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Author: Jeffrey M Heninger
Requested Type: Poster
Submitted: 2017-03-16 10:31:55

Co-authors: P.J.Morrison

Contact Info:
The University of Texas at Austin
2515 Speedway, C1600
Austin, Texas   78712
United States

Abstract Text:
The one-dimensional linearized Vlasov-Poisson system can be exactly solved using an integral transform based on the Hilbert transform. This ``G transform'' removes the electric field, leaving a simple advection equation. We investigate how this integral transform interacts with the Lenard-Bernstein collision operator. The commutator between this collision operator and the G transform (the ``shielding term'') is shown to be negligible for all but the smallest magnitude velocities and times. We explicitly solve the advection-diffusion equation without the shielding term. This solution allows us to determine when collisions dominate and when advection (which gives rise to Landau damping) dominates the Vlasov-Poisson system with collisions. We hope that the G transform will be used to simplify gyrokinetic codes or any other plasma model with a single velocity dimension. A model is also presented where the interaction of modes gives rise to an anti-Landau damping phenomenon. Nonlinearity in Vlasov systems can suppress Landau damping. After the bounce time, trapped particles stop the decay of the electric field. We investigate another mechanism which can suppress Landau damping. Modes with wave numbers $+k$ and $-k$ Landau damp in opposite ways, as demonstrated by the plasma echo. If these modes are coupled, energy from a partially Landau-damped wave can be transferred into the mode with the opposite wave number, where it anti-Landau-damps and recovers the wave's spatial dependence. We investigate a simple two-mode model that elucidates this behavior. We then consider how similar behavior can arise in a more general class of Vlasov equations with nonlinear coupling between different wave mode.