A new scheme for solving inhomogeneous Boltzmann equation for electrons in weakly ionised gases
- Universite Paul Sabatier, Toulouse (France)
In the case of weakly ionized gases, the numerical treatment of non-hydrodynamic regime involving spatial variation of distribution function due to boundaries (walls, electrodes, electron source, etc{hor_ellipsis}) by using direct Boltzmann equation always constitute a challenge if the main collisional processes occurring in non thermal plasmas are to be considered (elastic, inelastic and super-elastic collisions, Penning ionisation, Coulomb interactions, etc{hor_ellipsis}). In the non-thermal discharge modelling, the inhomogeneous electron Boltzmann equation is needed in order to be coupled for example to a fluid model to take into account the electron non-hydrodynamic effects. This is for example the case of filamentary discharge, in which the space charge electric field due to streamer propagation has a very sharp spatial profile thus leading to important space non-hydrodynamic effects. It is also the case of the cathodic zone of glow discharge where electric field has a rapid spatial decrease until the negative glow. In the present work, a new numerical scheme is proposed to solve the inhomogeneous Boltzmann equation for electrons in the framework of two-term approximation (TTA) taking into account elastic and inelastic processes. Such a method has the usual drawbacks associated with the TTA i.e. not an accurate enough at high E/N values or in presence of high inelastic processes. But the accuracy of this method is considered sufficient because in a next step it is destinated to be coupled to fluid model for charged particles and a chemical kinetic model where the accuracy is of the same order of magnitude or worse. However there are numerous advantages of this method concerning time computing, treatment of non-linear collision processes (Coulomb, Penning, etc{hor_ellipsis}).
- OSTI ID:
- 213018
- Report Number(s):
- CONF-950749--
- Country of Publication:
- United States
- Language:
- English
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