Correlation-Function Method for the Evaluation of Plasma Transport Coefficients: The Self-Diffusion Coefficient

The first two terms in the density expansion of the autocorrelation-function expression for the self-diffusion coefficient of a fully ionized plasma are obtained. The expression for the self-diffusion coefficient $D$ is $D={\mathrm{}\left[A\right(T)\mathrm{}\rho \ln \rho +B(T\left)\mathrm{}\rho \right]}^{-1\mathrm{}}$ The technique employed is that due to Zwanzig and Kawasaki and Oppenheim, suitably modified to remove the divergences due to the long-range Coulombic interactions. The pertinent expansion parameter is the plasma parameter ${\left(4\mathrm{}\pi \rho {\beta }^3{e}^6\right)}^{\frac{1}{2}}$. The dynamical operators appearing in the final expression are the linearized Lennard-Balescu operator, a Fokker-Planck operator, and a Boltzmann operator with the Coulomb potential replaced by a Debye-Hückel potential. The technique is easily generalized to obtain density expansions of the other plasma transport coefficients.