Particle and energy transport in a field reversed configuration

This work has been part of a collaboration between the University of Florida and the University of California, Irvine, aimed at building a fusion reactor which is compact, environmentally friendly, and easy to maintain. The specific work of this dissertation concerns theoretical issues about equilibrium and particle transport in such a reactor, which is based on magnetic configurations known as Field Reversed Configurations (FRC).;The equilibrium study shows how to obtain solutions for various physical quantities of interest in the case of fusion reactions with one or many types of ions. The main attribute that comes out of this study is the existence of mixed confinement states in a Colliding Beam Fusion Reactor (CBFR). In these mixed confinement states ions are confined magnetically while the electrons are confined electrostatically. A whole range of electric fields of different strengths can be accessed by tuning the externally applied magnetic field. A strong electric field that is confining for electrons can avoid their anomalous transport.;The next part of this work concerns the effect of collisions on particle orbits in a CBFR. Simulations of particle orbits show that there are two main types of orbits: (1) betatron orbits, which can be thought of as sine waves propagating along a circle, and (2) drift orbits, which can be thought of as small circles rolling over larger circles. It is shown that large-angle collisions between ions can change a betatron orbit to a drift orbit. The direction of rotation of the drift orbit is in the diamagnetic direction in all cases where the electric field is confining for electrons and the E&ar;xB&ar; drift dominates over the gradient drift B&ar;x1B . This is an important finding for the ion transport in a CBFR. Simulations show also that small angle collisions between electrons and ions do not change the topology of betatron orbits, but only increase the amplitude of their radial oscillations with time.;The last part of this work is related to the development of a formal diffusion theory that enables the calculation of the diffusion rates of betatron orbits and drift orbits due to small angle collisions. This diffusion theory is based on test particle methods used in kinetic theory of plasmas. It has the merit of being applicable to particle orbits of any size and rapidly varying magnetic fields that pass through zero.