Pair Correlation Function and Nonlinear Kinetic Equation for a Spatially Uniform Polarizable Nonideal Plasma

Abstract

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. [S0031-9007 (96)00077-4] PACS numbers: 52.25.Dg, 05.20.Dd The importance of the polarization effects on plasmas in the kinetic regime has been recognized for a long time. A first attempt to include these effects in the linearized collisional integral was made by Gasirowicz, Neuman, and Riddell [1]. Later, the nonlinear equation for weakly coupled polarizable plasma was derived by Balescu [2] with the help of Prigogine's diagram techniques [3] and by Lenard [4] who solved the Bogoliubov equation [5] for the pair correlation function in the plasma approximation. These results were generalized to the quantum case by Konstantinov and Perel [6] and by Wyeld and Pines [7]. Kadanoff and Baym [8] and Klimontovich [9]have noticed that the Balescu-Lenard (BL) equation takes into account the polarization of the system only in the collision integral while the thermodynamics corresponds to the ideal gas; the dissipative and nondissipative phenomena are not treated on an equal footing. They have shown that this discrepancy can be avoided if non-Markovian effects are taken into account. This means that Bogoliubov's condition [5] of the total synchronization of all correlation functions with the one-particle distribution function (df ) must be omitted. Klimontovich [10] wrote the system of equations for the one-particle df and the pair correlations for the electric field and for the charge density, but he did not solve the equation for the pair correlation function and thus did not obtain a closed kinetic equation. On the other hand, Résibois [11] and Dorfman and Cohen [12] have formally derived the fully non-Markovian generalization of the BL equation, but their results are not easily tractable in a practical case. In particular, they did not give the explicit expression for the correlation energy.In this Letter we solve, in the plasma approximation, the equation for the pair correlation function considering the first non-Markovian correction. In this way, we obtain a nonlinear kinetic equation which generalizes the BL equation for weakly nonideal plasma. This equation, which includes the dynamical screening of the interaction potential, describes correctly the conservation of the total energy in a nontrivial way.The non-Markovian correction, which is responsible for the offset of the variation of kinetic energy by the variation of potential energy, is of order g 2 , where g is the plasma parameter, while the BL collision integral, which is the Markovian contribution in the plasma approximation, is of order g. The BL approximation is thus consistent with the conservation of kinetic energy without potential energy. However, Markovian contribution...

Strong-coupling effects in the relaxation dynamics of ultracold neutral plasmas

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Exchange Correlation of Particles and Quantum Collision Integral in a Non‐Ideal Plasma with Polarization

“…possess the quantum symmetry properties: P (12)f ab (12) = f ab (12)P (12) etc., whereas the density matrices f ab (12) etc. possess only the classical symmetry properties: P (12)f ab (12)P (12) = f ab (12) etc. For the classically symmetric density matrices the usual conditions for disentanglement of equations hold, which are the same as those in the classical statistics.…”

“…The density matrices f ab (12) etc. possess the quantum symmetry properties: P (12)f ab (12) = f ab (12)P (12) etc., whereas the density matrices f ab (12) etc.…”