Amplitude and size scaling for interchange motions of plasma filaments

TL;DR

This paper investigates how plasma filament velocities scale with amplitude and size using a reduced fluid model, revealing different regimes for incompressible and compressible flows and providing numerical validation.

Contribution

It introduces a detailed analysis of velocity scaling laws for plasma filaments, including the effects of compressibility and magnetic field non-uniformity, supported by numerical simulations.

Findings

Maximum velocity scales with the square root of amplitude and size in incompressible flows.

In compressible flows, the scaling depends on the ratio of amplitude to size, with a threshold effect.

Acceleration is proportional to amplitude and independent of size across regimes.

Abstract

The interchange dynamics and velocity scaling of blob-like plasma filaments are investigated using a two-field reduced fluid model. For incompressible flows due to buoyancy the maximum velocity is proportional to the square root of the relative amplitude and the square root of its cross-field size. For compressible flows in a non-uniform magnetic field this square root scaling only holds for ratios of amplitudes to cross-field sizes above a certain threshold value. For small amplitudes and large sizes, the maximum velocity is proportional to the filament amplitude. The acceleration is proportional to the amplitude and independent of the cross-field size in all regimes. This is demonstrated by means of numerical simulations and explained by the energy integrals satisfied by the model.