Moment invariants for nonlinear Hamiltonian systems

In this paper we study the behavior of the moments of a particle distribution as it is transported through a Hamiltonian system. Functions of moments that remain invariant for an arbitrary nonlinear Hamiltonian system are constructed perturbatively. The perturbation expansion is carried out according to the degree of nonlinearity of the symplectic mapping associated with the Hamiltonian. The existence of these moment invariants is entirely a consequence of the symplectic nature of the flow generated by Hamiltonian systems. These invariants may be of use in accelerator design, in the general area of charged particle beam transport, and in other areas of Hamiltonian dynamics. (C) 2000 American Institute of Physics. [S0022-2488(00)04507-2].