On the kinetic theory of stable and weakly unstable plasma. Part 1

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Abstract
A kinetic theory is presented which is valid for both weakly unstable and stable plasma. The theory corrects the conventional Balescu—Guernsey—Lenard description for the weakly stable portions of the fluctuation spectrum. The theory is no longer Markoffian in the distribution function F alone but is in the pair F and Ik the spectrum of fluctuations. Further the evolution in time from an initially weakly unstable distribution to the stable regime can be described. Even after passage into the stable state the fluctuations can be large nd lead to enhanced diffusion across a magnetic field. The coefficient of spatial diffusion is given in this weakly stable (or untable) state. A strong coupling is found between plasmons and the particles in the distribution with velocities near the phase velocities of the plasmons. There is only weak thermal contact between the plasmons and these particles with the main body of the distribution whenever certain nonlinear processes are of secondary importance.