New formulation of noise in collision-free systems. III

Abstract

The problem of velocity fluctuations in collision-free systems is usually solved by introducing the concept of phase-space density and treating the corresponding position and velocity variables as random variables. It is shown that in order to account for density as well as velocity fluctuations the probabilistic content of the analysis must be enlarged and the phase-space density itself must be treated as a random function with position and velocity as parameters. This generalization makes it possible to retain the highly non-linear character of interaction between electric fields and charged particles (space-charge effects) ; consequently the method is particularly welt suited to the treatment of very shallow minima, where the usual perturbation procedures tend to break down. Also the method appears to be capable of extension to the analysis of crosaed-field systems. As an example the analysis of noise in thermionic diodes has been carried out in some detail. The numerical results appear to be in closer...