A Hamiltonian mechanics framework for charge particle optics in straight and curved systems

Charged particle optics, the description of trajectories in vicinity some optical axis, describe imaging properties optics devices. Here, we present a complete and compact charged employing perturbative expansion Hamiltonian mechanics. The derived framework allows straightforward computation transversal longitudinal (chromatic) static dynamic devices with straight curved axes. It furthermore gives rise to geometric integration schemes preserving symplectic phase space structure pertaining Lagrange invariants, which may be employed derive analytic approximations aberration coefficients efficient numerical trajectory solvers.