Deterministic and Stochastic Geometric Mechanics for Hall MHD

TL;DR

This paper develops new stochastic models for Hall MHD using geometric mechanics, enabling better uncertainty quantification and data assimilation in space physics.

Contribution

It introduces a symmetry-reduced stochastic variational principle for Hall MHD, providing coordinate-free models applicable in various spatial settings.

Findings

New stochastic Hall MHD models derived from variational principles

Potential applications in space weather and solar physics

Coordinate-free formulations for diverse spatial configurations

Abstract

We derive new models of stochastic Hall magnetohydrodynamics (MHD) by using a symmetry-reduced stochastic Euler-Poincar\'e variational principle. The new stochastic Hall MHD theory has potential applications for uncertainty quantification and data assimilation in space plasma (space weather) and solar physics. The stochastic geometric mechanics approach we take here produces coordinate-free results which may then be applied in a variety of spatial configurations.