Coherent radiations from electron beams propagating through a tapered wiggler and axial magnetic field

Hamiltonian approach to emanating coherent radiations in a free electron laser is presented. For this we consider the electron oscillations in a smoothly increasing helical undulator field and uniform magnetic field. The undulator field is supposed to be turned on abruptly or smoothly. In abrupt turn-on oscillations are excited both at bounce and gyro frequency but in smooth turn-on oscillations at only bounce frequency are excited and stimulated emission can be observed separately at the undulator and cyclotron resonances. (author)