Conditions for runaway phenomena in the kinetic theory of particle swarms

Abstract

The velocity distribution of a spatially uniform diluted guest population of charged particles moving within a host medium under the influence of a D. C. electric field is studied. A simplified one-dimensional Boltzmann model of the Kač type is adopted. Necessary conditions and sufficient conditions are established for the existence, uniqueness, and attractivity of a stationary non-negative distribution corresponding to a specified concentration level. Conditions for the onset of the runaway process are established.