Three-dimensional numerical simulations of particle injection and acceleration at quasi-perpendicular shocks

We present results from three-dimensional numerical simulations of quasi-pe rpendicular collisionless shocks in order to determine whether cross-field diffusion, which is otherwise artificially suppressed in simulations which contain at least one ignorable spatial coordinate, is large enough to effic iently accelerate thermal. particles and/or pickup ions. We find that altho ugh the simulated downstream distribution functions are quite steep, a frac tion of the particles are accelerated to energies well above the thermal en ergy. This occurs only if the system contains fluctuations with wavelengths that are considerably larger than the gyroradii of the particles of intere st (the high-energy ones). We find that this is due to the fact that the tr ansport of the particles normal to the shock, against the downstream convec tion, is mostly influenced by the meandering of field lines on large scales . We also show that if the system does not contain these long-wavelength wa ves, the scattering is not sufficient to accelerate thermal particles or pi ckup ions. We use two different types of simulations to demonstrate this. I n the first set of simulations we use the well-known hybrid simulation whic h treats the interaction between the particles and fields self-consistently . Far computational tractability these simulations use very small spatial d omains, and the effect of the large-scale field-line random walk is suppres sed. However, this approximation accurately addresses the physics of the sc attering at resonant wavelengths. Test-particle simulations, which are more computationally tractable than the hybrid simulations, are also performed for larger systems and to illustrate the effect of the long-wavelength wave s.