Using test particle simulations we study particle acceleration at highly perpendicular (θ Bn ≥ 75• ) shocks under conditions of modeling magnetic turbulence. We adopt a backward-in-time method to solve the Newton-Lorentz equation using the observed shock parameters for quasi-perpendicular interplanetary shocks, and compare the simulation results with ACE/EPAM observations to obtain the injection energy and timescale of particle acceleration. With our modeling and observations we find that a large upstream speed is responsible for efficient particle acceleration. Our results also show that the quasi-perpendicular shocks are capable of accelerating thermal particles to high energies of the order of MeV for both kappa and Maxwellian upstream distributions, which may originate from the fact that in our model the local background magnetic field has a component parallel to the shock normal.

We modify the NonLinear Guiding Center (NLGC) theory (Matthaeus et al. 2003) for perpendicular diffusion by replacing the spectral amplitude of the two-component model magnetic turbulence with the 2D component one (following Shalchi 2006), and replacing the constant a 2 , indicating the degree particles following magnetic field line, with a variable a ′2 as a function of the magnetic turbulence. We combine the modified model with the NonLinear PArallel (NLPA) diffusion theory (Qin 2007) to solve perpendicular and parallel diffusion coefficients simultaneously. It is shown that the new model agrees better with simula-tions. Furthermore, we fit the numerical results of the new model with polynomials, so that parallel and perpendicular diffusion coefficients can be calculated directly without iteration of integrations, and many numerical calculations can be reduced.Subject headings:

Shock acceleration is considered one of the most important mechanisms for the acceleration of astrophysical energetic particles. In this work, we calculate the trajectories of a large number of test charged particles accurately in a parallel shock with magnetic turbulence. We investigate the time evolution of the accelerated-particle energy spectrum in the downstream of the shock in order to understand the acceleration mechanism of energetic particles. From simulation results we obtain power-law energy spectra with a bend-over energy, E 0 , increasing with time. With the particle mean acceleration time and mean momentum change during each cycle of the shock crossing from diffusive shock acceleration model (following Drury), a time-dependent differential equation for the maximum energy, E acc , of particles accelerated at the shock, can be approximately obtained. We assume the theoretical bendover energy as E acc . It is found that the bend-over energy from simulations agrees well with the theoretical bend-over energy using the non-linear diffusion theory, NLGCE-F, in contrast to that using the classic quasi-linear theory (QLT).