Strong focusing for planar undulators

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Abstract
The range of parameters in which the free electron laser (FEL) is used has greatly expanded in recent years. The present trend towards short wavelength operation with long undulators places tight requirements on the electron beam quality. In particular, the need to maintain a well focused beam is critical to successful operation of such an FEL. This paper examines the use of alternating gradient (AG) sextupole focusing in planar undulators. After a brief review of various undulator focusing schemes, the equations of motion for an electron in an undulator field with a strong sextupole component are examined. It is shown that the mean electron longitudinal velocity can be kept constant through each fosusing and defocusing section. Thus, the betatron velocity modulation associated with transverse focusing can be limited. Analytic as well as smooth approximation solutions are provided for AG sextupole focusing. Examples using the proposed SLAC 4 nm FEL as well as th UCLA 10.6 μm FEL parameters are also discussed.

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