Ambipolar diffusion in smoothed particle magnetohydrodynamics

TL;DR

This paper introduces and tests a new implementation of ambipolar diffusion in smoothed particle magnetohydrodynamics (SPMHD), enabling more accurate simulations of partially ionized plasmas in astrophysical contexts.

Contribution

The authors develop an energy-conserving, positive-definite SPMHD implementation of ambipolar diffusion using the strong coupling approximation, tested in 1D and 3D codes.

Findings

Wave damping matches analytical results within 0.03-2%

Oblique C-shocks agree within 4% of semi-analytical solutions

Implementation is suitable for star formation simulations

Abstract

In partially ionised plasmas, the magnetic field can become decoupled from the neutral gas and diffuse through it in a process known as ambipolar diffusion. Although ambipolar diffusion has been implemented in several grid codes, we here provide an implementation in smoothed particle magnetohydrodynamics (SPMHD). We use the strong coupling approximation in which the ion density is negligible, allowing a single fluid approach. The equations are derived to conserve energy, and to provide a positive definite contribution to the entropy. We test the implementation in both a simple 1D SPMHD code and the fully 3D code PHANTOM. The wave damping test yields agreement within 0.03-2 per cent of the analytical result, depending on the value of the collisional coupling constant. The oblique C-shocks test yields results that typically agree within 4 per cent of the semi-analytical result. Our algorithm is therefore suitable for exploring the effect ambipolar diffusion has on physical processes, such as the formation of stars from molecular clouds.