Linear undular brightness: Sextupolar magnetic-field contributions and higher-orders energy corrections for low-energy electron beams

SummaryIn this paper we discuss the modifications to the undulator brightness and central wavelength expressions due to the low-energy effects and to the inclusion of the sextupolar magnetic-field components. The corrections are calculated up to the order (K/γ)4. The mathematical details are simplified by the use of generalized Bessel functions.