# Magnetic helicity and fluxes in an inhomogeneous alpha squared dynamo

## TL;DR

This paper investigates magnetic helicity fluxes in an inhomogeneous alpha squared dynamo with boundary conditions, revealing large-scale helicity losses and raising questions about behavior at higher magnetic Reynolds numbers.

## Contribution

It introduces simulations with boundary conditions that produce migratory dynamo waves, extending understanding beyond triply periodic domains.

## Key findings

- Magnetic helicity losses mainly occur at large scales at moderate Reynolds numbers.
- Boundary conditions influence dynamo wave behavior and helicity fluxes.
- Uncertainty remains about helicity flux behavior at very high Reynolds numbers.

## Abstract

Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudo-vacuum condition on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha^2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, most of the magnetic helicity losses occur at large scales. Whether this changes at even larger magnetic Reynolds numbers, as required for alleviating the catastrophic dynamo quenching problem, remains still unclear.