A simple approach for power density calculation of spontaneous radiation emission from a finite emittance electron beam in planar undulators

Abstract

We extend the angular power density formulae for spontaneous radiation emission from planar undulators to include finite emittance and angular misalignment of the electron beam. Then we calculate and compare power densities estimated from integral approach with Gaussian beam distribution and summation approach with the macro-particle allocation covering the particle beam phase space. After showing that both approaches converge to each other, we apply the macro-particle approach to study power absorbed and transmitted by various apertures at the front end of the 9-ID beamline at the National Synchrotron Light Source-II. Our analysis indicate that the electron beam misalignment could lead to unwarranted power deposition at tighter apertures that would have been otherwise difficult to account in the aperture design/choice process using the geometric ray-tracing approach.