Budget equations and astrophysical nonlinear mean-field dynamos

TL;DR

This paper investigates how the growth of large-scale magnetic fields in astrophysical objects affects turbulence and dynamo action, revealing a feedback mechanism that saturates magnetic field growth.

Contribution

It introduces a budget equation for turbulent energy that accounts for the turbulence modification by large-scale magnetic fields, advancing nonlinear dynamo theory.

Findings

Nonlinear dynamo number decreases with increasing magnetic field strength.

Large-scale magnetic fields lead to saturation of dynamo instabilities.

Turbulent energy dissipation influences magnetic field growth limits.

Abstract

Solar, stellar and galactic large-scale magnetic fields are originated due to a combined action of non-uniform (differential) rotation and helical motions of plasma via mean-field dynamos. Usually, nonlinear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity. However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence) for (i) a forced turbulence, (ii) a shear-produced turbulence and (iii) a convective turbulence. As the result of this effect, a nonlinear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field $\alpha\Omega$, $\alpha^2$ and $\alpha^2\Omega$ dynamo instabilities are always saturated by the strong large-scale magnetic field.