Inverse problem in Parker's dynamo

TL;DR

This paper presents a Monte-Carlo based inverse method to determine the source distributions of magnetic fields in Parker's dynamo model, revealing conditions where traditional symmetry assumptions are violated and hemispheric differences occur.

Contribution

It introduces a novel inverse solution approach for Parker's dynamo equations using cost-function minimization and explores new conditions affecting magnetic field symmetry and hemispheric properties.

Findings

The method can identify source distributions that violate traditional symmetry assumptions.

Hemispheric differences in magnetic field properties can occur under certain source configurations.

The sign of the dynamo-number does not always determine equatorial symmetry.

Abstract

The inverse solution of the 1D Parker dynamo equations is considered. The method is based on minimization of the cost-function, which characterize deviation of the model solution properties from the desired ones. The output is the latitude distribution of the magnetic field generation sources: the $\alpha$- and $\omega$-effects. Minimization is made using the Monte-Carlo method. The details of the method, as well as some applications, which can be interesting for the broad dynamo community, are considered: conditions when the invisible for the observer at the surface of the planet toroidal part of the magnetic field is much larger than the poloidal counterpart. It is shown that at some particular distributions of $\alpha$ and $\omega$ the well-known thesis that sign of the dynamo-number defines equatorial symmetry of the magnetic field to the equator plane, is violated. It is also demonstrated in what circumstances magnetic field in the both hemispheres have different properties, and simple physical explanation of this phenomenon is proposed.