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The runaway effect in a Lorentz gas

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Abstract

The Lorentz gas of charged particles in a constant and uniform electric field is studied. The gas flows through the medium of immobile, randomly distributed scatterers. Particles with velocity v suffer collisions with frequency proportional to ¦v¦n. Forn < 0 runaway of the gas is forced by the field: the mean velocity of the flow increases without bounds. By a simple physical argument an integral relation is established between the probability of collisionless motion and the velocity distribution. It is then shown that whenn < −1 a fraction of particles moves as if the scattering centers were absent. The detailed discussion of this uncollided runaway is presented. Some qualitative features of the velocity distribution are illustrated on rigorous solutions in one dimension.

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Warsaw, Warsaw, Poland

    J. Piasecki

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  1. J. Piasecki
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Piasecki, J. The runaway effect in a Lorentz gas. J Stat Phys 24, 45–58 (1981). https://doi.org/10.1007/BF01007634

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  • DOI: https://doi.org/10.1007/BF01007634

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