Speaker
Description
The Boltzmann equation describes the evolution of the electron and ion distributions over time through a six-dimensional phase space and is at heart of the plasma kinetic theory. For highly-collisional plasmas, scattering collisions keep the distribution function nearly isotropic in velocity space with small perturbations created by the hydrodynamic and electromagnetic forces. These plasmas are very common and include surface plasmas generated in pulsed power devices, plasma-filled microwave devices, air-breakdown in high-power microwave propagation, the plasmas generated by intense electron or ion beams, plasma medicine, electron-beam pumped excimer lasers, and hypersonic flows. For these plasmas, a spherical-harmonic expansion of the velocity-space distribution function is an effective technique for solving the Boltzmann equation. This talk will examine each of the terms in the Boltzmann equation in detail to derive conditions where a spherical harmonic expansion is useful. Expressions for the matrix elements in the expansion terms, which represent the projection of the various operators in the Boltzmann equation onto the spherical harmonics basis set, will be presented. The resulting multiple-term spherical-harmonic expansion makes no assumptions about either the direction of the E and B fields or the magnitude of the spatial gradients. Therefore, this expansion is appropriate for coupling with a Maxwell equation solver. When only the two lowest-order terms are kept, it is shown that the resulting equations are very similar in form to the continuity and force-balance fluid equations. Additional kinetic terms appear in the continuity-like equation which are related to collisions and to energy gains in the electric field that leads to Ohmic heating. Kinetic terms also appear in the force-balance-like equation. One related to collisions and another that is proportional to the derivative with respect to energy of the energy density.
*This work is supported by the NRL base program.
