A conservative implicit-PIC scheme for the hybrid kinetic-ion fluid-electron plasma model on curvilinear meshes

TL;DR

This paper introduces a new conservative implicit PIC scheme for hybrid plasma models on curvilinear meshes, ensuring energy conservation and demonstrating effectiveness in complex space and fusion plasma simulations.

Contribution

It extends implicit PIC methods to arbitrary curvilinear meshes with proven energy conservation, enabling accurate multi-scale plasma simulations in complex geometries.

Findings

Conserves total energy on arbitrary curvilinear meshes.

Demonstrates effectiveness in space weather and magnetic fusion simulations.

Maintains total momentum in electrostatic limit on all meshes.

Abstract

The hybrid kinetic-ion fluid-electron plasma model is widely used to study challenging multi-scale problems in space and laboratory plasma physics. Here, a novel conservative scheme for this model employing implicit particle-in-cell techniques is extended to arbitrary coordinate systems via curvilinear maps from logical to physical space. The scheme features a fully non-linear electromagnetic formulation with a multi-rate time advance - including sub-cycling and orbit-averaging for the kinetic ions. By careful choice of compatible particle-based kinetic-ion and mesh-based fluid-electron discretizations in curvilinear coordinates, as well as particle-mesh interpolations and implicit midpoint time advance, the scheme is proven to conserve total energy for arbitrary curvilinear meshes. In the electrostatic limit, the method is also proven to conserve total momentum for arbitrary curvilinear meshes. Although momentum is not conserved for arbitrary curvilinear meshes in the electromagnetic case, it is for an important subset of Cartesian tensor-packed meshes. The scheme and its novel conservation properties are demonstrated for several challenging numerical problems using different curvilinear meshes, including a merging flux-rope simulation for a space weather application, and a helical $m=1$ mode simulation for magnetic fusion energy application.