ASYMPTOTIC SCATTERING OPERATORS AND DRIFT VELOCITY IN CHARGED-PARTICLE TRANSPORT PROBLEMS

In this article the long-time behavior of the evolution of one species of charged particles in a neutral gas under the influence of an accel eration field is studied. After a short review of the literature on ru naway phenomenon, the mathematical definitions of drift velocity and r unaway phenomenon based on the distribution function are given. The li near Boltzmann equation in a three-dimensional spatially homogeneous s ystem is considered. Under suitable conditions on the acceleration fie ld and on the collision frequency, the existence of asymptotic operato rs is proven in a three-dimensional setting. Then wave operators are i ntroduced and are used to characterize the long-time behavior of the s olutions. Finally, using such operators the long-time behavior of the drift velocity is estimated.