Statistical mechanics of dense ionized matter. V. Hydrodynamic limit and transport coefficients of the classical one-component plasma

The static and dynamical correlations of density fluctuations in a classical one-component plasma (OCP) were studied in the framework of thermodynamic fluctuation theory and linearized hydrodynamics. First it is shown that the fluctuations of the local electric field stabilize the OCP against density fluctuations, even when the compressibility becomes negative for GAMMA approximately-greater-than 3, where GAMMA is the usual plasma coupling parameter. Then, following closely the work of Mountain, the dynamical structure factor in the hydrodynamic limit is calculated and the thermal Rayleigh peak is shown to vanish in the long-wavelength limit, in agreement with recent molecular dynamics results. The shear and bulk viscosity coefficients eta and zeta are calculated for large GAMMA in the framework of the ''generalized hydrodynamics'' formalism, using the known short-time expansion of the correlation functions. The coefficient eta is found to exhibit a minimum as a function of GAMMA and zeta is found to be negligible compared to eta in the OCP