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Spherical harmonics and cartesian tensor scalar product expansions of the distribution function

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Czechoslovak Journal of Physics B Aims and scope

Abstract

On the basis of the expansion of the distribution function in a sum of the spherical harmonics, the distribution functionf(v, r, t) is expanded in a series of scalar products of two Cartesian tensors term by term, i.e.

The tensors

and ℱ(l) (l=2, 3) are constructed in dependence on the spherical harmonic expansion coefficients (the tensors

and ℱ(l) (l=0, 1) have been constructed by Jancel and Kahan [3]). On the basis of the knowledge of the analytic form off 2 andf 3 the equations forf 1 f 2 andf 3 for the case of the Boltzmann's equation are determined.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Czech Technical University, Prague

    B. Šesták

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  1. B. Šesták
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Technická 2, Praha 6, Czechoslovakia.

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Šesták, B. Spherical harmonics and cartesian tensor scalar product expansions of the distribution function. Czech J Phys 22, 243–263 (1972). https://doi.org/10.1007/BF01689612

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  • DOI: https://doi.org/10.1007/BF01689612

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