Journal cover Journal topic
Annales Geophysicae An open-access journal of the European Geosciences Union
Ann. Geophys., 35, 683-690, 2017
https://doi.org/10.5194/angeo-35-683-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
ANGEO Communicates
24 May 2017
Causal kinetic equation of non-equilibrium plasmas
Rudolf A. Treumann1,2 and Wolfgang Baumjohann3 1Department of Geophysics and Environmental Sciences, Ludwig-Maximilians-Universität München, Munich, Germany
2International Space Science Institute Bern, Bern, Switzerland
3Space Research Institute, Austrian Academy of Sciences, Graz, Austria
Abstract. Statistical plasma theory far from thermal equilibrium is subject to Liouville's equation, which is at the base of the BBGKY hierarchical approach to plasma kinetic theory, from which, in the absence of collisions, Vlasov's equation follows. It is also at the base of Klimontovich's approach which includes single-particle effects like spontaneous emission. All these theories have been applied to plasmas with admirable success even though they suffer from a fundamental omission in their use of the electrodynamic equations in the description of the highly dynamic interactions in many-particle conglomerations. In the following we extend this theory to taking into account that the interaction between particles separated from each other at a distance requires the transport of information. Action needs to be transported and thus, in the spirit of the direct-interaction theory as developed by Wheeler and Feynman (1945), requires time. This is done by reference to the retarded potentials. We derive the fundamental causal Liouville equation for the phase space density of a system composed of a very large number of charged particles. Applying the approach of Klimontovich (1967), we obtain the retarded time evolution equation of the one-particle distribution function in plasmas, which replaces Klimontovich's equation in cases when the direct-interaction effects have to be taken into account. This becomes important in all systems where the distance between two points |Δq| ∼ ct is comparable to the product of observation time and light velocity, a situation which is typical in cosmic physics and astrophysics.

Citation: Treumann, R. A. and Baumjohann, W.: Causal kinetic equation of non-equilibrium plasmas, Ann. Geophys., 35, 683-690, https://doi.org/10.5194/angeo-35-683-2017, 2017.
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We extend the Klimontovich (1967) formulation of kinetic theory of the evolution of the microscopic phase space density to taking into account that the interaction between particles separated from each other at a distance is not instantaneous but requires the transport of information. This is done by reference to the retarded potentials. We derive the fundamental causal Liouville equation for the phase space density of a system composed of a very large number of charged particles.
We extend the Klimontovich (1967) formulation of kinetic theory of the evolution of the...
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