Field fine tuning by pole height adjustment for the undulator of the TTF–FEL

The field of the undulator for the VUV–FEL at the TESLA Test Facility has to meet very tough tolerances in order to guarantee a close overlap between the electron beam and the laser field. Consequently the undulator was designed to have height-adjustable poles in order to allow for fine tuning of the vertical undulator field in such a way that the trajectory is straightened. The signature of local pole height and gap changes on the field distribution was investigated. It was seen that changes are not restricted to the pole itself. Its effect can be seen up to the next eight neighboring poles. In this contribution we describe an algorithm in detail, which allows the prediction of required pole height changes in order to correct for field errors. As input data field errors deduced from precise magnetic field measurements are used together with the signatures of pole movements. A band diagonal system of linear equations has to be solved to obtain the pole height corrections. For demonstration of the method the field of the 0.9 m long prototype structure was optimized to have a straight trajectory. Since only a sparse band diagonal system of equations has to be solved, the method has the potential to be used in very long undulators having 600 –1000 poles