Suddenly switching-on interaction in the relativistic strophotron

The equations of motion in the transition layer of a free-electron laser of the relativistic strophotron type are studied. Two types of strophotrons are considered: electric and magnetic. It is shown, that the condition of a suddenly switching-on interaction: smallness of the transition layer at the entrance compared to the distance traveled by the electron in longitudinal direction in one period of transverse oscillations in strophotron is realistic and feasible.