Accurate models of collisions in glow discharge simulations

Abstract

Abstract-Very detailed, self-consistent kinetic glow discharge simulations are used to examine the effect of various models of collisional processes. The effects of allowing anisotropy in elastic electron collisions with neutral atoms instead of using the momentum transfer cross-section, the effects of using an isotropic distribution in inelastic electron-atom collisions, and the effects of including a Coulomb electron-electron collision operator are all described. It is shown that changes in any of the collisional models, especially the second and third described above, can make a profound difference in the simulation results. This confirms that many discharge simulations have great sensitivity to the physical and numerical approximations used. Our results reinforce the importance of using a kinetic theory approach with highly realistic models of various collisional processes.

Kinetic description of flow past a micro-plate

“…(The gs are the same for all locations and energies.) This approach was outlined in [16], where particle and energy conservation were also discussed. [16] provides details, including how large values of the mean velocity are handled.…”

“…This approach was outlined in [16], where particle and energy conservation were also discussed. [16] provides details, including how large values of the mean velocity are handled. Other angular distributions could be employed instead, for instance, to allow for an accurate differential cross-section.…”

“…Then the distribution of outgoing particles is chosen to conserve that momentum [9,16]. The form of the distribution is…”

“…Another important difference from the earlier models [13,14] is that we conserve momentum, giving our model the capability to describe a flowing gas. Two momentum conserving collision operators have been employed [16], a simple monoenergetic operator and the BGK model. The monoenergetic model offers advantages in terms of speed, while the BGK model offers a more realistic description, on a ÔfullÕ phase space mesh.…”

Boltzmann equation description of flows at long mean free paths

“…These issues have been discussed at length previously [9,14]. In this work our focus in implementing the method was twofold: (1) to handle reflecting boundaries extremely accurately, in a sense which will be defined below, and (2) to implement a collision operator which preserves the critical features of the flow-again, to very high accuracy.…”