Phase space distribution of brilliance of undulation sources

The radiation from undulators in phase space is studied, giving results on widths of distribution, and discussing the dependence on beam parameters and wavelength. Analogue between the brilliance and Wigner function is used to show that the depth-of-field and diffraction widths are essentially the same thing, and the electron beam angular spread is not seen to contribute to the depth-of-field broadening of the source. Other results include the peak brilliance demonstrating a broad maximum as a function of the beam beta function, but being practically independent of beta at short wavelengths. 13 references