Nonlinear Landau damping in collisionless plasma and inviscid fluid

Details Nonlinear Landau damping in collisionless plasma and inviscid fluid Nonlinear Landau damping in collisionless plasma and inviscid fluid

1996-12-14

arxiv.org/abs/chao-dyn/9612021v1

Phys. Rev. Lett. 78(12) 2369 (1997)

Nonlinear Sciences

Chaotic Dynamics

4 pages. 1 tex (revtex), 1 bbl, and 7 eps files to make 4 figures with psfig. Submitted to PRL

Scientific paper

The evolution of an initial perturbation in Vlasov plasma is studied in the intrinsically nonlinear long-time limit dominated by the effects of particle trapping. After the possible transient linear exponential Landau damping, the evolution enters into a universal regime with an algebraically damped electric field, $E\propto1/t$. The trick used for the Vlasov equation is also applied to the two-dimensional (2D) Euler equation. It is shown that the stream function perturbation to a stable shear flow decays as $t^{-5/2}$ in the long-time limit. These results imply a strong non-ergodicity of the fluid element motion, which invalidates Gibbs-ensemble-based statistical theories of Vlasov and 2D fluid turbulence.

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