Chapter 23 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 (vk) distribu- tions. Assuming that the FABs are produced in a quasi-adiabatic reflection process at the shock, we derive a probability distribution function for vk. These derived distributions exhibit second, third and fourth order moments that agree well with the observations for a large range of reflection efficiencies i, and depend strongly upon the average angle between the magnetic field and the shock normalBn0 .B est 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 (� Bn0) and the moments of the parallel velocity distribution, but with stronger tails extending to higher values ofBn0, a trend opposite to the observations.