A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm

TL;DR

This paper introduces a novel implicit hybrid particle-in-cell scheme for electromagnetic plasma simulations that conserves mass, momentum, and energy, and demonstrates superior stability and noise reduction compared to existing methods.

Contribution

The paper presents a fully implicit, conservative, multi-dimensional hybrid particle-ion/fluid-electron algorithm with advanced features like sub-cycling, orbit averaging, and noise reduction, not previously available.

Findings

The scheme conserves mass, momentum, and energy globally.

It exhibits no unstable growth of finite-grid instability in cold ion simulations.

The method demonstrates improved stability and noise reduction over non-conservative schemes.

Abstract

The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based scheme for the hybrid model is derived for multi-dimensional electromagnetic problems with multiple ion species, which features global mass, momentum and energy conservation. The scheme includes sub-cycling and orbit averaging of the ions, with cell-centered finite differences and implicit midpoint time advance. To reduce discrete particle noise, the scheme allows arbitrary-order shape functions for the particle-mesh interpolations and the application of conservative binomial smoothing. The algorithm is verified for a number of test problems to demonstrate the correctness of the implementation, the unique conservation properties, and the favorable stability properties of the new scheme. In particular, there is no indication of unstable growth of the finite-grid instability for a population of cold ions drifting through a uniform spatial mesh, in a set-up where several commonly used non-conservative schemes are highly unstable.