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  • Title: Coulomb expansion: analytical solutions.
    Author: Ivlev AV.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2013 Feb; 87(2):025102. PubMed ID: 23496647.
    Abstract:
    Exact and approximate analytical solutions are presented, describing expansion of a cloud of charged particles in one, two, and three dimensions (assuming the planar, axial, and spherical symmetries, respectively). The expansion occurs in a gas or dilute plasma, where the screening is unimportant, so that particles interact with each other via Coulomb repulsive forces. It is shown that, irrespective of dimensionality, the density distribution remains homogeneous across the cloud and the velocity increases linearly towards the cloud boundary. The density evolution obeys a universal dependence, asymptotically decreasing with time as t(-1). It is also shown that in the presence of an inhomogeneous external field the interparticle repulsion becomes negligible at an early stage of expansion and then the density decreases with time exponentially.
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