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

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