Electromagnetic waves interact strongly with charged particles in the Earth’s inner magnetosphere. It is important to be able to model the evolution of these particles, since we rely on the many satellites that orbit within this hazardous radiation environment. Our current approaches to modelling the effect of wave-particle interactions in the outer radiation belt, over macroscopic time and length-scales, rely heavily upon quasilinear wave theory (e.g. see [1]). This theory describes wave-particle interactions as diffusive processes in the plasma, flattening out gradients and slowly moving a small fraction of electrons to higher energies (leading to acceleration), or different pitch-angles (leading to loss). However, the quasilinear formalism relies upon a number of assumptions that may not hold for all important wave types in the radiation belts. Use of the DiRAC facilities has enabled us to carry out important studies into the efficacy of the quasilinear formalism.

In [2], we used the EPOCH particle-in-cell code (see [3]) to conduct numerical experiments to investigate electron interactions with an incoherent spectrum of whistler-mode waves. Our novel approach directly extracts diffusive characteristics across all energy and pitch angle space. This benchmarking work establishes a framework for future investigations on the nature of diffusion due to whistler-mode wave-particle interactions, using particle-in-cell numerical codes with driven waves as boundary value problems.

In [4], we use the techniques developed in [2] to investigate the electron response to whistler-mode waves as a function of increasing wave amplitude. We find that whistler-mode waves with amplitudes of order (dB/B)^{2 }~ O(10^{-10}) – O(10^{-6}) in a uniform **B **give diffusive and advective dynamics. Over appropriately short timescales the diffusive component of the dynamics agrees with quasilinear theory even for the highest amplitude waves. These timescales range from thousands to tens of gyroperiods for the lowest and highest amplitude waves respectively. This provides very helpful insight into the fundamental nature of electron dynamics in energy and pitch-angle space due to the wave-particle interaction under the uniform background-field assumption, used in the basic quasilinear theory. This also motivates a variety of future numerical experiments and theoretical investigations on the applicability (or otherwise) of quasilinear diffusion theory to electron dynamics in the Earth’s radiation belts, using the particle-in-cell method established in [2].

**References**

- [1] Glauert, S. A., and Horne, R. B. (2005), doi:10.1029/2004JA010851.
- [2] Allanson, O. et al. (2019), doi:10.1029/2019JA027088
- [3] Arber, T. D. et al. (2015), doi:10.1088/0741-3335/57/11/113001
- [4] Allanson, O. et al (2020), doi:10.1029/2020JA027949