Speaker
Description
In regime of diffraction-limited electron beams at x-ray wavelengths, the spectral width of fundamental spontaneous undulator radiation is at ~1% level, and down to 0.01% for free-electron lasers (FELs). Consequently, the traditional characterization of brilliance in units of 0.1% bandwidth tends to overestimate the actual brilliance of longitudinally coherent sources. An update version of the brilliance plot in units of 0.01% relative bandwidth is proposed. It is shown that, in order to match experimental and simulated data, the calculation has to take into consideration a non-uniform electron current profile in self-amplified spontaneous emission (SASE), whenever produced at the undulator, and the scaling of the light pulse duration with the harmonic jump in seeded architectures. More accurate and general brilliance expressions are therefore provided. A closed-form is found for the saturation length of SASE FELs, providing an exact value via Lambert function, in place of well-known but semi-quantitative estimations reported in the literature.
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