Matched pair analysis of the Vlasov plasma

Esen Oǧul; Sütlü Serkan

doi:10.3934/jgm.2021011

Article Contents

2021, Volume 13, Issue 2: 209-246. Doi: 10.3934/jgm.2021011

This issue Previous Article Quasi-bi-Hamiltonian structures and superintegrability: Study of a Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion Next Article A bundle framework for observer design on smooth manifolds with symmetry

Matched pair analysis of the Vlasov plasma

Esen Oǧul^1, and
Sütlü Serkan^2, ,

1.
Department of Mathematics, Gebze Technical University, 41400 Gebze-Kocaeli, Turkey
2.
Department of Mathematics, Işık University, 34980 Şile-İstanbul, Turkey

^* Corresponding author: Serkan Sütlü
^* Corresponding author: Serkan Sütlü

Received: June 30, 2020

Revised: December 31, 2020

Early access: May 2021

Published: June 2021

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Abstract

We present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of mutually interacting (Lie-Poisson) subdynamics. The mutual interaction is beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address the matched pair Lie-Poisson formulation allowing mutual interactions. Moreover, both for the kinetic moments and the Vlasov plasma cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the dynamics of the kinetic moments of order $ \geq 2 $. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma, along with its matched pair decomposition.

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Mathematics Subject Classification: Primary: 37K30, 35Q83; Secondary: 70H33.

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