Instantaneous joint distributions of ion microfield and its time derivatives and effects of dynamical friction in plasmas

The generalized joint simultaneous distribution of the electric microfield strength vector in plasmas and its time derivatives is presented. The results obtained consistently generalize the approach of Chandrasekhar and von Neuman to the problem of the temporal fluctuations of the plasma microfield, taking into account the complexity of the plasma composition and the screening by plasma electrons, the repulsion and the correlations between ions, and the plasma polarization. Analytical formulas for the universal functions describing the constraint moments of the first time derivative of the ion microfield are obtained on the basis of the Baranger-Mozer cluster expansion scheme. These results permit improvement in the theoretical approach to the ion dynamics effects based on the time expansion of the microfield, a theoretical basis for the inclusion of the microfield fluctuations due to the low-frequency collective plasma oscillations is developed. The results obtained modify the notion introduced by Chandrasekhar of the dynamical friction experienced by a test or radiating ion in plasmas over microscopic distances, if it has a nonzero velocity. These new contributions come from the totality of the effects considered, namely: the plasma composition; the repulsion and correlations of ions; screening by electrons and the neutralizing electron background; and low-frequency plasma oscillations.