A High-Order Low-Order extended moment method for the Vlasov-Darwin particle-in-cell system

TL;DR

This paper introduces a high-order low-order (HOLO) implicit method for the Vlasov-Darwin particle-in-cell system, enabling larger timesteps and accurate simulation of plasma dynamics by coupling a high-order particle evolution with a low-order fluid solver.

Contribution

The paper develops a novel HOLO method that couples high-order particle evolution with low-order fluid equations for the Vlasov-Darwin system, improving efficiency and accuracy.

Findings

HOLO method allows larger timesteps than explicit methods.

Accurately reproduces plasma phenomena like Landau damping and Weibel instabilities.

Choice of fluid moment equations affects nonlinear convergence.

Abstract

In this study, we develop an extended implicit moment method, namely, a coupled high-order low-order (HOLO) method and apply it to the electromagnetic Vlasov-Darwin model. The high-order (HO) system evolves particles in a manner that conserves charge, energy, and canonical momentum, while the low-order (LO) system solves the fluid moment and Darwin equations, acting as an algorithmic convergence accelerator to the HO system. We demonstrate the HOLO method's ability to take timesteps far larger than the explicit limit, and accurately recover the system's evolution so long as its dynamical timescale is respected. Also, we find that the choice of LO fluid moment equations has a strong impact on the nonlinear convergence of the coupled particle-field system. The HOLO algorithm is benchmarked against electrostatic Landau damping and the electromagnetic electron and ion Weibel instabilities.