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For the operation of the VUV-FEL at DESY, Hamburg, the longitudinal charge distribution of the electron bunches that drive the free electron laser is of high importance. One novel method to measure the bunch shape is to analyze the coherent far-infrared synchrotron radiation generated at the last dipole magnet of the first bunch compressor. For the correct interpretation of the results it is mandatory to know how various parameters, like the bunch shape and path, the vacuum chamber walls, the optical beamline, etc., influence the observed spectrum. The aim of this work is to calculate the generation of synchrotron radiation inside the bunch compressor with the emphasis of including the effects of the vertical and horizontal vacuum chamber walls in the vicinity of the last dipole magnet. Challenging problems for the numerical simulations are the very short wavelength and the broad frequency range of interest. As a first step, it is shown how the radiation leaving the vacuum chamber, that is generated by a single point charge, can be calculated with the help of the uniform theory of diffraction (UTD).
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