P. HUELSMANN, W.F.O. MUELLER (U. Frankfurt)
The operation of a Free Electron Laser (FEL) in the ultraviolet or in the X-ray regime requires the acceleration of electron bunches with an rms length of 25 to 50 micro meter. The wakefields generated by this sub picosecond bunches extend into the frequency range well beyond the threshold for Cooper pair breakup (about 700 GHz) in superconductive Niobium at 2 K. It could be shown, that the superconducting cavities could indeed be operated with 25 micro meter bunches without suffering a breakdown of superconductivity (quench), however at the price of a reduced quality factor and an increased heat transfer to the superfluid helium bath. This was first shown [1,2] by wakefield calculations based on the diffraction model. In the meantime a more conventional method of computing wake fields in the time domain by numerical methods was developed and used for the wakefield calculations . Both methods lead to comparable results. With an analytical approach we will show the general applicability of the diffraction model for wakefield calculations in the high relativistic regime.
 P. Huelsmann, H. Klein, C. Peschke, W.F.O. Mueller: QThe Influence of Wakefields on Superconducting TESLA-Cavities in FEL-Operationl, Proceedings of the eighth Workshop on Superconductivity, Abano Terme, Italy, 06.10. - 10.10.1997
 R. Brinkmann, M. Dohlus, D. Trines, DESY: A. Novokhatski, M. Timm, T. Weiland, TU Darmstadt: P. Huelsmann, Frankfurt University: C.T. Rieck, K. Scharnberg, P. Schmueser, Hamburg University: QTerahertz Wakefileds in the Superconducting Cavities of the TESLA-FEL Linacl: TESLA-Report, DESY, Hamburg, December 1999
*Work supported by DESY/Hamburg and BMBF under contract No. 06OF841
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