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Betatron motion and linear undulator brightness: Inhomogeneous broadening effects due to electron-beam emittance and Twiss parameters.

The combined effects of electron-beam betatron motion and non-negligible emittance provide a rich phenomenology of the radiation emitted in linearly polarized undulators. Indeed, even harmonics may be radiated on axis and the induced inhomogeneous broadenings depend on the electron-beam matching condition. We discuss the dependence of undulator brightness on electron-beam betatron motion and also analyze how the harmonic spectrum depends on the electron-beam emittance and Twiss parameters. We present independent analytical and numerical analyses, make a comparison between the two methods, and comment on the limits of the analytical treatment. (c) 1995 The American Physical Society