Magnetohydrodynamics In The Context Of Nelson's Stochastic Mechanics

TL;DR

This paper extends classical magnetohydrodynamics by incorporating stochastic fluctuations in plasma configurations, modeling velocity and magnetic fields as random processes within Nelson's stochastic mechanics framework.

Contribution

It introduces a stochastic generalization of MHD equations accounting for kinetic effects at small scales, bridging plasma physics and stochastic mechanics.

Findings

Stochastic fields model plasma fluctuations.

Classical MHD equations serve as mean field equations.

Framework captures kinetic effects in plasma dynamics.

Abstract

A simple generalization of the MHD model accounting for the fluctuations of the configurations due to kinetic effects in plasmas in short times small scales is considered. The velocity of conductive fluid and the magnetic field are considerd as the stochastic fields (or random trial trajectories) for which the classical MHD equations play the role of the mean field equations in the spirit of stochastic mechanics of E. Nelson.