Modeling the Earth's ULF Foreshock: Self-consistent Monte Carlo Simulations versus Hybrid-Vlasov Simulations

Quasi-parallel astrophysical shocks are considered to develop the so-called foreshock regions featuring enhanced levels of plasma turbulence. Foreshock plays a key role in the concept of diffusive shock acceleration (DSA) mechanism of ion acceleration in shocks. There have been several simulation models addressing particle acceleration/energization coupled with foreshock evolution. One of those is the self-consistent Monte Carlo simulation model, which is built on the quasi-linear theory of ion interactions with Alfvén waves. This model has been applied to simulate ion acceleration in coronal and interplanetary shocks. A more fundamental plasma simulation model, which can be used to study the same processes, is the hybrid-Vlasov (kinetic ions, fluid electrons) approach. The latter is utilized by the Vlasiator code simulating the near-Earth global plasma environment. In this work, we employ both models in application to the Earth's ULF foreshock with the aim to better understand limitations of quasi-linear modeling of foreshock development/ion acceleration. Our study shows that the models are consistent with each other in terms of the dominant wave polarization and the shape of the power spectrum of magnetic fluctuations. The work has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 637324 (HESPERIA).