Path integrals for mean-field equations in nonlinear dynamos

TL;DR

This paper applies the path-integral method to derive nonlinear mean-field dynamo equations, modeling magnetic field evolution as a Wiener process influenced by magnetic forces, providing a novel approach to nonlinear dynamo theory.

Contribution

It introduces a path-integral approach to derive nonlinear mean-field dynamo equations considering velocity-field realizations affected by magnetic forces.

Findings

Derivation of nonlinear dynamo equations using Wiener integrals.

Modeling magnetic field evolution as a three-dimensional Wiener process.

Equations resemble conventional mean-field equations but include magnetic-force effects.

Abstract

Mean-field dynamo equations are addressed with the aid of the path-integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener integral over all the trajectories of fluid particle. The form of the equations is just the same as the conventional mean-field equations, but the present equations are derived with the velocity-field realization affected by the magnetic-field force. In this sense, the present ones are nonlinear dynamo equations.