Stationary solution for quasi-homogeneous small-scale magnetic field advected by non-Gaussian turbulent flow

TL;DR

This paper investigates the conditions under which a stationary magnetic field can exist in a turbulent flow, considering non-Gaussian statistics and external forcing, and calculates the mean-square magnetic field.

Contribution

It introduces a model accounting for non-Gaussian velocity gradients and finite forcing regions, demonstrating stationary solutions for magnetic fields in turbulent flows.

Findings

Stationary magnetic solutions exist under non-Gaussian turbulence.

Mean-square magnetic field can be calculated for various velocity statistics.

Feedback effects are negligible across wide parameter ranges.

Abstract

We consider fluctuations of magnetic field excited by external force and advected by isotropic turbulent flow. It appears that non-Gaussian velocity gradient statistics and finite region of pumping force provide the existence of stationary solution. The mean-square magnetic field is calculated for arbitrary velocity gradient statistics. An estimate for possible feedback of magnetic field on velocity shows that, for wide range of parameters, stationarity without feedback would take place even in the case of intensive pumping of magnetic field.