Resonant scattering of energetic protons off magnetic irregularities is the main process in cosmic ray diffusion. The typical theoretical description uses Alfvén waves in the low frequency limit. We demonstrate that the usage of Particlein-Cell (PiC) simulations for particle scattering is feasible. The simulation of plasma waves is performed with the relativistic electro-magnetic PiC code ACRONYM and the tracks of test particles are evaluated in order to study particle diffusion. Results for the low frequency limit are equivalent to those obtained with an MHD description, but only for high frequencies results can be obtained with reasonable effort. PiC codes have the potential to be a useful tool to study particle diffusion in kinetic turbulence.

A large number of wave modes exist in a magnetized plasma. Their properties are determined by the interaction of particles and waves. In a simulation code, the correct treatment of field quantities and particle behavior is essential to correctly reproduce the wave properties. Consequently, plasma waves provide test problems that cover a large fraction of the simulation code.The large number of possible wave modes and the freedom to choose parameters make the selection of test problems time consuming and comparison between different codes difficult. This paper therefore aims to provide a selection of test problems, based on different wave modes and with well defined parameter values, that is accessible to a large number of simulation codes to allow for easy benchmarking and cross validation.Example results are provided for a number of plasma models. For all plasma models and wave modes that are used in the test problems, a mathematical description is provided to clarify notation and avoid possible misunderstanding in naming.

Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfvén waves are considered for this process, although dispersive waves are also present throughout the heliosphere.We investigate resonant interaction of energetic electrons with dispersive, right-handed waves. For the interaction of particles and a single wave a variable transformation into the rest frame of the wave can be performed. Here, wellestablished analytic models derived in the framework of magnetostatic quasilinear theory (QLT) can be used as a reference to validate simulation results. However, this approach fails as soon as several dispersive waves are involved. Based on analytic solutions modeling the scattering amplitude in the magnetostatic limit, we present an approach to modify these equations for the use in the plasma frame. Thereby we aim at a description of particle scattering in the presence of several waves.A Particle-in-Cell (PiC) code is employed to study wave-particle scattering on a micro-physically correct level and to test the modified model equations. We investigate the interactions of electrons at different energies (from 1 keV to 1 MeV) and right-handed waves with various amplitudes. Differences between model and arXiv:1611.00310v1 [astro-ph.HE] 1 Nov 2016 -2 -simulation arise in the case of high amplitudes or several waves. Analyzing the trajectories of single particles we find no microscopic diffusion in the case of a single plasma wave, although a broadening of the particle distribution can be observed.