Variational Integrators for Inertial Magnetohydrodynamics

TL;DR

This paper introduces a variational integrator for inertial magnetohydrodynamics that preserves key physical invariants and magnetic topology, enabling accurate long-term simulations of plasma dynamics.

Contribution

It develops a novel variational integrator for inertial MHD that conserves energy and helicities exactly, and maintains magnetic topology when electron inertia is neglected.

Findings

The integrator preserves total energy and helicities to machine precision.

It maintains magnetic field line topology in the ideal case.

Numerical examples demonstrate excellent conservation properties.

Abstract

Recently, an extended version of magnetohydrodynamics that incorporates electron inertia, dubbed inertial magnetohydrodynamics, has been proposed. This model features a noncanonical Hamiltonian formulation with a number of conserved quantities, including the total energy and modified versions of magnetic and cross helicity. In this work, a variational integrator is presented which preserves these conservation laws to machine accuracy. As long as effects due to finite electron mass are neglected, the scheme preserves the magnetic field line topology so that unphysical reconnection is absent. Only when effects of finite electron mass are added, magnetic reconnection takes place. The excellent conservation properties of the method are illustrated by numerical examples in 2D.