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 point-like 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.

中文翻译：

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具有任意相干度的自发同步辐射的统计特性

在存储环中，由于两种机理，会发生自发同步加速器辐射强度的匝间波动。第一种机制是发射光子数量的量子不确定性。第二种机制是束中经典点状电子相对位置的匝间变化。我们对量子光学框架中的两种效应进行统一描述。我们推导了任意相干度波动的方程，该方程概括了先前报告的时间不相干辐射的结果。我们将计算的预测结果与布鲁克海文国家实验室的先前实验（后者的机制占主导）进行了比较，并提议在费米实验室的可积分光学测试加速器（IOTA）中进行一项新的专用实验，这两种机制可能会对波动产生可比的贡献。最后，我们的计算表明，波动的幅度对电子束的尺寸和形状相当敏感，从而表明了在电子束仪器中的可能应用。尤其是，可以通过这些波动来估计IOTA中扁平光束的较小垂直尺寸，而由于衍射极限，传统的同步辐射计很难进行测量。