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tokens: of the mean pitch angle remains similar over the whole energy range . However, evolution timescales and peak amplitudes change as expected. Next, the influence of the amplitude of the magnetic field of the plasma wave has been studied (Section 5 ). Again, simulation results and analytic predictions have been compared. Since QLT works with the assumption that the wave’s amplitude is negligible compared to the background magnetic field B 0 , it could be expected that the analytic model fails to describe simulations with larger . We have shown that this is the case, although the model still yields a surprisingly good approximation. However, the magnetostatic QLT model fails to describe the interaction of particles and several waves correctly, as further simulations have shown. In a study of the trajectories of individual particles in a simulation with only one plasma wave we have found that particles follow closed trajectories in pitch angle space, i.e., that their motion is deterministic rather than diffusive (Section 6 ). This situation only changes if several plasma waves with different wave numbers or frequencies are included. 7.2. Conclusions In the fully kinetic PiC simulations the propagating waves lead to changes of the absolute momenta p of the individual particles in the plasma frame. This momentum diffusion is not included in the magnetostatic QLT model, where is assumed. However, a comparison of magnetostatic and full PiC simulations, as well as an analysis of the change of particle energy over time in a PiC simulation have shown that momentum diffusion plays only a minor role. The assumption of constant particle energy, which was a prerequisite for the analytic expressions developed by Lange et al. ( 2013 ), can still be applied in the electrodynamic model of PiC simulations. This explains why the electric fields can still be neglected and why the magnetostatic model describes PiC results reasonably well after the transformation of the model equations into the plasma frame has been performed. We found that the analytic model has difficulties in describing the effect of several waves on particle scattering. In Sections 5.2 and 5.3 we present data from simulations with two and four plasma waves. It can be seen that the predicted scattering amplitudes only match the simulation data if the resonances for the different waves are well-separated in pitch angle space. Looking at single particles in pitch angle space, as illustrated in Figure 11 in Section 6 , it can be seen that in the case of single waves (or sufficiently separated resonances) each particle travels along a closed, elliptical trajectory. In the case of single plasma waves we therefore conclude that a particle starting at some pitch angle will be scattered to different pitch angles, but will always come back to at some point in time. This is consistent with the idea of particle trapping developed by Sudan Ott ( 1971 ): the magnetic field of the wave leads to effective