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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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V. I. Arnold 1978 Mathematical Methods of Classical Mechanics. Springer.

A. H. Boozer 1980 Phys. Fluids, 23, 904.

J. R. Cary 1981 Phys. Rep. 79, 131.

A. J. Dragt & J. M. Finn 1976 J. Math. Phys. 17, 2215.

E. A. Frieman & L. Chen 1982 Phys. Fluids, 25, 502.

R. J. Hastie , J. B. Taylor & F. A. Haas 1967 Ann. Phys. 41, 302.

R. G. Littlejohn 1979 J. Math. Phys. 20, 2445.

R. G. Littlejohn 1981 Phys. Fluids, 24, 1730.

R. G. Littlejohn 1982 aJ. Math. Phys. 23, 742.

T. G. Northrop & J. A. Rome 1978 Phys. Fluids, 21, 384.

J. B. Taylor 1964 Phys. Fluids, 7, 767.

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Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
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