Modelling of simple cases in view of active stabilisation for a future linear collider

Final focus magnet stabilisation is an important issue when working with nanometre size beams. The present study focuses on mechanical stabilisation. As a first step, the case of a 1m free-fixed aluminium beam placed on a table with active stabilisation has been studied. This work describes three aspects, namely, sensors and actuators to measure and compensate ground motion, mechanical simulations and a feedback loop. Measurements done with low frequency velocity sensors (down to 0.1Hz) in our Annecy lab during office hours show that the displacement RMS on the active table is 1nm at 4Hz compared to 10nm without active stabilisation. Simulations of the dynamic response of the beam have been compared to measurements done with accelerometers placed on the clamping and on the free end of the aluminium beam. The results are in good agreement. We are therefore able to predict by simulation the response of a structure subjected to an external excitation. A first sketch of a feedback loop to compensate specific vibrations has also been developed and allows the simultaneous elimination of several resonance peaks on a reduced-size mock-up. This algorithm will be applied to stabilise a larger mock-up, leading to more realistic experimental conditions. In future tests, the active table will globally stabilise in a range of frequencies from 0.5Hz to 50Hz whereas the feedback loop will compensate single strong resonances.