Abstract
Although the FEL interaction is predominantly longitudinal in nature, transverse physics cannot be neglected if one wants to have a complete picture of the FEL. Specifically, we must understand the roles of radiation diffraction and how the electron’s betatron motion in the undulator affects performance. We discuss these effects emphasizing the underlying physical picture. A high-gain FEL has a set of transverse modes, of which the fundamental mode has the largest growth rate and thus become dominant as the radiation-electron beam system travels along the undulator. To maximize the growth rate, the electron beam phase space distribution should be matched to the guided optical beam, leading to criteria on electron beam parameters. The FEL gain length is presented near the end of this chapter.
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