1:00 pm Friday, April 14, 2023
Analysis Seminar: The survival threshold for plasma oscillations by
Toan T. Nguyen (Penn State University) in PMA 10.176
Plasmas in a nonequilibrium state experience complex behavior at the large time due to their collective meanfield interaction, including phase mixing, Landau damping, dispersion, and oscillations also known as Langmuir's oscillatory waves. Part of the talk is to overview a complete linear theory of the dynamics of charged particles near spatially homogeneous equilibria, focusing on the classical collision-less models including Vlasov-Poisson and Vlasov-Maxwell systems, while the other part surveys some recent nonlinear results on the subject. Amusingly, a threshold of the wavenumber is provided for the survival of oscillations: namely, below the threshold pure oscillatory waves that obey a Klein-Gordon’s type dispersion relation are found, at the threshold waves are damped by the classical Landau damping (i.e. the faster electrons decay or vanish, the weaker Landau damping is), and above the threshold waves decay polynomially or exponentially fast via the phase mixing mechanism, the full picture of which is deeply linked to the resonant interaction between waves and particles. Submitted by
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