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Abstract

It is well-known that the electron trajectory in anundulator is influenced by the focusing properties (bothhorizontal and vertical) of the magnetic field. Theapproximate solutions of motion equations for electronsin the 3-dimensional magnetic field, which describe thesefocusing properties, can be found by means of averagingover the short-length oscillations. On the other hand, theequations of motion can be solved numerically, byapplying the Runge-Kutta algorithm. It is shown in thispaper that numerically computed trajectories, which canbe considered as figure of merit, on frequent occasionsdiffer considerably from the correspondent approximatesolutions obtained through the averaging method. Itmeans that actually the undulator field influence on theelectron trajectory is complicated and often cannot bereduced to the well-known focusing phenomena along.

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