Hamiltonian model of a free electron laser

Both the Compton and the Raman regimes of a free electron laser are described by a relative hamiltonian which originates the evolution equations for 2 N + 2 canonically conjugate electron and field variables, with the space coordinate as the independent variable. Space charge and field contribution to electron transverse velocity are included. Scaled variables are introduced which allow for a description of the behaviour of the system in terms of a single electron-beam parameter.