This thesis investigates both the release of energy in solar flares, and the acceleration and transport of particles in various astrophysical situations. While numerical simulations are central to this thesis, these are always motivated by analytical arguments.
A review of flare energy release is given in Chapter 2, with results presented in Chapters 3 and 4. The main goal of the flare work is to investigate the effect of viscosity on energy release rates. Scaling arguments and exact solutions of the magnetohydrodynamic equations are used to interpret the results of two-dimensional numerical simulations of magnetic reconnection. The results support viscous energy dissipation accounting for a significant fraction of flare energy release.
Chapter 5 contains an introduction to astrophysical particle acceleration, using the Fokker-Planck formulation. The theory introduced in this chapter is used to study electron transport in solar flare loops (Section 5.5). A key aspect of the analysis is the expression of the Fokker-Planck equation as a system of stochastic differential equations. A generalisation to the flare loop hard X-ray emission prediction of Conway et al. (1998) is obtained, giving a stronger dependence on density for dispersed initial distributions.
Chapter 6 uses the methods of the previous chapter to study the acceleration of cosmic-rays at the heliospheric termination shock. The applicability of the focused acceleration mechanism of Schlickeiser and Shalchi (2008) is examined using numerical simulations, which are interpreted using analytical arguments based on averaging the stochastic equations. The results show significant limitations in assuming a near-isotropic distribution, a requirement for the focused acceleration mechanism. In addition, momentum diffusion provides a significant effect that cannot be neglected. The theory is extended to include focused deceleration and pure momentum diffusion
