Transport Equations for Plasmas in Strong External Fields

Abstract

In an intense field plasma particles are much more strongly coupled to the field to each other, the motion of each particle depending on the strength and direction of the field rather than on its individual interactions with other particles. Pair and higher correlations become unimportant, and singlet superposition for the $n$-particle distribution function provides an excellent approximation. The singlet distribution function is then given by a Vlasov-type transport equation. This conjecture is proven correct on expanding the reduced Liouville equation in powers of a dimensionless field parameter, $\lambda =\frac{e}{E{\alpha }^2}$ (with $\alpha$ interpreted as an average approach distance), which expresses the ratio of the intensity of interparticle interactions to that of particle-field interactions; singlet superposition is then exact through terms linear in $\lambda$. A general closed hierarchy valid through any given power of $\lambda$ is derived: solution exact through ${\lambda }^m$ retains correlations through order $m$. Thus we see that, as the field becomes weaker, successively higher order correlations become important. Examples of the range of validity of the new treatment are given, and the lack of justification for the use of Boltzmann or Fokker-Planck type equations for microwave plasma diagnostics is briefly discussed, considering the low intensity of microwave beams, and thus the probable importance of pair and higher correlations.