Effect of Shock Normal Orientation Fluctuations on Field-Aligned Beam Distributions

We address the unsolved question of how foreshock field-aligned beam (FAB) parallel temperatures are produced. Studies including numerical simulations and recent observations have indicated that shocks can be nonstationary and include embedded spatial structures with varied scales. As a first step towards assessing the impact of such variability on backstreaming ions, we examine how a randomly distributed shock normal direction will affect FAB parallel velocity (v ∥) distributions. Assuming that the FABs are produced in a quasi-adiabatic reflection process at the shock, we derive a probability distribution function for v ∥. These derived distributions exhibit second, third and fourth order moments that agree well with the observations for a large range of reflection efficiencies δ, and depend strongly upon the average angle between the magnetic field and the shock normal θ Bn0. Best agreement is obtained for fluctuations of the normal orientation of a few degrees about a nominal direction. The derived model predicts a strong correlation between the shock geometry (θ Bn0) and the moments of the parallel velocity distribution, but with stronger tails extending to higher values of θ Bn0, a trend opposite to the observations.