Modelling of solar energetic particles by stochastic processes
Van den Berg, Jacobus Petrus
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The focused transport of solar energetic particles has received increasingly more interest in the last couple of years due to upcoming missions to the Sun. Stochastic differential equations offer a numerically robust way to model solar energetic particle events, but very few models exist which utilize the full capability of this approach. This dissertation summarises the fundamental physics underlying the propagation of solar energetic particles and develops a numerical code to model a solar energetic particle event. In order to understand the microphysics involved in the propagation of solar energetic particles, wave-particle interactions are investigated and charged particles propagating in model slab turbulence are simulated to build a conceptual understanding of the influence of magnetic turbulence on the propagation of charged particles. It is shown that the classical idea of hard-sphere collisions should not be naively applied to charged particles interactingwith turbulence due to the unique nature of the wave-particle interactions. These insights motivate the terms in the focused transport equation, which is derived from physical arguments and processes. Stochastic differential equations are used to solve the focused transport equation in one spatial dimension with energy losses. The developed model is extensively benchmarked and is shown to correctly model solar energetic particle events. It is found that different numerical integration schemes, of increasing accuracy, do not yield any improvement in the model solutions as the results are governed by stochastic behaviour. The effects of solar wind advection and energy losses upon observable characteristics of solar energetic particle events are explored and it is shown that the neglect of these processes would predict incorrect event onset times and peak intensities. The somewhat unexplored topics of propagation times and energy losses are also investigated and it is shown that high energy particles have short propagation times and experience little energy losses. It is found that the average propagation time can be described by the diffusion approximation for cosmic rays, while an improved expression is derived for the average energy loss.