Influence of the inhomogeneity of electromagnetic wave and undulator fields on the operation of a free-electron laser

Equations are derived for the motion of particles in a free-electron laser subject to an allowance for the inhomogeneity of electromagnetic wave and undulator fields. A study is made of the influence of the inhomogeneity of these fields on the laser gain. An analysis is made of the conversion of the energy of a particle beam into radiation when initial conditions of particle injection into the laser undulator are modulated. It is shown that a suitable selection of the modulation depth and phase can increase the average energy lost from the beam.