Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S19 / 2 / f

Lower energy changes the source spectrum as well as emittance. At fixed bending geometry, bending-radiation critical energy scales as ${\gamma }^3$, so it falls by $10^{3/2}$; for fixed undulator period and deflection parameter the fundamental wavelength grows as ${\gamma }^{-2}$, by ten. A smaller electron emittance therefore does not automatically improve brightness at the original 10 nm wavelength: the device may no longer radiate there on its fundamental, flux and harmonic operation change, and diffraction remains. Lattice redesign can retain beam energy and target spectrum while reducing emittance, which is why energy reduction alone is not a generally satisfactory substitute.