Deterministic and stochastic geometric mechanics for Hall magnetohydrodynamics

We derive new models of stochastic Hall magnetohydrodynamics (MHD) by applying Lie group symmetry reduction in a stochastic Euler-Poincar & eacute; variational principle. The resulting new theory of stochastic Hall MHD has potential applications for uncertainty quantification and data assimilation in space plasma (space weather), planetary science and solar physics. The stochastic geometric mechanics approach we take here produces coordinate-free results that may then be applied in a variety of spatial configurations.