In a storage ring, turn-to-turn fluctuations in the intensity of spontaneous synchrotron radiation occur due to two mechanisms. The first mechanism is the quantum uncertainty in the number of emitted photons. The second mechanism is the turn-to-turn variations in the relative positions of classical pointlike electrons in the bunch. We present a unified description of both effects in the framework of quantum optics. We derive an equation for the fluctuations for an arbitrary degree of coherence, which generalizes previously reported results for temporally incoherent radiation. We compare the predictions of our calculation with a previous experiment at Brookhaven National Laboratory, where the latter mechanism was dominant and propose a new dedicated experiment in the Integrable Optics Test Accelerator (IOTA) at Fermilab, where the two mechanisms may have comparable contributions to the fluctuations. Finally, our calculation shows that the magnitude of the fluctuations is rather sensitive to the dimensions and the shape of the electron bunch, thereby indicating possible applications in beam instrumentation. In particular, the small vertical size of the flat beams in IOTA may be estimated via these fluctuations, whereas measurement by a conventional synchrotron radiation monitor is difficult due to the diffraction limit.

We study turn-by-turn fluctuations in the number of emitted photons in an undulator, installed in the IOTA electron storage ring at Fermilab with an InGaAs PIN photodiode and an integrating circuit. Our study was motivated by the previous experiment [1]. We propose a theoretical model for the experimental data from [1] and in our own experiment we attempted to verify the model in an independent and more systematic way. Moreover, these fluctuations are an interesting subject for a study by itself, since they act as a seed for SASE in FELs. We improve the precision of the measurements from [1] by subtracting the average signal amplitude using a comb filter with a one-turn IOTA delay, and by using a special algorithm for noise subtraction. We obtain a reasonable agreement between our theoretical model and experiment. Along with repeating the experiment from [1], which was performed at a constant beam current, we also collect data for fluctuations in undulator light at different beam current values. Lastly, in our experiment we were able to see the transition from Poisson statistics to Super-Poisson statistics for undulator light, whereas in [1] only the latter statistics was observed.

The study of single and multiple intrabeam scattering was carried out in the IOTA ring at Fermilab. The report discusses the results of the measurements and outlines still unresolved problems

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MOTIVATIONAs previously stated in the experiment proposal [1], the goal of the URSSE experiment was to study statistical properties of the undulator radiation generated by a single electron, circulating in the IOTA storage ring. Namely, the idea was to study the distribution of the number of photons detected in a certain time window, and the distribution of the inter-arrival times of the photons.We wanted to see if the photostatistics was exactly Poissonian, as predicted by [2][3][4], or if there was some deviation towards Sub-Poissonian light, similar to what was observed in [5].

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