Subgrid modelling of pitch-angle diffusion for ion-scale waves in a global hybrid-Vlasov simulation

Numerical simulations play a central role in modern sciences. The trade-off between the accuracy of the physical processes described and the cost of computational resources is often the main limiting factor in these simulations. In global hybrid-Vlasov simulations, such as Vlasiator, lowering the spatial resolution in order to save on resources can lead to key processes being unresolved. A previous study has shown how insufficient resolution of the proton cyclotron instabilities leads to a misrepresentation of ion dynamics. This leads to larger temperature anisotropy and loss-cone shaped velocity distribution functions. In this study, we present a numerical model to introduce pitch-angle diffusion in velocity space, at a spatial resolution where this process was previously not correctly resolved. We test two different methods to enable pitch-angle diffusion in the 3D cartesian velocity space of Vlasiator. We show that we are successfully able to isotropise loss-cone shaped velocity distribution functions, and that this method could be applied to large simulations in order to save computational resources and still correctly model the Earth's magnetosheath.