The Collisionless Shock in Hybrid-Vlasov Simulations

We will present an overview of the recent numerical results on collisionless shocks obtained from Vlasiator, a hybrid-Vlasov simulation designed to model the Earth's magnetosphere. We will present results on the Earth bow shock under different solar wind and interplanetary magnetic field conditions and compare them with results on planar shocks for similar Mach numbers. As the simulation treats only ions kinetically, we will limit our study to the ion scales and beyond, characterizing the nature of fluctuations and ion distribution functions under different conditions and numerical settings. We will also investigate the role of dimensionality of the system, i.e., compare simulations performed in 2D and 3D in ordinary space (with full 3D in velocity space in both cases). In particular, we will characterize the foreshock ULF waves reproduced by the simulations and compare them with quasi-linear theory and observations of ion foreshocks ahead of the quasi-parallel bow shock and interplanetary shocks. The reasons for the differences in the foreshock characteristics under different modeling approximations will be discussed, in particular concerning the oblique propagation and dispersion relations of the foreshock waves, which are markedly different from quasi-linear theory and in quantitative agreement with spacecraft observations.