Hybrid simulations of multiple reflection of protons and heavy ions at Earth’s bow shock

Ion reflection is known to be a key component of particle energisation and heating in super-critical collisionless shockwaves. As a source of free energy, reflected ions drive stream instabilities in the shock foot, create magnetic perturbations, and contribute to magnetic field amplification in the upstream and downstream regions of quasi-perpendicular shocks. Where ions reflect from the shock ramp multiple times, a longer dwell time in the shock foot allows for more opportunities for interaction with non-stationary and turbulent shock processes, which can result in injection into processes such as diffusive shock acceleration and shock drift acceleration. To characterise the pathway to multiple ion reflection, we perform a series of 2D and 3D hybrid particle-in-cell simulations (fluid electron, particle ions) over a parameter range typical of Earth’s bow shock, varying Mach number, plasmas betas, and the angle between the shock normal and upstream magnetic field (θ_Bn). This enables a parametric investigation of the density fraction of multiply reflected ions both upstream and downstream of the shock, for protons and for heavier ion components of the solar wind such as He²⁺. We discuss methods for identification of multiply-reflected ions in kinetic plasma simulations, corresponding analogues for observations (where available), and investigate their impact on shock energetics. By examining the partial moments of reflected ions in two- and three-dimensional simulations, we also explore which shock processes drive multiple reflection.