On the Kinetic Equation for a High Temperature Plasma

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Abstract
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 follows, δ= 1.05{(e2/κT)3n}1/2. The damping factor γ is determined to be γ= 0.028{(e2/κT)3n}1/2(k/kd)2·ωp 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.

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