Frontiers in Fusion Research by Mitsuru Kikuchi

Author:Mitsuru Kikuchi
Language: eng
Format: epub
Publisher: Springer London, London

(5.29)

The free streaming term is produced from the pole of integration of Equation 5.29, and the density perturbation in velocity space oscillates more strongly with time. The resulting density perturbation and electric field after integration in velocity space will damp with time due to this phase mixing. It might be thought that this collisionless damping by phase mixing would be inconsistent with the reversibility of the Vlasov equation (similar to the discussion with Loschmidt’s “reversibility paradox” against the Boltzmann equation). For the solution , the time reversal solution is also a solution of the Vlasov equation and the density perturbation increases exponentially with time. However, this time reversal solution may have an initial value and is not smooth since it includes . After passes, the density perturbation reaches a maximum where is a smooth function. Then, the density will decay again with time due to phase mixing [5.16].

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