Journal of Plasma Physics

Research Article

Variational principles of guiding centre motion

Robert G. Littlejohna1

a1 Department of Physics, University of California, Los Angeles, California 90024


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.

(Received March 11 1982)

(Revised June 28 1982)