Date of Award
Doctor of Philosophy (PhD)
Ravindra P. Joshi
Linda L. Vahala
Plasma is currently a hot topic and it has many significant applications due to its composition of both positively and negatively charged particles. The energy distribution function is important in plasma science since it characterizes the ability of the plasma to affect chemical reactions, affect physical outcomes, and drive various applications. The Boltzmann Transport Equation is an important kinetic equation that provides an accurate basis for characterizing the distribution function—both in energy and space.
This dissertation research proposes a multi-term approximation to solve the Boltzmann Transport Equation by treating the relaxation process using an expansion of the electron distribution function in Legendre polynomials. The elastic and 29 inelastic cross sections for electron collisions with nitrogen molecules (N2) and singly ionized nitrogen molecules ([special characters omitted]) have been used in this application of the Boltzmann Transport Equation.
Different numerical methods have been considered to compare the results. The numerical methods discussed in this thesis are the implicit time-independent method, the time-dependent Euler method, the time-dependent Runge-Kutta method, and finally the implicit time-dependent relaxation method by generating the 4-way grid with a matrix solver. The results show that the implicit time-dependent relaxation method is the most accurate and stable method for obtaining reliable results. The results were observed to match with the published experimental data rather well.
"Multi-Term Approximation to the Boltzmann Transport Equation for Electron Energy Distribution Functions in Nitrogen"
(2012). Doctor of Philosophy (PhD), Dissertation, Electrical/Computer Engineering, Old Dominion University, DOI: 10.25777/rn1d-j255