Two‐dimensional simulations of magnetic pulsations upstream of the Earth's bow shock

Abstract

The development of turbulence upstream of the quasi‐parallel portion of the Earth's bow shock is investigated using two‐dimensional hybrid simulations involving the injection of a very hot ion beam against a cold incident ion flow. Initially, waves are produced in the right‐hand resonant ion beam mode and with wave vectors mainly parallel to the ambient magnetic field B0 as expected in linear theory. The waves attempt to propagate upstream but are convected back toward the shock by the incident flow and strongly grow in amplitude as they encounter larger beam densities. Wave growth is associated with reduction of both incident and beam ion bulk velocities. Differential slowing of the incident flow between the different wave fronts and, when the angle θBn between B0 and the shock normal n is non zero, along the fronts themselves, leads to wave front refraction parallel to the shock and fragmentation into smaller structures. Simultaneously, strong scattering by the waves generates beam ion clumps containing a significant fraction of ions with velocities antiparallel to the beam bulk velocity, which enables the destabilization of the left‐hand resonant ion beam mode. The beam ions ultimately form a diffuse distribution whose density ratio relative to the solar wind is a few percents in average, but increases up to about 20% in the immediate vicinity of the shock. These processes result in the formation of magnetic pulsations whose extension parallel and perpendicular to n is typically 15 and a few tens of ion inertial lengths, respectively. These structures can reach total amplitudes δB of 3 to 4 B0, and exhibit most of the time a left‐handed polarization in the plasma rest frame, in agreement with spacecraft observations upstream of the Earth's bow shock. The simulations show that pulsations induce slowing and moderate heating of the incident flow and play an active role in the quasi‐parallel shock transition.