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Author: Jeffrey Heninger
Requested Type: Poster
Submitted: 2018-03-01 15:45:56

Co-authors: P.J.Morrison

Contact Info:
University of Texas at Austin
1 University Station C1600
Austin, Texas   78712
United States

Abstract Text:
The one-dimensional linearized Vlasov-Poisson system can be exactly solved using the G-transform, an integral transform based on the Hilbert transform. This transform removes the electric field, leaving a simple advection equation. We investigate how this integral transform interacts with the Fokker-Planck collision operator. The commutator of this collision operator with the G-transform (the ``shielding term'') is shown to be negligible. We exactly solve the advection-diffusion equation without the shielding term. This solution determines when collisions dominate and when advection (i.e. Landau damping) dominates. This integral transform can also be used to simplify gyrokinetic equations. We present new gyrofluid equations formed by taking moments of the G-transformed equation. Since most gyrokinetic codes use Hermite polynomials as basis elements, we include an explicit calculation of their G-transform.