Investigation of particle dynamics and energisation processes in models of collapsing magnetic traps with application to solar flares

In this thesis we examine the energisation of particles in Collapsing Magnetic Trap (CMT) models. It has been suggested that these CMT models may partially explain the energies and distributions of non-thermal particles in solar flares. We begin by investigating the key energisation mechanisms in simple CMT models, which are betatron acceleration and Fermi acceleration caused by the curvature of loop tops. We then assess the relative importance of these processes in a 2D CMT model, a 2.5D CMT model with a guide field and an untwisting 3D CMT model. In each case, we find that Fermi acceleration becomes more important for particles on the most initially stretched field lines and that betatron acceleration is dominant for particles on field lines that start in a more collapsed state. The guide field introduced in the 2.5D model reduces Fermi acceleration, as field lines become less curved, but increases betatron acceleration for almost all particles. The effect of the untwisting of the 3D field on the relative importance of betatron and Fermi acceleration is less clear, but the overall energising effect of this untwisting is small compared to the collapse of field lines. Next, we consider the more complicated case of an untwisted 3D CMT model which incorporates a radially-decaying braking jet. The inclusion of this feature gives rise to distinct types of particle orbit and can lead to a sensitive dependence between the initial pitch angle of an orbit and its final energy. Most particles tested gain energy due to both betatron and Fermi acceleration, but some lose energy by becoming loop leg trapped or by experiencing Fermi deceleration at an inwardly curved loop top, deformed by the braking jet. Finally, we construct a simplified estimator for particle energisation in both a 2D and untwisted 3D CMT models with the aim of reliably calculating the final energies of particles much faster than with test particle orbits. It works by neglecting the trajectory of the orbit and instead averages the contributions of betatron and Fermi acceleration at a given time, using only the initial conditions of the particle and the properties of the magnetic, electric and velocity fields. The estimator is highly effective for a wide range of particle orbits and represents a significant speed up when compared to a test particle orbit code for both the 2D and untwisted 3D models tested. Throughout the thesis, we find that while particles can be substantially energised in CMT models, the vast majority of the particle orbits that we investigated experienced only modest energy gains. This indicates that further processes might be needed to produce the observed populations of particle energies.