Inelastic scattering models in transport theory and their small mean free path analysis

✍ Scribed by J. Banasiak; G. Frosali; G. Spiga

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 188 KB
• Volume: 23
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(20000125)23:2<121::aid-mma107>3.0.co;2-5

✦ Synopsis

In this paper we perform an asymptotic analysis of a singularly perturbed linear Boltzmann equation with inelastic scattering operator in the Lorentz gas limit, when the parameter corresponding to the mean free path of particles is small. The physical model allows for two-level "eld particles (ground state and excited state), so that scattering test particles trigger either excitation or de-excitation processes, with corresponding loss or gain of kinetic energy. After examining the main properties of the collision mechanism, the compressed Chapman}Enskog expansion procedure is applied to "nd the asymptotic equation when the collisions are dominant. A peculiarity of this inelastic process is that the collision operator has an in"nite dimensional null-space. On the hydrodynamic level this is re#ected in the small mean free path approximation being rather a family of di!usion equations than a single equation, as is the case in classical transport theory. Also the appropriate hydrodynamic quantity turns out to be di!erent from the standard macroscopic density.