Abstract
The undulator is a machine that induces amplitude fluctuations in normally rectilinear electron trajectories, causing coherently-re-inforced radiation to appear along the direction of electron motion. Presently, such machines operate on electrons traveling in straight sections of synchrotron rings. The inherently large number of variables characterizing the undulator-electron beam interaction makes it difficult to identify the principal parameters for optimization when designing synchrotron rings dedicated to undulator operation. This paper presents the results of a variational analysis of the equation describing single electron undulator radiation. In particular, the results identify the optimum electron trajectories in undulators, in the sense of maximizing the intensity density of the radiation in the forward direction and establish the optimum amplitudes of the electron motion in terms of the total electron speed, βc, and the average on-axis component of the electron velocity, β ∗c . These results, besides providing a valuable insight into undulator operation, rigorously establish the principal optimization parameters for associated synchrotron ring design.
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