EVALUATION OF THE MODIFIED PLASMA DISPERSION FUNCTION FOR HALF-INTEGRAL INDEXES

Space and astrophysical plasmas typically possess particle distributio n functions with a power-law tail (in energy) that are well modeled by generalized Lorentzian distributions with an associated spectral inde x kappa. Dispersion equations for linear waves of any mode in a plasma described by a Lorentzian-type particle distribution involve the modi fied plasma dispersion function Z(kappa), a special function analogou s to the plasma dispersion function Z that arises when the particle di stribution is Maxwellian. The function Z(kappa), originally defined b y Summers and Thorne [Phys. Fluids B 3, 1835 (1991)] for integral valu es of kappa, was recently generalized to real values of kappa by Mace and Hellberg [Phys. Plasmas 2, 2098 (1995)]. In the present paper, a g eneral formula is derived for the modified plasma dispersion function Z(kappa) corresponding to half-integral values of kappa, and simple, explicit closed-form expressions are given for the functions Z(3/2), Z(5/2), Z(7/2)*, Z(9/2)*, and Z(11/2)*. These results complement the simple, closed-form expressions for the functions Z(kappa), for kappa =1, 2, 3,..., that already exist in the literature. (C) 1996 American Institute of Physics.