On quantum effects in the theory of conductivity of fully ionized quasiclassical plasma
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On Quantum Effects in the Theory of Conductivity of Fully Ionized Quasiclassical Plasma V. B. Bobrov and S. A. Trigger Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya ul. 13/19, Moscow, 125412 Russia Received January 21, 2010; in final form, March 13, 2010
Abstract—A study is made of the static conductivity of a fully ionized plasma in a parameter range where the effect of electron–electron collisions can be ignored. It is shown that a convergent expression for the static conductivity of a fully ionized, weakly nonideal plasma in the range of large wave vectors can be obtained from a quantum statistical description of correlation functions, without using an artificial truncation procedure. DOI: 10.1134/S1063780X10090060
1. INTRODUCTION One of the familiar problems in the kinetic theory of a fully ionized plasma is the Coulomb divergence of collision integrals at large wave vectors transferred (or equivalently, at small distances between the particles) in the description of a classical plasma (see, e.g., [1]). This, in turn, leads to a similar divergence in calculat ing the frequency of electron–electron collisions in order to determine the static conductivity of a classical plasma. At present, the problem is resolved by repre senting the collision integrals for such a plasma as a combination of Boltzmann and Lenard–Balescu inte grals (see, e.g., [1–3]). An important point in this approach is that the result should be classical: it should not contain Planck’s constant. In our opinion, how ever, it is questionable that such combinations of colli sion integrals can be used for a plasma as a system of particles undergoing Coulomb interactions. Note that, at small wave vectors transferred (large interparticle distances), the divergence of collision integrals is eliminated by taking into account screen ing effects, in which case perturbation theory (the Born approximation, which is in essence quantum) can be used. In this way, possible quantum effects are accounted for by assuming that the particles are iden tical, an assumption that is not of fundamental impor tance in ensuring the divergence in the range of small wave vectors and in describing a quasiclassical plasma. Hence, it is the range of small wave vectors transferred to which the classical description of a plasma with the corresponding thermodynamic parameters is certainly applicable. At the same time, in the range of large wave vectors (small interparticle distances), the effects of interac tion via the Coulomb potential should be accounted for as fundamentally quantum ones. It is for this rea son that, in numerical experiments and computer sim ulations, a classical plasma is described not by the
Coulomb electron–ion interaction potential but by model pseudopotentials that are finite at small dis tances and differ radically from the Coulomb potential (see, e.g., [4, 5]). It is also necessary to take into account the fact that, for Coulomb systems, expan sions in integer powers of the density are impossib
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