Determination of pitch-angle diffusion coefficient from bi-Maxwellian velocity distribution functions

<p>Pitch-angle diffusion is one of the main processes of isotropisation of ions in the Earth's magnetosheath. It results from the proton cyclotron and mirror instabilities, arising from temperature anisotropy in the magnetosheath, and is governed by the pitch-angle diffusion coefficient D_{&#956;&#956;.} We have previously developed a sub-grid model to describe pitch-angle diffusion in global-hybrid Vlasov simulations when coarse spatial grid resolution leads to a lack of diffusion. In this study, we present an analytical solution for a pitch-angle diffusion coefficient derived from bi-Maxwellian velocity distribution functions in order to apply this solution to the sub-grid model. This will allow us to model accurately the isotropisation of the distribution functions and to reduce the temperature anisotropy of the plasma while saving computational resources.&#160;</p>