Prog. Theor. Phys. Vol. 24 No. 5 (1960) pp. 1083-1108
On the Kinetic Equation for a High Temperature Plasma
Department of Physics, College of Science and Engineering, Nihon University, Chiyoda-ku, Tokyo
(Received July 4, 1960)
Effects of binary and ternary correlations in a high temperature
plasma are examined in detail on the basis of the so-called B-B-G-K-Y
equation for a system of charged particles. It is shown that the
effects of ternary correlation are essential in giving rise to
shielding of the interaction between particles and have important
influences upon disturbances of the binary correlations. The effects
of binary correlation can be divided into the correction terms of the
self-consistent field of the Boltzmann-Vlasov equation and the terms
representing the collision effects between particles through the
shielded interaction. The effects of the collision terms are
investigated in detail by deriving a generalized Fokker-Planck
equation which can be reduced to the equation derived by Tchen for a
special case. The effects of the correction terms of the
self-consistent field are examined by deriving an equation of motion
of the density fluctuation which describes the longitudinal plasma
oscillations. The correction terms give rise to a shift of the
κ2-term of the plasma frequency and a damping factor. The
frequency of the plasma oscillations is determined to be given by
ω2 = ωp2+(1+δ)(3κT/m)k2
where the shift due to the binary correlations δ is given as
The damping factor γ is determined to be
at the limit of k →0. It is shown that the damping factor due to the long-range binary correlations predominates over the Landau damping in the range of small value of k. On the basis of present investigation, it is concluded that the equation derived by Balescu does not involve any information concerning the plasma oscillations. Since the plasma oscillations are nothing but the appearance of periodical spatial inhomogeneity in the system, it is evident that the assumption of the spatial homogeneity introduced by Temko, Tchen and Balescu in their derivations of the fundamental equations rules out the possible occurrence of the plasma oscillation.
DOI : 10.1143/PTP.24.1083
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Citing Article(s) :
Progress of Theoretical Physics Vol. 25 No. 5 (1961) pp. 843-845
The Kinetic Equation for Plasmas and Its Solution
Progress of Theoretical Physics Vol. 28 No. 2 (1962) pp. 265-282
Transport Coefficients of Quantum Plasma
Progress of Theoretical Physics Vol. 28 No. 5 (1962) pp. 946-948
On the Mode-Coupling Damping of Plasma Oscillations
Kenya Matsuura and Kiyoshi Ogawa
Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 1077-1092
Sum-Rule Analysis of Long-Wavelength Excitations in Electron Liquids
Setsuo Ichimaru, Hiroo Totsuji, Toshio Tange and David Pines