Magnetohydrodynamic-guiding-center-particle-in-cell Method for Multiscale Plasma Kinetic Simulations

TL;DR

The work develops the MHD-gPIC framework that couples magnetohydrodynamic fluid dynamics with guiding-center particles to simulate multiscale plasma kinetics while mitigating gyro-scale constraints. By deriving Galilean-invariant particle equations, incorporating perpendicular particle pressure into the fluid pressure, and carefully formulating particle backreaction, the method enables large-scale MHD dynamics with non-thermal particle feedback. Validation across trajectory tests, wave-particle interactions, noise-reduction tests, and magnetic reconnection scenarios demonstrates accurate particle transport, energy transfer, and acceleration predominantly via Fermi mechanisms in plasmoid-dominated reconnection, with ions strongly influencing the MHD environment. This approach offers a robust, scalable path toward realistic, multi-scale plasma simulations on the Athena++ platform, with implications for cosmic-ray transport, solar flares, and related astrophysical processes.

Abstract

We present the formulation, algorithm and numerical tests of the magnetohydrodynamic-particle-in-cell (MHD-PIC) method with particles treated under the guiding center approximation, which we term the MHD-gPIC method, and it is implemented in the Athena++ MHD code. The new MHD-gPIC model consists of thermal (cold) fluid and high-energy particles whose dynamics are integrated through guiding center equations including drift motion, with carefully evaluated source terms as particle backreaction. The code is validated with a series of tests, and it is expected to be primarily applicable to study particle acceleration and transport in systems where gyro-resonance is considered insignificant. We also present preliminary studies of particle acceleration during non-relativistic magnetic reconnection.

Figures (10)

• Figure 1: The performance for MHD-gPIC compare to pure MHD and MHD-PIC, with the test in Section \ref{['sec:cpaw']}. The total time cost for integrating one cell relies on the number of particle per cell, as the sum of pure MHD cost and particle cost. The precision is in double and the simulation dimensions are referred to colors.
• Figure 2: Numerical result of a particle moving with a 2D magnetic field loop. (a) Schematic diagram of the test. (b) The trajectory in x-y plane, (c) drift in z direction, where shadowed region (though not quite visible) stands for $z\pm r_{L}$. (d) Parallel velocity in gas co-moving coordinate. (e) Phase error. Different colors/symbols indicate simulations with the MHD-PIC module, MHD-gPIC module and its variants, labeled in the legend.
• Figure 3: CPAW and firehose instability test results. The upper panel shows simulation results of tests with particle electrons, and the lower panel shows simulation results of tests with both electrons and ions in the gPIC part. The left half of both panels shows the phase speed of modified CPAW, and the right half shows the growth rate of the firehose instability, both as a function of pressure anisotropy. Simulation results from different dimensions are plotted against analytical theory.
• Figure 4: EAW angular frequency as a function of damping rate. Different colors corresponds to different $n_c/n_h$, lines are theoretic solution. Dots of same color are from simulations with different $T_c/T_h$.
• Figure 5: Simulation results for Alfvén wave propagation in horizontal direction with different initial particle distribution. First and Second row: initial particle distribution, titles describe the simulation size and whether include ${\sf P}_{p\perp}$ in ${\sf P}$; Third row: $B_y$ distribution at $t=5.0$