Variational principle for nonlinear gyrokinetic Vlasov-Maxwell equations

Physics of Plasmas

Volumn 7, Issue 12, 2000, Pages 4816-4822

  Brizard, Alain J ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b SAINT MICHAEL'S COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0006910373     PISSN: 1070664X     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1322063     Document Type: Article

References (24)

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9. Here, the reduced coordinates are the three spatial coordinates, the parallel velocity (or kinetic momentum), and the magnetic moment (an adiabatic invariant). Since the magnetic moment is considered an invariant as far as the reduced particle dynamics are concerned, the reduced particle dynamics actually takes place on a four-dimensional reduced phase space (a submanifold defined by specifying a value for the magnetic moment), which has its own Hamiltonian structure.
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23. The connection between the Lagrange bracket (and the phase-space Lagrangian) and the Poisson bracket is well known; see, for example, H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, 1950) and Ref. 12. Hence, if the gyrocenter phase-space Lagrangian has the same form as the guiding-center phase-space Lagrangian, then their associated Poisson brackets will be identical.
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