Microphonics and detuning control

To allow operation at highest loaded Q and such at lower power levels for a given field amplitude microphonics detuning control is mandatory. A multi-cell cavity is a complex mechanical system and it was observed that mostly mechanical eigenmodes are excited by the externally induced vibrations.
Figure 5 shows a Wavelet analysis of microphonics detuning, showing the variation with time of the dominating spectral content.

Time domain detuning and its Wavelet analysis showing variations of the detuning amplitude of the first mechanical eigenmode.

This is confirmed by transfer functions measured between excitation of the piezo tuner and the detuning amplitude of the cavity at the given modulating frequency. The obtained spectrum shows a collection of mechanical eigenmodes of the cavity-tuner system (see Figures 6).

Transfer function between piezo excitation and cavity detuning response for a TESLA cavity (left). On the right side a 2D map of excitation frequency and detuning response spectrumis shown. The diagonal line represents the transfer function on the left.

The presence of these eigenmodes prohibits the usage of any classical feedback system. Such for detuning control several advanced adaptive feedforward or state space techniques have been or are currently under study. A detuning reduction by one order of magnitude at 1.8 K was demonstrated using the adaptive feedforward technique (Figure 7), even though the given microphonics background at HoBiCaT was already low.

Detuning compensation of a mechanical eigenmode using LMS based adarptive feedforward.