The effects of shape and amplitude on the velocity of scrape-off layer filaments

TL;DR

This paper develops a simplified two-dimensional model to analyze how the shape and amplitude of scrape-off layer filaments influence their velocity, providing new analytical scalings validated by simulations.

Contribution

It introduces a generalized analytical scaling for filament velocity considering elliptical cross-sections and arbitrary amplitudes, extending previous circular models.

Findings

Derived new scaling laws for filament velocity based on shape and amplitude.

Validated analytical models with extensive 2D simulations.

Compared 2D and 3D simulation results showing reasonable agreement.

Abstract

A complete model of the dynamics of scrape-off layer filaments will be rather complex, including temperature evolution, three dimensional geometry and finite Larmor radius effects. However, the basic mechanism of $\boldsymbol{E}\times\boldsymbol{B}$ advection due to electrostatic potential driven by the diamagnetic current can be captured in a much simpler model; a complete understanding of the physics in the simpler model will then aid interpretation of more complex simulations, by allowing the new effects to be disentangled. Here we consider such a simple model, which assumes cold ions and isothermal electrons and is reduced to two dimensions. We derive the scaling with width and amplitude of the velocity of isolated scrape-off layer filaments, allowing for arbitrary elliptical cross-sections, where previously only circular cross-sections have been considered analytically. We also put the scaling with amplitude in a new and more satisfactory form. The analytical results are extensively validated with two dimensional simulations and also compared, with reasonable agreement, to three dimensional simulations having minimal variation parallel to the magnetic field.