Poisson brackets for guiding-centre and gyrocentre theories

Abstract

Poisson brackets in the phase space of averaging Kruskal coordinates are obtained in a clear and straightforward way. The derivation makes use of the equations of motion of guiding centres and gyrocentres derived from a gyroangle-independent Lagrangian, and from generally valid relations of Hamiltonian mechanics. The usual procedure of matrix inversion to obtain the Poisson tensor from the Lagrange tensor is not required.