# Magnetorotational Dynamo Action in the Shearing Box

## TL;DR

This study investigates how the geometry of the shearing box influences magnetic dynamo action driven by the magnetorotational instability, highlighting the importance of box aspect ratio and turbulent magnetic flux distribution.

## Contribution

It demonstrates that the dynamo's efficiency depends on the box aspect ratio and provides a physical explanation involving magnetic flux spreading and turbulence.

## Key findings

- Dynamo action is easier in tall boxes than in long boxes.
- Large magnetic Reynolds number is necessary for dynamo in both geometries.
- Intermittency of azimuthal magnetic flux correlates with dynamo efficiency.

## Abstract

Magnetic dynamo action caused by the magnetorotational instability is studied in the shearing-box approximation with no imposed net magnetic flux. Consistent with recent studies, the dynamo action is found to be sensitive to the aspect ratio of the box: it is much easier to obtain in tall boxes (stretched in the direction normal to the disk plane) than in long boxes (stretched in the radial direction). Our direct numerical simulations indicate that the dynamo is possible in both cases, given a large enough magnetic Reynolds number. To explain the relatively larger effort required to obtain the dynamo action in a long box, we propose that the turbulent eddies caused by the instability most efficiently fold and mix the magnetic field lines in the radial direction. As a result, in the long box the scale of the generated strong azimuthal (stream-wise directed) magnetic field is always comparable to the scale of the turbulent eddies. In contrast, in the tall box the azimuthal magnetic flux spreads in the vertical direction over a distance exceeding the scale of the turbulent eddies. As a result, different vertical sections of the tall box are permeated by large-scale nonzero azimuthal magnetic fluxes, facilitating the instability. In agreement with this picture, the cases when the dynamo is efficient are characterized by a strong intermittency of the local azimuthal magnetic fluxes.