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  • Quasi-linear and Landau kinetic equations for magnetised plasmas: Compact propagator formalism, rotation matrices and interaction representation.


As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field.

The quasi-linear approximation is applied to general kinetic equation obtained previously from the KLIMONTOVICH exact equation, by means of a generalized DUPREE-WEINSTOCK method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases.

For an electrostatic turbulence, a diffusion equation in velocity space is obtained for the particle distribution function, along with an important non-Markovian contribution for non-uniform systems. This latter term seems to be entirely new in the kinetic description of magnetized plasma. It appears to give essential contribution to the spatial diffusion of guiding centers across the magnetic field, and this results is in agreement with direct trajectory calculations as found in ICHIMARU's book.

Magnetic fluctuations are described here in a similar and compact manner. Averaging the kinetic equation over the gyrophase with the assumption of a gyrotropic distribution function, leads to a diffusion equation in pitch angle. The classical quasi-linear results are obtained for cosmic ray diffusion in the "slab model" of magnetostatic turbulence in the solar wind. The validity of this description is discussed in connection with the problem of diffusion across the 90 degree pitch angle (which is necessary in a diffusion model in order to describe the observed isotropisation of solar cosmic rays) and the appearance of a delta term. It is suggested that a non-linear renormalized description of cosmic ray diffusion should take non-uniformity fully into account, including the non-Markovian contribution presented here.

Last but not least, Landau collisions in a magnetic field are der

Additional information

Authors: MISGUICH J H, Département de Recherches sur la Fusion Contrôlée, Association Euratom-CEA sur la Fusion, CEA Cadarache, Saint-Paul-lez-Durance (FR)
Bibliographic Reference: An article published by: CEA Cadarache, Saint-Paul-lez-Durance (FR) Refference: EUR-CEA-FC-1734
Availability: Available from Association EURATOM-CEA, Département de Recherches sur la Fusion Contrôlée, CEA Cadarache, F-13108 St Paul-Lez-Durance, France Tel: (+33) 4 42 25 70 01; Fax: (+33) 4 42 25 64 21 E-mail:
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