We have used coherent Smith-Purcell radiation (cSPr) in order to determine the temporal profile of sub-ps long electron bunches at the Facility for Advanced Accelerator Experimental Tests, at SLAC. The measurements reported here were carried out in June 2012 and April 2013. The rms values for the bunch length varied between 356 to 604 fs, depending on the accelerator settings. The resolution of the system was limited by the range of detectable wavelengths which was, in turn, determined by the choice of the grating periods used in these experiments and the achievable beam-grating separation. The paper gives the details of the various steps in the reconstruction of the time profile and discusses possible improvements to the resolution. We also present initial measurements of the polarization properties of cSPr and of the background radiation.

The phase retrieval problem occurs in a number of areas in physics and is the subject of continuing investigation. The one-dimensional case, e.g., the reconstruction of the temporal profile of a charged particle bunch, is particularly challenging and important for particle accelerators. Accurate knowledge of the longitudinal (time) profile of the bunch is important in the context of linear colliders, wakefield accelerators and for the next generation of light sources, including x-ray SASE FELs. Frequently applied methods, e.g., minimal phase retrieval or other iterative algorithms, are reliable if the Blaschke phase contribution is negligible. This, however, is neither known a priori nor can it be assumed to apply to an arbitrary bunch profile. We present a novel approach which gives reproducible, most-probable and stable reconstructions for bunch profiles (both artificial and experimental) that would otherwise remain unresolved by the existing techniques.

Coherent Smith-Purcell radiation has the potential of providing information on the longitudinal profile of an electron bunch. The E-203 experiment at the FACET User Facility measures bunch profiles from the SLAC linac in the hundreds of femtoseconds range and the SPESO collaboration at Synchrotron SOLEIL is planning to make an accurate 2D map of the Coherent Smith-Purcell Radiation emission.

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