Non-Linear Guiding Theory and particle acceleration at a quasi-perpendicular shock

We study particles are accelerated at a quasi-perpendicular shock use a test-particle simulation. We use the Non-Linear Guiding Theory to describe particle perpendicular diffusion coefficient. Particles are assumed to move along ordered background magnetic field lines. The motion of particles along the magnetic field line is modeled as a parallel diffusion. Using a hard-sphere model, the frequency of scattering is governed by λ||. The perpendicular diffusion is modeled by field line hopping, the frequency is governed by λ⊥. At a quasi-perpendicular shock, the number of shock crossings, and therefore, the maximum particle energy, is largely decided by λ⊥. We show that the perpendicular diffusion can greatly enhance the acceleration process. We examine how the energetic particle power spectrum depends on λ⊥ and investigate the effects of local structures (such as ripples on the shock surface) as well.