A recent beam splitting experiment at LCLS apparently demonstrated that after a microbunched electron beam is kicked on a large angle compared to the divergence of the FEL radiation, the microbunching wave front is readjusted along the new direction of motion of the kicked beam. Therefore, coherent radiation from an undulator placed after the kicker is emitted along the kicked direction without suppression. This strong emission of coherent undulator radiation in the kicked direction cannot be explained in the framework of conventional synchrotron radiation theory. In a previous paper we explained this puzzle. We demonstrated that, in accelerator physics, the coupling of fields and particles is based, on the one hand, on the use of results from particle dynamics treated according to the absolute time convention and, on the other hand, on the use of Maxwell equations treated according to the standard (Einstein) synchronization convention. Here lies the misconception which led to the strong qualitative disagreement between theory and experiment. After the beam splitting experiment at LCLS, it became clear that the conventional theory of synchrotron radiation cannot ensure the correct description of coherent and spontaneous emission from a kicked electron beam, nor the emission from a beam with finite angular divergence, in an undulator or a bending magnet. However, this result requires further experimental confirmation. In this publication we propose an uncomplicated and inexpensive experiment to test synchrotron radiation theory at 3rd generation light sources.
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