Strong nonlocality variations in a spherical mean-field dynamo

TL;DR

This paper explores how relaxing standard assumptions in mean-field dynamo theory reveals new effects, showing that nonlocality influences magnetic field structures and excitation conditions, especially in spherical geometries like the Sun.

Contribution

It introduces a nonlocal reaction-diffusion model for mean-field dynamo equations, extending traditional approaches to include spatial and temporal nonlocality effects.

Findings

Nonlocality lowers dynamo excitation thresholds.

Sharp magnetic structures are suppressed by nonlocal effects.

Surface magnetic fields remain similar despite nonlocal modifications.

Abstract

To explain the large-scale magnetic field of the Sun and other bodies, mean-field dynamo theory is commonly applied where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the scale of the turbulent eddies becomes comparable to the scale of the variations of the mean magnetic field. Models showing sharp magnetic field structures have therefore been regarded as unreliable. Our aim is to look for new effects that occur when we relax the restrictions of the standard approach, which becomes particularly important at the bottom of the convection zone where the size of the turbulent eddies is comparable to the depth of the convection zone itself. We approximate the underlying integro-differential equation by a partial differential equation corresponding to a reaction-diffusion type equation for the mean electromotive force, making an approach that is nonlocal in space and time feasible under conditions where spherical geometry and nonlinearity are included. In agreement with earlier findings, spatio-temporal nonlocality lowers the excitation conditions of the dynamo. Sharp structures are now found to be absent. However, in the surface layers the field remains similar to before.