Matched injection in a helical undulator taking into account the orbit amplitude and the longitudinal magnetic field

Helical undulators are widely used in FELs because they are inexpensive and easy to fabricate. Also, because field amplitudes can be conveniently adjusted with high accuracy. Their main weakness is their use of adiabatic input and output (up to 10 periods each) for matched injection (ejection) of the electron beam in the undulator field. This leads to considerable lengthening of the undulator and optical resonator, without simultaneously providing, in a number of cases, the required injection accuracy (due to some angle error and failure to account for orbit amplitude). Here alternative methods of matched injection are described that take into account orbit amplitude and external magnetic field. The length of correcting elements does not exceed one-half of the undulator period. When the overall length of the helical undulator is large, their application permits its realization in the form of a set of successive sections with free straight gaps in which devices can be placed for measuring beam parameters and correction of the trajectory.