Calculation and analysis of the magnetic field of a linearly tapered undulator

There is an empirical formula describing the relationship between the peak magnetic field and the undulator structure parameters for a uniform-parameter hybrid undulator. In this paper, we investigate the relationship for a linearly tapered undulator through numerical calculation by using the code RADIA, and check it with the empirical formula. The results imply that this empirical formula is also effective for linearly tapered undulators at a big enough scope for the requirements of normal FEL experiments. Therefore, for a linearly tapered undulator, we can use the empirical formula to design the variation of the undulator gap. For the tapering rate demanded by normal FEL experiments, the gap of a linearly tapered undulator increases almost linearly, and the tapering rate will keep constant while adjusting the undulator gap with the same variation for each undulator period.