Analytical Evaluation of the Fully Relativistic Plasma Dispersion Function Using Binomial Expansion Theorems

2009 ◽  
Vol 37 (9) ◽  
pp. 1770-1773
Author(s):  
B.A. Mamedov
Keyword(s):  
Relativistic Plasma ◽  
Dispersion Function ◽  
Analytical Evaluation ◽  
Binomial Expansion ◽  
Plasma Dispersion

Generalized Trubnikov functions for unmagnetized plasmas

1999 ◽  
Vol 62 (2) ◽  
pp. 249-253 ◽  
Author(s):  
D. B. MELROSE
Keyword(s):  
Thermal Plasma ◽  
Thermal Plasmas ◽  
Relativistic Plasma ◽  
Dispersion Function ◽  
Recursion Relations ◽  
Relativistic Dispersion ◽  
Plasma Dispersion ◽  
Class Of Functions ◽  
Explicit Expressions

A class of relativistic dispersion functions for unmagnetized thermal plasmas is defined by generalizing functions first defined by Trubnikov in 1958. Recursion relations are derived that allow one to generate explicit expressions for the class of functions in terms of the relativistic plasma dispersion function T(z, ρ) introduced by Godfrey et al. in 1975. These functions are relevant to the description of the response of a weakly mangetized, highly relativistic, thermal plasma.

A Relativistic Plasma Dispersion Function

1975 ◽  
Vol 3 (2) ◽  
pp. 60-67 ◽  
Author(s):  
Brendan B. Godfrey ◽  
Barry S. Newberger ◽  
Keith A. Taggart
Keyword(s):  
Relativistic Plasma ◽  
Dispersion Function ◽  
Plasma Dispersion

New representations of dielectric tensor elements in magnetized plasma

1986 ◽  
Vol 35 (2) ◽  
pp. 319-331 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Functional Expression ◽  
Relativistic Plasma ◽  
Magnetized Plasma ◽  
Dispersion Function ◽  
Dielectric Tensor ◽  
Relativistic Case ◽  
Plasma Dispersion ◽  
Derivatives Of

Each of the dielectric tensor elements in a Maxwellian magnetoplasma is expressed in terms of various derivatives of a single functional expression. The relationships for all the elements are given, first for the general case of a relativistic plasma, then for the slightly relativistic case, and finally for the non-relativistic case, when the perpendicular wavenumber is either large or small. We also derive new relations useful for the computation of the slightly relativistic plasma dispersion function.

Expansions of the mildly relativistic dispersion function for nearly perpendicular electron cyclotron ray tracing

1999 ◽  
Vol 61 (1) ◽  
pp. 121-128 ◽  
Author(s):  
I. P. SHKAROFSKY
Keyword(s):  
Ray Tracing ◽  
Computer Programs ◽  
Higher Order ◽  
Electron Cyclotron ◽  
Dispersion Function ◽  
Relativistic Dispersion ◽  
Plasma Dispersion ◽  
Derivatives Of ◽  
Cyclotron Harmonic ◽  
Experienced Difficulty

To trace rays very close to the nth electron cyclotron harmonic, we need the mildly relativistic plasma dispersion function and its higher-order derivatives. Expressions for these functions have been obtained as an expansion for nearly perpendicular propagation in a region where computer programs have previously experienced difficulty in accuracy, namely when the magnitude of (c/vt)2 (ω−nωc)/ω is between 1 and 10. In this region, the large-argument expansions are not yet valid, but partial cancellations of terms occur. The expansion is expressed as a sum over derivatives of the ordinary dispersion function Z. New expressions are derived to relate higher-order derivatives of Z to Z itself in this region of concern in terms of a finite series.

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