Statistical properties of undulator radiation

Most often, noise is encountered in a negative context and is considered something that needs to be minimized. However, there are multiple examples where noise is used as a noninvasive probe into the parameters of a certain system, and even to measure fundamental constants. In this paper, we describe two experiments, which were carried out to study the statistical properties of undulator radiation in the Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab. The first experiment studied the turn-to-turn fluctuations in the power of the radiation generated by an electron bunch. The magnitude of these fluctuations depends on the 6D phase-space distribution of the electron bunch. In IOTA, we demonstrated that this effect can be used to measure some electron bunch parameters, small transverse emittances in particular. In the second experiment, a single electron was stored in the ring, emitting a photon only once per several hundred turns. In this regime, any classical interference-related collective effects were eliminated, and the quantum fluctuations could be studied in detail to search for possible deviations from the expected Poissonian photon statistics. In addition, the photocount arrival times were used to track the longitudinal motion of a single electron and to compare it with simulations. This allowed us to determine several dynamical parameters of the storage ring such as the RF cavity phase jitter and the dependence of the synchrotron motion period on amplitude.