The Boltzman equation theory of charged particle transport
Abstract
The construction of a formally exact Kubo-like response theory equivalent to the Boltzmann equation theory of charged particle transport in a neutral medium is presented. This response theory provides the general wavevector and time-dependent velocity distribution at any time in terms of an initial distribution function, to which is added the response induced by a generalized perturbation over the intervening time. The usual Kubo linear response result for the distribution function is found to be recovered by choosing the initial velocity distribution to be Maxwellian. An exponential convergence function is introduced into the response time integral for completeness. This is equivalent to employing a modified Boltzmann equation, although the general form of the transport theory is not changed. It is shown that the modified transport theory can be used successfully where possible convergence difficulties occur in numerical solutions of the Boltzmann equation.
- Publication:
-
Australian Journal of Physics
- Pub Date:
- 1983
- DOI:
- 10.1071/PH830163
- Bibcode:
- 1983AuJPh..36..163M
- Keywords:
-
- Boltzmann Transport Equation;
- Charged Particles;
- Distribution Functions;
- Transport Theory;
- Convergence;
- Green'S Functions;
- Iterative Solution;
- Time Dependence;
- Velocity Distribution;
- Thermodynamics and Statistical Physics