Premium
Zur statistischen Theorie der Diffusion geladener Teilchen
Author(s) -
Ebeling Werner
Publication year - 1967
Publication title -
beiträge aus der plasmaphysik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0005-8025
DOI - 10.1002/ctpp.19670070103
Subject(s) - charged particle , physics , ambipolar diffusion , distribution function , diffusion , particle (ecology) , langevin equation , correlation function (quantum field theory) , anomalous diffusion , diffusion equation , classical mechanics , statistical physics , thermodynamics , quantum mechanics , plasma , ion , knowledge management , oceanography , innovation diffusion , economy , service (business) , computer science , dielectric , economics , geology
A diffusion equation for a charged particle in an oscillating electric field is derived. We start with the Liouville equation for the distribution function of the whole system consisting of the host fluid and the charged particle. In order to obtain the time evolution of the distribution function of the charged particle in the coordinate space we utilize the technique of projection operators developed by Zwanzig. We find frequency‐ independent diffusion coefficients D = ζ(0) and frequency‐dependent mobilities B = ζ(ω)/ kT . in terms of the correlation functionHere ζ is the microscopic velocity of the charged particle and the average is over the equilibrium distribution function of the fluid in the presence of this charged particle. Under appropriate circumstances the correlation function ζ (omega;) may be computed by means of the Langevin‐Kirkwood equation. The relation between our theory and that obtained by Lebowitz and Resibois is discussed. We further show that at higher concentrations of charged particles the gradient of the concentration must be replaced by the gradient of the local osmotic pressure. The theory is applied to ambipolar diffusion.