Guiding center Hamiltonian theory of free-electron lasers

The relativistic guiding center ponderomotive Hamiltonian for free-electron lasers is derived. The ponderomotive Hamiltonian together with the Poisson structure gives the full dynamical description of the slow electron motion. The derivation takes into account arbitrary signal wave polarization and wiggler field geometry including guide field nonuniformities. In particular, it is allowed (i) for a tapered axial guide quasistatic magnetic field along its direction of propagation, (ii) for a realizable wiggler to be tapered both in amplitude and in period, and (iii) for the signal electromagnetic wave to be a growing modulated wave of arbitrary geometry propagating in the direction of the static magnetic field. The equations of motion are then derived including the guiding center perpendicular drifts and beam quasistatic self-fields.