Kinetic Equations and Fluctuations in μ Space of One-Component Dilute Plasmas

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Kinetic equations for a spatially coarse-grained electron density in μ phase space A(p,r; t) with a length cutoff b and for its fluctuations are studied by a scaling method and a time-convolutionless approach developed by the present authors. An electron gas with a small plasma parameter ε≡l/cλ_D^3 has three characteristic lengths; the Landau cutoff γ_L≡ελ_D,the Debye length λ_D≡√<k_BT/4πe^2c> and the mean free path l_f≡λ_D/ε, e and c being electronic charge and mean electron density, respectively. It is shown that there are two characteristic regions of the length cutoff b. One is a coherent region where r_L≪b≪λ_D. Its characteristic scaling is c→0, b→∞, t→∞, with b√<c> and t√<c> being kept constant. The Vlasov equation is derived in this limit. The other is a kinetic region where λ_D≪b≪l_f. Its characteristic scaling is c→0, b→∞, t→∞ with bc and tc being kept constant. The Vlasov term disappears and the Balescu-Lenard-Boltzmann-Landau equation, which is free of divergence for both close and distant collisions, is derived in this limit. It is shown that the fluctuations of A(p, r; t) obey a Markov process with scaling exponents α=0, β=1/2 in the coherent region near thermal equilibrium, while they obey a Gaussian Markov process with α=0, β=1 in the kinetic region. The present theory does not need the factorization ansatz and Bogoliubov's functional ansatz.
理論物理学刊行会の論文
1977-07-25

Kinetic Equations and Fluctuations in μ Space of One-Component Dilute Plasmas

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