On the particle number conservation inherent in the diffusion approach of the Fokker-Planck equation

Details On the particle number conservation inherent in the diffusion approach of the Fokker-Planck equation On the particle number conservation inherent in the diffusion approach of the Fokker-Planck equation

Jun 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978ap%26ss..56...81k&link_type=abstract

Astrophysics and Space Science, vol. 56, no. 1, June 1978, p. 81-87.

Astronomy and Astrophysics

Astrophysics

2

Conservation Laws, Fokker-Planck Equation, Particle Diffusion, Transport Properties, Anisotropy, Diffusion Coefficient, Solar Flux, Solar Wind

Scientific paper

Conservation rules are derived for charge-particle distributions whose time evolution in randomly fluctuating magnetic fields is governed by the Fokker-Planck equation and which are in a quasi-equilibrium near-isotropic state. It is proven that these conservation rules are valid for both a constant mean magnetic field and an exponentially diverging magnetic field and are probably valid for more general field configurations as well. The diffusion equation obtained from the Fokker-Planck equation is shown to imply conservation of the integrated particle numbers even in very arbitrary velocity intervals; this conservation does not limit the degree of local anisotropies but implies a balance over an integrated global scale. An analysis is performed which indicates that diffusion and the transport of all higher-order modes are not valid prior to conservation of the integrated particle number but that in the near-isotropic state, the transport equations are valid approximations of the real conditions. It is concluded that the final state of phase-state density will always be an overall constant and that the several integrated particle numbers per velocity interval must be identical.

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