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

The purpose of this paper is to report about a. self-consistent study of ac celeration of multiply reflected pickup protons at a quasi-perpendicular so lar wind termination shock and the influence of these protons on the sl loc k's structure. A time-dependent formulation is developed by treating the so lar 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 accele rated pickup protons if the width of the termination shock's (sub)ramp woul d be smaller than four times the thermal electron inertial length L-e. Ther e are examples in observations of the Earth's bow shock with a width close to such values. For a shock width of 2L(e) and a multiply reflected ion (MR I) distribution function f(MRI) alpha v(-a) with a = 4, the shock compressi on ratio is reduced to similar to 2.4 compared with the initial value of si milar to 3.1 and the fraction of reflected pickup protons is similar to 11% . For this width the accelerated pickup protons reach a maximum energy of u p to similar to 51 keV, if a is an element of [3,4]. Such extended MRI spec tra for pickup protons, if realistic, might enable a direct injection of th ese particles into the process of diffusive shock acceleration at the termi nation shock. Therefore the model also provides a theoretical basis for a s tudy of the formation of anomalous cosmic rays.