Numerical Solutions to the Two Dimensional Boltzmann Equation
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A strict kinetic, two-dimensional model of the electron kinetics within a glow discharge positive column is developed. The problem is solved in cylindrical geometry using the standard two-term Legendre expansion of the electron velocity distribution function. The model establishes a steady state solution, such that the net ionization rate is exactly balanced by the wall loss. In addition to a thorough analytic development, we present the numerical techniques used to solve the resulting elliptic partial differential equation, including an efficient method to treat sparse banded matrices. The mo...
A strict kinetic, two-dimensional model of the electron kinetics within a glow discharge positive column is developed. The problem is solved in cylindrical geometry using the standard two-term Legendre expansion of the electron velocity distribution function. The model establishes a steady state solution, such that the net ionization rate is exactly balanced by the wall loss. In addition to a thorough analytic development, we present the numerical techniques used to solve the resulting elliptic partial differential equation, including an efficient method to treat sparse banded matrices. The model is validated against published results, local and nonlocal kinetic approximations, and a previous Monte Carlo treatment. Having created a working model, we conduct an investigation into current flow within the solution area of a neon column, made possible by this 2-D treatment. Furthermore, we investigate the range of applicability of the earlier local and nonlocal kinetic approximations and finally present a short discussion on the effect different forms of wall loss have on the overall distribution function.
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