Particle Acceleration in Dynamical Collisionless Reconnection

Abstract

The work presented in this thesis is concerned with how particle acceleration can take place in the context of dynamical magnetic reconnection in collisionless coronal plasmas. The energy production mechanism in solar flares has been a long standing problem of solar physics. The mechanism that provides the energy during solar flares is thought to be magnetic reconnection. However, timescales from different models disagree. Most rnagnetohydrodynamic models do not explain the high energy particles observed during solar flares and most collisionless models fail in that they do not account for the dynamic evolution of the solar flare environment. This thesis is divided in seven chapters. I will summarise each chapter individually. Chapter 1 contains a brief overview of the properties of the Sun and the structure of its atmosphere. Then follows a much more detailed discussion of energetic phenomena in the Sun concentrating primarily on solar flares and solar noise storms, and their manifestations in the electromagnetic spectrum and production of high energy particles. An introduction to magnetic reconnection is given in Chapter 2. Magnetic reconnection is defined as the process whereby plasma flows across a surface that separates regions containing topologically different magnetic field lines. We briefly discuss some of the most important models for magnetic reconnection. The models are divided in hydro- magnetic and collisionless models. We also discuss mechanism for particle acceleration in cosmic plasmas. The mechanisms of particle acceleration are: diffusive shock acceleration, stochastic acceleration and electric field acceleration. I review some mechanism of particle accelaration in X-type neutral points and their implications for energy distributions produced. In Chapter 3 we present the results of a non self-consistent calculation for collisionless magnetic reconnection. First we assume the form of the electric and magnetic fields, a procedure which is not necessarily self-consistent. The magnetic field is taken to have an X-type neutral point. Two cases for the imposed electric fields are considered, one constant and the other time-varying. The amplitude of the electric field is treated as a parameter. We calculate the particle orbits in these fields and the resulting energy distributions and show that protons and electrons may gain relativistic energies in times < 15 for plausible (small) electric field amplitudes and active region magnetic fields. We note the effectiveness of acceleration of protons and electrons varies according to the frequency of oscillation invoked. It seems that electrons, when they are accelerated, are accelerated more rapidly than protons, although numerical limitations prevented us from investigating this possibility in full. Protons are accelerated to 7 ray producing energies. In Chapter 4 we formally derive an analytical description for the time and space dependence of a linear incompressible, azimuthally symmetric disturbance propagating in a medium with a neutral point. In deriving the expression for the magnetic disturbance we follow Craig and McClymont (1991) fairly closely. There are however the important differences between our treatment and theirs: we recast the problem in dimensionless variables for consistency with the integration of the particle orbits, and introduce a slight restriction on the possible modes of interest. The latter has the consequence that the final, hypergeometric function form of the solution is always exact (cf. Craig, 1994). Also we give heavier emphasis than other work to the numerical evaluation of the eigenfunctions. We use this description to study the detailed form and behaviour of reconnective eigenvalues, as a preliminary step in addressing the problem of the particle orbits. In the Chapter 5 we study particle orbits in the presence of such a disturbance. A general feature of the orbits is that particles remain relatively close to the neutral point during the integration time of 1 second. The particles that are accelerated to high energies are those that are trapped close to neutral point area. This happens for specific values of the 'resistivity' owing to the spatial form of the electric and magnetic field perturbation. Particle orbits are calculated for the fundamental and higher eigenmodes. In Chapter 6 we attempt to match the MHD and test particle calculations. To do this we compare the energy loss of the wave during 1 second and the energy gained by the particles during the same time. For all the vaues of the resistivity investigated, the wave loses energy much faster than the particles gain energy. The calculations presented in this Chapter force us to re-examine the nature of 'resistivity'. Particles trapped for long periods near the neutral point are freely accelerated and clearly extract energy from the wave. However, they do not contribute to the resistivity. Despite the difficulties in defining the 'correct' value of the 'resistivity', we have demonstrated that the passage of such a reconnective disturbance may accelerate protons to ? ray producing energies, and certainly to energies where they could play a role in energy transport