Measurement of bunch length using spectral analysis of incoherent radiation fluctuations

A measurement of the longitudinal beam profile of a relativistic charged particle beam is an important tool in modern accelerators. For bunch lengths in the range of picoseconds, such measurements can be performed by means of a streak camera. Shorter bunches usually require special techniques. In this paper we describe a novel technique that allows obtaining properties of a bunch of charged particles through measurement of the fluctuations of incoherent radiation from the bunch. Due to shot-noise fluctuations in the longitudinal beam density, this incoherent radiation has a spectrum, which consists of random spikes with width inversely proportional to the bunch length. The convolution of the beam current can also be obtained from the radiation spectrum. After the convolution function is found, the phase retrieval technique can be applied to recover the bunch shape. This technique has been used to analyze the shape of the 4-ps-long bunches at the Advanced Photon Source self-amplified spontaneous emission free-electron laser (SASE FEL) experiment.