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Variational principles of guiding centre motion

  • Robert G. Littlejohn (a1)


An elementary but rigorous derivation is given for a variational principle for guiding centre motion. The equations of motion resulting from the variational principle (the drift equations) possess exact conservation laws for phase volume, energy (for time-independent systems), and angular momentum (for azimuthally symmetric systems). The results of carrying the variational principle to higher order in the adiabatic parameter are displayed. The behaviour of guiding centre motion in azimuthally symmetric fields is discussed, and the role of angular momentum is clarified. The application of variational principles in the derivation and solution of gyrokinetic equations is discussed.



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Arnold, V. I. 1978 Mathematical Methods of Classical Mechanics. Springer.
Boozer, A. H. 1980 Phys. Fluids, 23, 904.
Cary, J. R. 1979 Ph.D. Thesis, University of California, Berkeley.
Cary, J. R. 1981 Phys. Rep. 79, 131.
Cary, J. R. & Littlejohn, R. G. 1982 (To be published.)
Dragt, A. J. & Finn, J. M. 1976 J. Math. Phys. 17, 2215.
Frieman, E. A. & Chen, L. 1982 Phys. Fluids, 25, 502.
Goldstein, H. 1980 Classical Mechanics, 2nd ed.Addison-Wesley.
Hastie, R. J., Taylor, J. B. & Haas, F. A. 1967 Ann. Phys. 41, 302.
Kruskal, M. D. 1965 Plasma Physics, p. 67. IAEA.
Landau, L. D. & Lifshitz, E. M. 1969 Mechanics, 2nd ed.Pergamon.
Littlejohn, R. G. 1979 J. Math. Phys. 20, 2445.
Littlejohn, R. G. 1981 Phys. Fluids, 24, 1730.
Littlejohn, R. G. 1982 a J. Math. Phys. 23, 742.
Littlejohn, R. G. 1982 b Physica Scripta, (To be published.)
Morozov, A. I. & Solov'ev, L. S. 1966 Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 2, p. 201. Plenum.
Northrop, T. G. 1963 The Adiabatic Motion of Charged Particles. Interscience.
Northrop, T. G. & Rome, J. A. 1978 Phys. Fluids, 21, 384.
Taylor, J. B. 1964 Phys. Fluids, 7, 767.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Interscience.
Wong, H. V. 1981 University of Texas Fusion Research Center Report FRCR 230.
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