Measurements of undulator radiation power noise and comparison with $\textit{ab initio}$ calculations

Generally, turn-to-turn fluctuations of synchrotron radiation power in a storage ring depend on the 6D phase-space distribution of the electron bunch. This effect is related to the interference of fields radiated by different electrons. Changes in the relative electron positions and velocities inside the bunch result in fluctuations in the total emitted energy per pass in a synchrotron radiation source. This effect has been previously described assuming constant and equal electron velocities before entering the synchrotron radiation source. In this paper, we present a generalized formula for the fluctuations with a non-negligible beam divergence. Further, we corroborate this formula in a dedicated experiment with undulator radiation in the Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab. Lastly, possible applications in beam instrumentation are discussed.