Abstract
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 acceleration field is studied. After a short review of the literature on runaway phenomenon, the mathematical definitions of drift velocity and runaway phenomenon based on the distribution function are given. The linear Boltzmann equation in a three-dimensional spatially homogeneous system is considered. Under suitable conditions on the acceleration field and on the collision frequency, the existence of asymptotic operators is proven in a three-dimensional setting. Then wave operators are introduced and are used to characterize the long-time behavior of the solutions. Finally, using such operators the long-time behavior of the drift velocity is estimated.
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