Abstract
In a recently developed kinetic theory for low-frequency turbulence propagating parallel to the ambient magnetic field [P. H. Yoon, Phys. Plasmas 14, 10230 (2007); P. H. Yoon and T.-M. Fang, Phys. Plasmas 14, 102303 (2007); P. H. Yoon and T.-M. Fang, Plasmas Phys. Control. Fusion 50, 085007 (2008)], the effects arising from the discrete particle nature, or the spontaneous thermal effects were ignored. Such an assumption thus limited the theory to purely collisionless “Vlasov” regime. In the present paper the previous formalism is generalized to include discrete-particle effects by reformulating the problem on the basis of the Klimontovich equation. The new terms that appear in the particle and wave kinetic equations as a result of the new formalism are the spontaneous drag term associated with the particles and the spontaneous emission and scattering terms associated with the waves.
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