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.
The theory of the semiclassical evolution of wave packets is developed as a version of WKB theory in phase space. Special attention is given to the transformation properties of wave packets, their Wigner functions, and their classical analogs under operations in phase space. A complete development of the Heisenberg and metaplectic operators is presented, including their interaction with the Wigner-Weyl formalism and the questiQn of caustics. A metaplectically covariant wave packet propagator is presented and discussed. Finally, a group theoretical discussion of Gaussian wave packets is given. fPermanent address:
Nonrelativistic guiding center motion in the magnetic field BB(x), with E=0, is studied using Hamiltonian methods. f'J The drift equations are carried to second order in the perpendicular motion. The Hamiltonian methods which are used are described in detail in order to facilitate possible applications. Unusual mathematical techniques are called upon, especially the use of noncanonical coordinates in phase space. Lie transforms are used to carry out the perturbation expansion. Applications in kinetic theory, in the area of adiabatic invariants, and in other areas are anticipated.
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