Multiple magnetic field-shock crossings and particle acceleration at quasi-perpendicular shocks

Abstract

The importance of accounting for diffusion perpendicular to the mean magnetic field during nearly perpendicular shock acceleration is well documented. Here we note that perpendicular diffusion is typically envisioned as due to the random walk of field lines, with particle guiding centers closely tied to and diffusing back and forth along the field. We first simulate one-dimensional magnetic field turbulence by using a slab model, in which the turbulence depends on the z direction only. Then we simulate three-dimensional magnetic field turbulence by superimposing two types of turbulence, a 2D model depending on x and y, and the slab model, in the admixture of 80% 2D turbulence and 20% slab turbulence, which provides a good fit to interplanetary turbulence. If these turbulent field lines can cross and recross a shock at N magnetic field-shock crossing that are separated by distances L>lambda11, the scattering mean free path, a particle will cross the shock an average of N2 times before escaping. This could increase the total shock-drift distance and energization of particles. We have verified that multiple field-shock crossing do occur for reasonable values of (triangleB/B0)2 near the shock, and have measured the distribution of N, theta (the angle at which the field crosses the shock), and L for 1000 simulated random magnetic fields. For the special case of the solar wind termination shock, this mechanism may help to explain the observationally inferred drift of anomalous cosmic rays (ACR) over much of the distance from the heliospheric equator to the poles or vice-vers.