Scaling of Small-Scale Dynamo Properties in the Rayleigh-Taylor Instability

TL;DR

This paper derives and tests scaling relations for the small-scale dynamo in Rayleigh-Taylor instability, predicting magnetic energy amplification and saturation timescales in astrophysical and laboratory plasmas.

Contribution

It introduces new scaling relations based on free-fall and isotropy assumptions for the small-scale dynamo in RTI, validated through 3D MHD simulations.

Findings

Scaling relations hold during saturation phase

Discrepancies found during mixing and decay phases

Predicted rapid dynamo saturation in neutron star mergers

Abstract

We derive scaling relations based on free-fall and isotropy assumptions for the kinematic small-scale dynamo growth rate and amplification factor over the course of the mixing, saturation, and decay phases of the Rayleigh-Taylor instability (RTI) in a fully-ionized plasma. The scaling relations are tested using sets of three dimensional, visco-resistive MHD simulations of the RTI and found to hold in the saturation phase, but exhibit discrepancies during the mixing and decays phases, suggesting a need to relax either the free-fall or isotropy assumptions. Application of the scaling relations allows for quantitative prediction of the net amplification of magnetic energy in the kinematic dynamo phase and therefore a determination of whether the magnetic energy either remains sub-equipartition at all velocity scales or reaches equipartition with at least some scales of the turbulent kinetic energy in laboratory and astrophysical scenarios. As an example, we consider the dynamo in RTI-unstable regions of the outer envelope of a binary neutron star merger and predict that the kinematic regime of the small-scale dynamo ends on the time scale of nanoseconds and then reaches saturation on a timescale of microseconds, which are both fast compared to the millisecond relaxation time of the post-merger.