Thesis (Ph.D.)--University of California, Berkeley, 1961. / "UC-20 Controlled Thermonuclear Processes" -t.p. "TID-4500 (16th Ed.)" -t.p. Includes bibliographical references (p. 97-98).

Thesis (M.Sc.)--Saint Mary's University, 2008. / Includes abstract and appendix. Supervisor: David Clarke. Includes bibliographical references (leaves 88-90).

Jorna and Wood recently developed a program that numerically solved the Fokker-Planck equation in spherical geometry. In this thesis, we describe how the original program has been redeveloped to produce a program that is an order of magnitude quicker and that has superior energy and density conservation. The revised version of the program has been used to extend the work of Jorna and Wood on thermal conduction in laser produced plasmas. It has been shown that the effect of curvature on heat flow can be described from a purely geometrical argument and that for aspect ratios similar to those found in targets, the heat flow is reduced by approximately 10%. Also, it has been shown, in contradiction with Jorna and Wood, that the inclusion of the anisotropic portion of the Rosenbluth potentials does not have a significant effect on the heat flow. Even for highly anisotropic plasmas, the inclusion of the anisotropic portion only increases the heat flow by 10%. In addition, the revised version of the program has been used to study the energy relaxation of model distributions It has been shown that the relaxation time of most non - thermal distributions depends on the detailed structure of the distribution and that the normal Spitzer collision time can under-estimate or over-estimate the time required for energy relaxation.

In this thesis we discuss the theory of symmetric MHD equilibria with anisotropic pressure. More specifically, we focus on gyrotropic pressures, where the pressure tensor can be split into components along and across the magnetic field. We first explore 2D solutions, which can be found using total field type formalisms. These formalisms rely on treating quantities as functions of both the magnetic flux function and the magnetic field strength, and reduce the equilibrium equations to a single Grad-Shafranov equation that can be solved to find the magnetic flux function. However, these formalisms are not appropriate when one includes a shear field component of magnetic flux, since they lead to a set of equations which are implicitly coupled. Therefore, in order to solve the equilibrium problem with a magnetic shear field component, we introduce the poloidal formalism. This new formalism considers quantities as functions of the poloidal magnetic field strength (instead of the total magnetic field strength), and yields a set of two equations which are not coupled, and can be solved to find the magnetic flux function and the shear field. There are some situations where the poloidal formalism is difficult to use, however, such as in rotationally symmetric systems. Thus we require a further formalism, which we call the combined approach, which allows a more general use of the poloidal formalism. One finds that the combined formalism leads to multi-valued functions, which must be dealt with appropriately. Finally, we present some numerical examples of MHD equilibria, which have been found using each of the three formalisms mentioned above.

I begin this study by presenting an overview of the theory of magnetohydrodynamics and the necessary conditions to justify the fluid treatment of a plasma. Upon establishing the fluid description of a plasma we move on to a discussion of magnetohydrodynamics in both the ideal and Hall regimes. This framework is then extended to include multiple plasmas in order to consider two problems of interest in the field of theoretical space physics. The first is a study on the evolution of a partially ionized plasma, a topic with many applications in space physics. A multi-fluid approach is necessary in this case to account for the motions of an ion fluid, electron fluid and neutral atom fluid; all of which are coupled to one another by collisions and/or electromagnetic forces. The results of this study have direct application towards an open question concerning the cascade of Kolmogorov-like turbulence in the interstellar plasma which we will discuss below. The second application of multi-fluid magnetohydrodynamics that we consider in this thesis concerns the amplification of magnetic field upstream of a collisionless, parallel shock. The relevant fluids here are the ions and electrons comprising the interstellar plasma and the galactic cosmic ray ions. Previous works predict that the streaming of cosmic rays lead to an instability resulting in significant amplification of the interstellar magnetic field at supernova blastwaves. This prediction is routinely invoked to explain the acceleration of galactic cosmic rays up to energies of 10¹⁵ eV. I will examine this phenomenon in detail using the multi-fluid framework outlined below. The purpose of this work is to first confirm the existence of an instability using a purely fluid approach with no additional approximations. If confirmed, I will determine the necessary conditions for it to operate.

No description available.

The upper atmosphere of the sun, the solar corona, is approximately 1,000,000K hotter than the surface of the Sun, a property which cannot be explained by the normal processes of heat conduction and radiation. It is now commonly believed that the magnetic fields which fill the solar atmosphere, and propagate down into the interior of the Sun, are important for transferring and transforming energy from the strong plasma flows inside the Sun into the corona as heat. I have investigated an elementary flux interaction which forms a fundamental building block of the coronal heating process. This interaction involves two opposite polarity sources on the Sun's surface in the presence of an overlying magnetic field. To fully understand how this interaction transfers heat into the solar corona, the magnetic skeleton is required, which shows possible sites of heating that are due to magnetic reconnection. A magnetic field is best described by its magnetic skeleton. The most important parts of the magnetic skeleton to find are the null points, from which separatrix surfaces extend that divide magnetic flux of different topology. Part of this thesis proposes a new method of finding null points, for which the accuracy is shown and then compared with another commonly used method (which gave false results). Using these techniques for finding the magnetic skeleton in the magnetic interaction above, the evolution of the skeleton was found to head through seven distinct states, some of which were far more complicated than expected. This included a high number of separators (the intersection of two separatrix surfaces), which are a known location of magnetic reconnection. This separator reconnection was shown to be the main heating mechanism in this interaction, from which the total amount and rates of reconnection in the experiment was calculated. This led to the discovery of recursive reconnection, a process where magnetic flux is reconnected before reconnecting back to its original state, to allow for the process to repeat again. This recursive reconnection was shown to allow far more reconnection than would have been previously expected, all of which releases heat into the neighbouring areas of the atmosphere. Finally, the interaction was modelled with sources of different magnetic radii but of equal flux. This showed that when the antisymmetric nature of the previous interactions was removed, there was little change in the reconnection rates, but when the strength of the overlying magnetic field was increased, the reconnection rates were found to increase. This increase in the overlying magnetic field strength also produced a new magnetic feature called a bald-edge, which was found to replace some of the null points. These bald-edges were found to be associated with surfaces similar to separatrix surfaces that divide flux of different topology but do not extend from a null point. Also features similar to separators extend from these bald-edges.

We present the results of fully three dimensional, post-Newtonian hydrodynamical simulations of the dynamical evolution of mergers between compact stellar remnants (neutron stars and black holes). Although the code is essentially Newtonian, we simulate gravitational wave emission and the corresponding effect on the fluid flow via a post-Newtonian correction. Also, we use a modified Newtonian potential which reproduces certain aspects of the Schwarzschild and Kerr solutions to improve the physics in the vicinity of the black hole. Changes to the energy by neutrino/antineutrino emission are accounted for by an extensive neutrino leakage scheme. The hydrodynamical equations are integrated using the piecewise parabolic method (PPM) and the neutron star matter is described by a tabulated equation of state (EoS). Since the physics of matter at the extreme densities found in neutron stars is not yet certain, we compare results computed using two such tables to ascertain whether this uncertainty in the micro-physics extends to an uncertainty in the energy available to power a short-period gamma-ray burst. With an aim to including magnetic field physics to these simulations, we present a survey of approximate Riemann solvers which may be more easily extended to the system of equations of magnetohydrodynamics (MHD) than the exact or iterative Riemann solver used in the PPM scheme. Tests are performed using the linearised solver of Roe and the approximate Harten, Lax, van Leer and Einfeldt Riemann solvers (HLLE and HLLEM) with the PPM reconstruction scheme. Finally, we discuss the effectiveness of these approximate Riemann solvers in the simulation of mergers between compact stellar remnants.

No description available.

Experimental studies of MHD modes, including dynamics and stability, using a biased electrode for rotation control on the High Beta Tokamak –- Extended Pulse (HBT-EP) are presented. When the probe is inserted into the edge of the plasma and a voltage applied, the rotation of long-wavelength kink instabilities is strongly modified. A large poloidal plasma flow results at the edge, measured with a bi-directional Mach probe with changes in edge kink mode rotation at different biases. This poloidal plasma rotation cannot fully account for the large mode rotation frequency on HBT-EP. By including the electron fluid motion, the mode rotation predictions agree with measurements, indicating that the modes travel with the electron fluid. A GPU-based digital feedback system is used to adjust the probe voltage in real time for controlling both the plasma flow and mode rotation. This active mode rotation control is desirable because it allows for MHD stabilization, as well as studies under conditions of varying mode rotation rates. Mode dynamics were studied using various diagnostics to understand how plasma conditions fluctuate during mode activity and to understand the interaction of the bias probe with the plasma during this activity. Phase-dependent mode behavior was observed, especially at slow mode rotation, which might be attributed to an intrinsic error field or a nonlinear interaction between the bias probe and the mode. Applied resonant magnetic perturbations were used to study the dynamic response of a stable plasma with different mode rotations. At slower rotation, the plasma had a greater response to the perturbations and the plasma reached a saturated response with large perturbations, similar to previous results. At large positive biases, the probe current induces a torque that opposes the natural direction of mode rotation. By applying a sufficiently large torque, a transition is induced into a fast rotation state (both mode and plasma rotation). High poloidal shear flows at the edge were measured in this state, similar to conditions in H-mode plasmas on other devices. The bias required to induce the transition is shown to depend on an applied error field. A technique was established using this transition to determine the natural error field on HBT-EP.