Stochastic Flux-Freezing and Magnetic Dynamo

TL;DR

This paper introduces a novel statistical perspective on magnetic flux conservation in turbulent plasmas, emphasizing the role of spontaneous stochasticity and demonstrating its implications for magnetic dynamo processes.

Contribution

It establishes stochastic flux-freezing in turbulent plasmas and links spontaneous stochasticity to magnetic dynamo mechanisms through new numerical and theoretical insights.

Findings

Flux-conservation is valid in a statistical sense due to spontaneous stochasticity.

Numerical results support the presence of spontaneous stochasticity in turbulent plasmas.

Stochastic particle methods reveal similarities between different magnetic Prandtl number regimes.

Abstract

We argue that magnetic flux-conservation in turbulent plasmas at high magnetic Reynolds numbers neither holds in the conventional sense nor is entirely broken, but instead is valid in a novel statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. We discuss empirical evidence for spontaneous stochasticity, including our own new numerical results. We then use a Lagrangian path-integral approach to establish stochastic flux-freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux-conservation must remain stochastic at infinite magnetic Reynolds number. As an important application of these results we consider the kinematic, fluctuation dynamo in non-helical, incompressible turbulence at unit magnetic Prandtl number. We present results on the Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. We finally consider briefly some consequences for nonlinear MHD turbulence, dynamo and reconnection