Analytical Evaluation of the Plasma Dispersion Function Using Binomial Coefficients and Incomplete Gamma Functions

Abstract

Series expansions are obtained for a plasma dispersion function that appears in the description of smallamplitude waves in very hot plasmas. However, the numerical implementation of this function is required in diverse areas of physics and applied mathematics. An explicit representation for the plasma dispersion function is developed in terms of series of binomial coefficients and incomplete gamma functions. The series expansions obtained herein give a more accurate and efficient way to compute values for this integral over the entire permissible range of its parameters. The results of the calculations are compared with literature data as well as those obtained by different approximate method.

Analytical treatment of the force acting on a relativistic electron beam spreading in dense gas plasma by the ohmic plasma channel

“…(1), the choice of reliable formulas for the evaluation of the force expression F (G) (g, Y ch1 ) has prime importance in the accurate calculation of force exerted by the plasma currents on the beam. In order to establish expressions for the F (G) (g, Y ch1 ) we shall first consider the well-known binomial expansion theorems as follows [23,24]: ðx AE yÞ n ¼ …”

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