A New Derivation of the Kinetic Equation for an Inhomogeneous Plasma

1966 ◽  
Vol 7 (12) ◽  
pp. 2211-2216 ◽  
Author(s):  
A. Kuszell
Keyword(s):  
Kinetic Equation ◽  
Inhomogeneous Plasma

KINETIC EQUATION DESCRIBING IRREVERSIBLE PROCESSES IN IONIZED GASES, II

1963 ◽  
Vol 41 (7) ◽  
pp. 1193-1225
Author(s):  
R. L. Rosenberg ◽  
Ta-You Wu
Keyword(s):  
Kinetic Equation ◽  
Inhomogeneous Plasma ◽  
Effective Field ◽  
Collision Integral ◽  
Spatial Inhomogeneity ◽  
Irreversible Processes ◽  
First Order ◽  
Spatially Inhomogeneous ◽  
The Fourier Transform ◽  
The One

In a previous paper, the authors formulated the theory of irreversible processes in a spatially inhomogeneous plasma on the basis of Bogoliubov's theory as extended by Guernsey and Uhlenbeck. The kinetic equation, in terms of g(κ, n, t), the Fourier transform of the spatially inhomogeneous part f(r, n, t) of the one-particle distribution function F(r, n, t), has been obtained to the first order in 4πe2, all orders in (4πe2/ν), and the first order in κ which is related to the spatial inhomogeneity. In the present work, the mathematical part of the previous paper, especially the expansion in various orders in κ, has been revised. The kinetic equation is given in (33), in which are exhibited: (a) the stream term; (b) the corrections to the stream term arising from the "collisions"; (c) the Vlasov term; (d) the corrections, in the zeroth and the first order in κ, to the Vlasov term depending not only on the "static" effective field but also on the divergence of the mean current, these corrections being momentum-dependent and time-irreversible in nature; (e) the main "collision integral" which is time-irreversible, in the zeroth and the first order in κ.

ON THE ASYMPTOTIC KINETIC EQUATION FOR INHOMOGENEOUS PLASMAS

1967 ◽  
Vol 45 (1) ◽  
pp. 179-202 ◽  
Author(s):  
Ralph L. Guernsey
Keyword(s):  
Kinetic Equation ◽  
Initial Value Problem ◽  
Inhomogeneous Plasma ◽  
Pair Correlation ◽  
Initial Value

The equations for the pair correlation of a slightly inhomogeneous plasma obtained under two different forms of Bogolubov's assumptions are solved and the results are shown to be identical. The results are then compared with the corresponding result for the initial value problem. The contribution of the latter to the kinetic equation is shown to relax slowly [Formula: see text] to the asymptotic (in the sense of Bogolubov) result. The present result differs from that of Wu and Rosenberg, who appear to have linearized their equations improperly.

Kinetic equation for an inhomogeneous plasma in a magnetic field

1968 ◽  
Vol 48 (2) ◽  
pp. 221-236 ◽  
Author(s):  
O De Barbieri ◽  
E Montaldi ◽  
R.L Guernsey
Keyword(s):  
Magnetic Field ◽  
Kinetic Equation ◽  
Inhomogeneous Plasma

Deep Impurities with Collision Delay

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Wave Function ◽  
Kinetic Equation ◽  
Elastic Scattering ◽  
Response Function ◽  
Plasma Oscillation ◽  
Impurity Scattering ◽  
Fermi Momentum ◽  
Screening Length ◽  
Plasma Mode ◽  
Dissipative Mechanism

The linearised nonlocal kinetic equation is solved analytically for impurity scattering. The resulting response function provides the conductivity, plasma oscillation and Fermi momentum. It is found that virial corrections nearly compensate the wave-function renormalizations rendering the conductivity and plasma mode unchanged. Due to the appearance of the correlated density, the Luttinger theorem does not hold and the screening length is influenced. Explicit results are given for a typical semiconductor. Elastic scattering of electrons by impurities is the simplest but still very interesting dissipative mechanism in semiconductors. Its simplicity follows from the absence of the impurity dynamics, so that individual collisions are described by the motion of an electron in a fixed potential.

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