 98308 J. L.Lebowitz, A. Rokhlenko
 Hydrodynamical Equation for Electron Swarms
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Apr 27, 98

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Abstract. We study the long time behavior of light particles, e.g.\ an electron swarm
in which Coulomb interactions are unimportant, subjected to an external
field and elastic collisions with an inert neutral gas. The time evolution
of the velocity and position distribution function is described by a
linear Boltzmann equation (LBE). The small ratio of electron to neutral
masses, $\epsilon$, makes the energy transfer between them very
inefficient. We show that under suitable scalings the LBE reduces, in the
limit $\epsilon \to 0$, to a formally exact equation for the
speed (energy) and position distribution of the electrons which
contains mixed spatial and speed derivatives. When the system is spatially
homogeneous this equation reduces to and thus justifies, for $\epsilon$
small enough, the commonly used ``twoterm'' approximation.
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