been conducted using M3D-C1-K, including fishbone, toroidal Alfv\'en eigenmodes and reversed shear Alfv\'en eigenmodes. Good agreement with previous results from other eigenvalue, kinetic and hybrid codes has been achieved.