Particle acceleration in noisy magnetised plasmas

Particle dynamics in the solar corona are of interest since the behaviour of the coronal plasma is important for the understanding of how the solar corona is heated to such high temperatures compared to the photosphere (≈ 1 million Kelvin, compared to a photospheric temperature of ≈ 6 thousand Kelvin ). This thesis deals with particle behaviour in various forms of magnetic and electric fields. The method via which particles are accelerated at reconnection regions is of particular interest as particle acceleration at a magnetic reconnection region is the basis for many solar flare models. Solar flares are releases of energy in the solar corona. The amounts of energy released range from the very small amounts released by nanoflares, that cannot be observed individually, to large events such as X-class flares and coronal mass ejections. Chapter one provides background information about the structure of the Sun and about various forms of solar activity, including solar flares, sunspots, and the generation of the solar magnetic field. Chapter 2 explores various theories of magnetic reconnection. Magnetic reconnection re- gions are usually characterised as containing a central ’null’, a region where the magnetic field is zero, and particles can be freely accelerated in the presence of an electric field, as they decouple from the magnetic field and move non-adiabatically. Chapter 2 gives examples of how such reconnection regions could be formed. Chapter 3 deals with the construction of a ’noisy’ reconnection region. For the purposes of this work, ’noisy’ fields were created by perturbing the magnetic and electric fields with a superposition of eigenmode oscillations. The method for the calculation of such eigenmodes, and the creation of the electric and magnetic fields is detailed here. Chapter 4 details the consequences for particle behaviour in a noisy reconnection region. The behaviour of electrons and protons in such fields was studied. It was found that adding perturbations to the magnetic field caused many smaller nulls to form, which increased the size of the non-adiabatic region. This increased non-adiabatic region led to greater energisa- tion of particles. The X-ray spectra that could be produced by the accelerated electrons were 4 5 also calculated. In this chapter I also investigate the consequences of altering the distribution of the spectrum of modes, and altering the value of the inertial resistivity. In chapter 5, the effects of collisional scattering on particles was also investigated. Colli- sional scattering was introduced by integrating particle trajectories using a stochastic Runge- Kutta method (which is a form of numerical integration). It was found that adding collisional scattering at a reconnection region causes a significant change in particle dynamics in suffi- ciently small electric fields. Particles which undergo collisional scattering in the presence of a small electric field gain more energy than those which do not undergo collisional scatter- ing. This effect decreases as the size of the electric field is increased. The correct relativistic expressions for particle collisions were derived. It was found that collisions have a negligible effect on relativistic particles. Collisional scattering was also used to simulate the drift of particles across magnetic fields. It was found that adding more scattering caused the trajectories of the particles to change from normal gyromotion around the magnetic field, and that particles instead travelled across the magnetic field. I also developed a diffusion coefficient to allow the calculation of a particle’s drift across a magnetic field using only 1D equations. Chapter 6 discusses the findings made in this thesis, and explores how these findings could be built upon in the near future.