Ion distributions in the Earth's foreshock region: Hybrid-Vlasov simulations and spacecraft observations

On the Importance of Spatial and Velocity Resolution in the Hybrid-Vlasov Modeling of Collisionless Shocks

“…This is also evident in the near-total and total lack of foreshock waves in runs R09 and R08, respectively. R10, R00, and R11 are near and below the f min values typically used in global magnetospheric simulations [44,45,[47][48][49] and they result in similar states. In particular the latter R00 and R11 are very similar, as can be seen in Figure 4.…”

“…A high-density transient wave front travels through the downstream region until it exits the simulation box after approximately 350 s. By that time, the reflected ion population forming the foreshock [44] has propagated upstream and the right-hand resonant beam instability grows, generating typical foreshock ULF waves [30,45]. In the downstream region, the anisotropic heating of the ion population drives the 1D equivalent of mirror mode waves [47].…”

“…The shock parameters are chosen to be similar to those used in global magnetospheric simulations [44,45,47], in an effort to explain differences in the foreshock distribution functions. The discussion of this aspect is given in section 4.5 below.…”

“…Vlasiator is the first hybrid-Vlasov model to have been applied to model the terrestrial magnetosphere at global scales, albeit in a 2D-3V reduced configuration so far [30,[43][44][45][46][47][48][49]. The purpose of this work is to provide a benchmark of the behavior of a hybrid-Vlasov model when varying several key numerical parameters.…”

“…The reduced spatial dimensionality eases the intercomparison of the runs and allows to sample a range of resolutions at a moderate computational cost. Furthermore, the test case is tailored toward the comparison with previously reported simulations which model the interaction of the solar wind with the bow shock upstream of the Earth [44,45].…”