On the “injection problem” at the solar wind termination shock

This article presents an integrated analytical model on the injection efficiencies of the different ion species of the Anomalous component of the Cosmic Rays (ACRs) at the solar wind termination shock. We find that the injection into diffusive (first-order Fermi) acceleration is dominated by parallel ion diffusion and not by perpendicular diffusion unless the angle  Ψ between the shock normal and the heliospheric magnetic field is almost exactly 90° ($89.3^\circ < \Psi \approx 90^\circ$). In steady state the threshold speed for injection into first-order Fermi acceleration at a not exactly perpendicular solar wind termination shock – with the Parker shock angle $\Psi \approx 89.3^\circ$ – adjusts itself self-consistently. Increased anisotropic ACR flux amplifies Alfvenic turbulence which in turn suppresses parallel diffusion. It therefore increases the injection threshold and decreases the ACR flux until equilibrium is reached. For this equilibrium situation, we estimate the injection efficiencies of different species of suprathermal ions at the termination shock. We consider the following pre-acceleration processes: 1) momentum diffusion in compressional (ion-acoustic and magnetosonic) turbulence in the upstream supersonic solar wind and adiabatic cooling during convection to the termination shock; 2) reflection, transmission, and acceleration in the electric potential of the termination shock; and 3) momentum diffusion (stochastic or second-order Fermi acceleration) in the subsonic solar wind downstream of the termination shock in the inner heliosheath region. Our model results are compared to data from instruments on board the SOHO, ACE, Ulysses, and Voyager spacecraft.