Self‐consistent acceleration of multiply reflected pickup ions at a quasi‐perpendicular solar wind termination shock: a fluid approach

Abstract

The purpose of this paper is to report about a self‐consistent study of acceleration of multiply reflected pickup protons at a quasi‐perpendicular solar wind termination shock and the influence of these protons on the shock's structure. A time‐dependent formulation is developed by treating the solar wind and low‐energy pickup protons as one fluid under the influence of the accelerated pickup protons as a second fluid. The results suggest that the termination shock would experience significant mediation by such accelerated pickup protons if the width of the termination shock's (sub)ramp would be smaller than four times the thermal electron inertial length Le. There are examples in observations of the Earth's bow shock with a width close to such values. For a shock width of 2Le and a multiply reflected ion (MRI) distribution function fMRI ∝ v−a with a = 4, the shock compression ratio is reduced to ∼2.4 compared with the initial value of ∼3.1 and the fraction of reflected pickup protons is ∼11%. For this width the accelerated pickup protons reach a maximum energy of up to ∼ 51 keV, if a ε [3,4]. Such extended MRI spectra for pickup protons, if realistic, might enable a direct injection of these particles into the process of diffusive shock acceleration at the termination shock. Therefore the model also provides a theoretical basis for a study of the formation of anomalous cosmic rays.