Abstract
This work studies the electron-beam envelopes and matching conditions for a combined wiggler and alternating-gradient quadrupole field for a free electron laser (FEL) that will be operated in the VUV or XUV wavelength region. The quadrupole field is assumed to vary continuously along the symmetry axis. The linearized equations of electron motion are solved analytically by using the two-scale perturbation method for a plane polarized wiggler. The electron-beam envelopes and the envelope equations, as well as the matching conditions in phase space, are obtained from the electron trajectories. A comparison with the numerical solution is presented.
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