Plasma dispersion function for a Fermi-Dirac distribution

Melrose, D B; Mushtaq, A

doi:10.1063/1.3528272

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Plasma dispersion function for a Fermi-Dirac distribution

Melrose, D B·Mushtaq, A

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Abstract

A plasma dispersion function (PDF) is defined for a nonrelativistic Fermi-Dirac distribution and its properties are explored. The degree of degeneracy is described by a parameter {xi}=e{sup {mu}}{sub e}{sup /T}{sub e}, for electrons, with {mu}{sub e}/T{sub e} large and negative in the nondegenerate limit, and large and positive in the completely degenerate limit. The PDF is denoted Z(y,{xi}), where the variable y={omega}/{radical}(2)kV{sub e}, is the argument of the conventional PDF, Z(y)=Z(y,0), for a Maxwellian distribution. In the completely degenerate limit, Z(y,{xi}) approaches a logarithmic function that depends on the Fermi temperature and is independent of T{sub e}. Analytic approximations to Z(y,{xi}) are derived in terms of polylogarithmic functions for y{sup 2}>>1 and for y{sup 2}<<1.

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70 PLASMA PHYSICS AND FUSION TECHNOLOGY 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS DISPERSION RELATIONS DISTRIBUTION FERMI STATISTICS ION ACOUSTIC WAVES ION WAVES PLASMA PLASMA WAVES

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Melrose, D B, Mushtaq, A. 2010-12-15. Plasma dispersion function for a Fermi-Dirac distribution. https://doi.org/10.1063/1.3528272

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