Evaluation of the modified plasma dispersion function for half-integral indices
- Radio Atmospheric Science Center, Kyoto University, Uji, Kyoto 611 (Japan)
- Department of Atmospheric Sciences, University of California at Los Angeles, Los Angeles, California 90095 (United States)
Space and astrophysical plasmas typically possess particle distribution functions with a power-law tail (in energy) that are well modeled by generalized Lorentzian distributions with an associated spectral index {kappa}. Dispersion equations for linear waves of any mode in a plasma described by a Lorentzian-type particle distribution involve the modified plasma dispersion function {ital Z}{sub {kappa}}{sup {asterisk}}, a special function analogous to the plasma dispersion function {ital Z} that arises when the particle distribution is Maxwellian. The function {ital Z}{sub {kappa}}{sup {asterisk}}, originally defined by Summers and Thorne [Phys. Fluids B {bold 3}, 1835 (1991)] for integral values of {kappa}, was recently generalized to real values of {kappa} by Mace and Hellberg [Phys. Plasmas {bold 2}, 2098 (1995)]. In the present paper, a general formula is derived for the modified plasma dispersion function {ital Z}{sub {kappa}}{sup {asterisk}} corresponding to half-integral values of {kappa}, and simple, explicit closed-form expressions are given for the functions {ital Z}{sub 3/2}{sup {asterisk}}, {ital Z}{sub 5/2}{sup {asterisk}}, {ital Z}{sub 7/2}{sup {asterisk}}, {ital Z}{sub 9/2}{sup {asterisk}}, and {ital Z}{sub 11/2}{sup {asterisk}}. These results complement the simple, closed-form expressions for the functions {ital Z}{sub {kappa}}{sup {asterisk}}, for {kappa}=1, 2, 3,..., that already exist in the literature. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 285569
- Journal Information:
- Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 7 Vol. 3; ISSN PHPAEN; ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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