Date of Award:
Doctor of Philosophy (PhD)
Robert W. Schunk
First, I attempt to present a unified approach to the study of transport phenomena in multicoponent anisotropic space plasmas. In the limit of small temperature anisotropies this system of generalized transport equations reduces to Grad's 13-moment system of transport equations. In the collisionless limit, the generalized transport equations account for collisionless heat flow, cillisionless viscosity, and large temperature anisotropies. Also, I show that with the appropriate assumptions, the system of generalized transport equations reduces to all of the other major systems of transport equations for anisotropic plasmas that have been derived to date.
Next, for application to aeronomy and space physics problems involving strongly magnetized plasma flows, I derive momentum and energy exchange collision terms for interpenetrating bi-Maxwellian gases. Collision terms are derived for Coulomb, Maxwell molecule, and constant collision cross section interaction potentials. The collision terms are valid for arbitrary flow velocity differences and temperature differences between the interacting gases as well as for arbitrary temperature anisotropies. The collision terms have to be evaluated numerically and the appropriate coefficients are presented in tables However, the collision terms are also fitted with simplified expressions, the accuracy of which depends on both the interaction potential and the temperature anisotropy. In addition, I derive the closed set of transport equations that are associated with the momentum and energy collision terms.
Finally, I study the extent to which Maxwellian and bi-Maxwellian series expansions can describe plasma flows characterized by non-Maxwellian velocity distributions, with emphasis given to modeling the anisotropic character of the distribution function. The problem considered is the steady state flow of a weakly-ionized plasma subjected to homogeneous electric and magnetic fields, and different collision models are used. In the case of relaxation collision model, a closed form expression is found for the ion velocity distribution function, while for more regorous models (polarization and hard sphere) I have to use the Monte Carlo simulation. These provided a basis for determining the adequacy of a given series expansion. I find that, in general, the bi-Maxwellian-based expansions for the velocity distribution function is better suited to describing anisotropic plasmas than the Maxwellian-based expansions. (166 pages)
Barakat, Abdallah R., "On the Transport Equations for Anisotropic Plasmas" (1982). All Graduate Theses and Dissertations. 6854.