中国物理B ›› 2012, Vol. 21 ›› Issue (5): 55204-055204.doi: 10.1088/1674-1056/21/5/055204

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Analytical evaluation of the plasma dispersion function for a Fermi–Dirac distribution

B.A. Mamedov   

  1. Department of Physics, Faculty of Arts and Sciences, Gaziosmanpaşa University, Tokat, Turkey
  • 收稿日期:2011-09-12 修回日期:2012-04-27 出版日期:2012-04-01 发布日期:2012-04-01

Analytical evaluation of the plasma dispersion function for a Fermi–Dirac distribution

B.A. Mamedov†   

  1. Department of Physics, Faculty of Arts and Sciences, Gaziosmanpaşa University, Tokat, Turkey
  • Received:2011-09-12 Revised:2012-04-27 Online:2012-04-01 Published:2012-04-01

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摘要： An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi--Dirac distribution is proposed. The new method has been developed using the binomial expansion theorem and the Gamma functions. The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency. The obtained results for the plasma dispersion function are in good agreement with the known numerical data.

关键词: Fermi--Dirac distribution, plasma dispersion function, binomial coefficients, incomplete gamma functions

Abstract: An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi--Dirac distribution is proposed. The new method has been developed using the binomial expansion theorem and the Gamma functions. The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency. The obtained results for the plasma dispersion function are in good agreement with the known numerical data.

Key words: Fermi--Dirac distribution, plasma dispersion function, binomial coefficients, incomplete gamma functions

中图分类号:  (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))

  • 52.35.Mw
52.25.Dg (Plasma kinetic equations) 52.27.-h (Basic studies of specific kinds of plasmas)