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Chin. Phys. B, 2012, Vol. 21(5): 055204    DOI: 10.1088/1674-1056/21/5/055204
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES Prev   Next  

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

B.A. Mamedov
Department of Physics, Faculty of Arts and Sciences, Gaziosmanpaşa University, Tokat, Turkey
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.
Keywords:  Fermi--Dirac distribution      plasma dispersion function      binomial coefficients      incomplete gamma functions  
Received:  12 September 2011      Revised:  27 April 2012      Accepted manuscript online: 
PACS:  52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))  
  52.25.Dg (Plasma kinetic equations)  
  52.27.-h (Basic studies of specific kinds of plasmas)  

Cite this article: 

B.A. Mamedov Analytical evaluation of the plasma dispersion function for a Fermi–Dirac distribution 2012 Chin. Phys. B 21 055204

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