On the motion of electrons in a spiral ondulator

The off-axial motion of electrons in the ondulator field generated by two spiral tapes located antipodally on the cylinder surface and forming direct and inverse wires of the chain with current is studied. In the linear (by the ratio of the field parameter to the particle dimensionless energy) approximation of perturbation theory, trajectories of motion at arbitrary initial conditions have been found. At the injection at a small angle to the ondulator axis, electrons are shown to move by a periodical trajectory with a period that is independent of the initial transverse deviation. This fact may be used to increase the power of free electron lasers as well as in other applications of beams in a spiral ondulator