scholarly journals Dispersion in a Relativistic Quantum Electron Gas. I. General Distribution Functions

1984 ◽  
Vol 37 (6) ◽  
pp. 615 ◽  
Author(s):  
Leith M Hayes ◽  
DB Melrose
Keyword(s):  
Relativistic Electron ◽  
Occupation Number ◽  
Relativistic Quantum ◽  
Electron Gas ◽  
Distribution Functions ◽  
Quantum Limit ◽  
General Distribution ◽  
Electron Positron ◽  
Quantum Electron ◽  
Plasma Dispersion

The covariant response tensor for a relativistic electron gas is calculated in two ways. One involves introducing a four-dimensional generalization of the electron-positron occupation number, and the other is a covariant generalization of a method due to Harris. The longitudinal and transverse parts are. evaluated for an isotropic electron gas in terms of three plasma dispersion functions, and the contributions from Landau damping and pair creation to the dispersion curve are identified separately. The long-wavelength limit and the non-quantum limit, with first quantum corrections, are found. The plasma dispersion functions are evaluated explicitly for a completely degenerate relativistic electron gas, and a detailed form due to Jancovici is reproduced.

scholarly journals Dispersion in a Relativistic Quantum Electron Gas. II. Thermal Distributions

1984 ◽  
Vol 37 (6) ◽  
pp. 639 ◽  
Author(s):  
DB Melrose ◽  
Leith M Hayes
Keyword(s):  
Quantum Theory ◽  
Relativistic Quantum ◽  
Electron Gas ◽  
Phase Speed ◽  
Standard Technique ◽  
Quantum Limit ◽  
Response Functions ◽  
Relativistic Quantum Theory ◽  
Thermal Electron ◽  
Quantum Electron

The dispersion functions which appear when the response of a non-degenerate thermal electron gas is treated using a relativistic quantum theory are shown to be the same as the functions which appear in the non-quantum limit. These functions are evaluated at two speeds V1 and V2 which in the non-quantum limit reduce to the phase speed ca/I k I. It is shown that the effects of partial degeneracy may be included by expanding about the non-degenerate limit, and the expansion of the response functions is given explicitly. It is also pointed out that thermal corrections to the completely degenerate limit may be included using a standard technique and the lowest order corrections are given.

MAGNETIC SUSCEPTIBILITY OF THE RELATIVISTIC ELECTRON GAS

1999 ◽  
Vol 13 (26) ◽  
pp. 3133-3147 ◽  
Author(s):  
LAUREAN HOMORODEAN
Keyword(s):  
Magnetic Susceptibility ◽  
Relativistic Electron ◽  
Electron Gas ◽  
Electron Gases ◽  
Magnetic Susceptibilities ◽  
Electron Positron

The magnetic susceptibilities of the degenerate and nondegenerate relativistic electron gases, and of the nondegenerate electron–positron gas are presented.

scholarly journals Derivation of the Quantum Vlasov Equation and Dispersion Relation of a Relativistic Electron Gas

1967 ◽  
Vol 22 (6) ◽  
pp. 869-872 ◽  
Author(s):  
D. BlSkamp
Keyword(s):  
Dispersion Relation ◽  
Relativistic Electron ◽  
Vlasov Equation ◽  
Thermal Equilibrium ◽  
Electron Gas ◽  
Quasi Equilibrium ◽  
Electron Positron ◽  
The One ◽  
Special Case ◽  
Quantum Vlasov Equation

The selfconsistent field equation (VLASOV equation) is derived for the one-particle WIGNER function of a relativistic electron-positron gas. From the linearized form we obtain the dispersion relation for any quasi-equilibrium state, which for the special case of thermal equilibrium has already been derived by TSYTOVICH 1.

Physical interpretation of the Padé approximation of the plasma dispersion function

2000 ◽  
Vol 64 (3) ◽  
pp. 287-296 ◽  
Author(s):  
ANDERS TJULIN ◽  
ANDERS I. ERIKSSON ◽  
MATS ANDRÉ
Keyword(s):  
Distribution Function ◽  
Physical Interpretation ◽  
Distribution Functions ◽  
Padé Approximant ◽  
General Distribution ◽  
Dispersion Function ◽  
Complex Velocity ◽  
Pade Approximant ◽  
Maxwellian Plasma ◽  
Plasma Dispersion

It is shown that using Padé approximants in the evaluation of the plasma dispersion function Z for a Maxwellian plasma is equivalent to the exact treatment for a plasma described by a ‘simple-pole distribution’, i.e. a distribution function that is a sum of simple poles in the complex velocity plane (v plane). In general, such a distribution function will have several zeros on the real v axis, and negative values in some ranges of v. This is shown to be true for the Padé approximant of Z commonly used in numerical packages such as WHAMP. The realization that an approximation of Z is equivalent to an approximation of f(v) leads the way to the study of more general distribution functions, and we compare the distribution corresponding to the Padé approximant used in WHAMP with a strictly positive and monotonically decreasing approximation of a Maxwellian.

scholarly journals Relativistic Quantum Response of a Strongly Magnetised Plasma. I. Mildly Relativistic Electron Gas

1992 ◽  
Vol 45 (2) ◽  
pp. 131 ◽  
Author(s):  
WEP Padden
Keyword(s):  
Relativistic Electron ◽  
Cyclotron Frequency ◽  
Relativistic Quantum ◽  
Quantum Plasma ◽  
Plasma Dynamics ◽  
X Ray ◽  
Analytic Expressions ◽  
Graphical Technique ◽  
Plasma Dispersion ◽  
Wave Properties

Approximate analytic expressions are derived for the linear response 4-tensor of a strongly magnestised, mildly relativistic electron plasma. The results are obtained within the framework of quantum plasma dynamics, thus the response contains relativistic and quantum effects that are essential in a super-strong magnetic field. The response is obtained in terms of relativistic plasma dispersion functions known as Shkarofsky functions. These functions allow the wave properties of the plasma to be studied without resorting to complicated numerical schemes. The response derived is valid for radiation with frequency up to about the cyclotron frequency and is of use in the theory of spectra formation in X-ray pulsars. In addition, a simple graphical technique is introduced that allows one to visually locate the roots of the resonant denominator occurring in the response, as well as determine the conditions under which both roots are valid and contribute to absorption.

Quantum plasmadynamics: role of the electron self-energy and the vertex correction

1996 ◽  
Vol 56 (1) ◽  
pp. 95-105 ◽  
Author(s):  
D. B. Melrose ◽  
S. J. Hardy
Keyword(s):  
Ponderomotive Force ◽  
Relativistic Quantum ◽  
Electron Gas ◽  
Vertex Correction ◽  
Radiative Corrections ◽  
Self Energy ◽  
New Class ◽  
Quantum Electron ◽  
Vacuum Polarization Tensor

The linear response 4-tensor for a relativistic quantum electron gas may be calculated by reinterpreting the electron propagator in the expression for the vacuum polarization tensor as statistical averages over the electron gas. We apply a similar procedure to two other radiative corrections: the electron self-energy and the vertex correction. When the photon propagator in these expressions is interpreted as a statistical average over a distribution of waves in the medium, these radiative corrections lead to a relativistic quantum expression for the ponderomotive force and to a new class of ‘hybrid’ emission processes.

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