1. Warren Schappert Yuriy Pischalnikov FNAL SRF2011, Chicago

2. Lorentz Force Detuning  SCRF cavity walls are deliberately kept thin to allow them to be easily cooled  Electromagnetic pulse applies pressure to the cavity walls leading to mechanical vibrations of the cavity  Vibrations can detune the cavity  Detuned cavity requires more RF power to maintain accelerating gradient  Higher RF power requirement increase both capital and fixed costs of an accelerator

3. Standard LFD Compensation  Piezo actuator connected to one end of cavity  Half-sine impulse applied to the actuator prior to the arrival of the RF pulse  Pulse parameters (amplitude, delay, width,bias) usually optimized manually  Can give excellent results for short pulses used to drive Tesla/ILC style cavities TEST RESULTS OF THE INTERNATIONAL S1-GLOBAL CRYOMODULE This Conference Courtesy of Y. Yamamoto

4. Limitations of the Standard Approach  Pros  Standard approach gives good results  Employs a relatively ‘simple’ waveform  Cons  Requires time consuming manual non-linear multi- dimensional optimization to determine pulse parameters  Pulse parameters need to be re-determined each time the operating conditions, e.g. gradient, changes  Difficult to automate because pulse detuning does not depend linearly on waveform parameters  Automated control would be easier if compensation could be reformulated as a linear problem

5. Measuring Detuning  Need to measure detuning before it can be controlled  Standard approach  Change the length of the RF pulse and look at the frequency during the decay region  Pros  Conceptually simple procedure  Cons  Time consuming  Not possible to measure detuning this way during routine operation TEST RESULTS OF THE INTERNATIONAL S1-GLOBAL CRYOMODULE This Conference Courtesy of Y. Yamamoto

6. Measuring Detuning During the Pulse  Cavity baseband waveforms well described by equation for an oscillator driven by a slowly modulated carrier  Terms of equation can be rearranged to isolate the half-width and detuning  Same formula in slightly different form used by DESY

7. Real-Time Detuning Measurement  Piezo Scan  Change piezo DC bias from RF pulse to RF pulse  Formula allows the detuning for during each pulse to be determined  Complete scan takes a few minutes

8. Forward/Reflected Cross- Contamination  Substantial variations in forward power levels observed during piezo scans  Variations attributed to cross-contamination between forward and reflected signals  Contamination levels of up to 15% in amplitude seen in Fermilab HTS  15% contamination during the flattop could bias the detuning measurement by up to 30% of the cavity half bandwidth

9. Correcting for Cross- Contamination  Three step procedure  Normalize reflected signal to match probe during decay region  Assume ‘tail’ of forward power is due entirely to cross- contamination by reflected power  Use cavity equation to determine relative gain of forward and probe signals  Reduces contamination to a few percent in the FNAL Horizontal Test Stand

10. Detuning Transfer Functions  If the piezo-to-detuning transfer functions (impulse response) and the Lorentz Force-to-detuning transfer functions are both known it is possible to construct an compensation waveform that minimizes the RMS cavity detuning  Piezo impulse response easiest to measure using CW  Often measured but never used  Lorentz force transfer function more difficult to measure  Automation will require a procedure that can be used to characterize cavity response during routine pulsed operation

11. Delay Scan  Variation of procedure used to determine delay of standard half- sine pulse  Drive piezo with impulse 10 ms prior to arrival of the RF pulse  Systematically reduce the interval by 0.5 ms with each successive RF pulse  Scan also includes changes of piezo DC bias  Record the detuning during the pulse at each delay  Array of data relating the small-signal detuning at each sample during the RF pulse to the delay of the piezo pulse

12. Delay Scan and the Impulse Response  Each line of the delay scan can be shifted in time so that the piezo impulses are aligned  Result agrees well with CW measurements of the piezo impulse response

13. Calculating the Waveform  Accurate measurements of the detuning due to Lorentz force  Accurate characterization of the detuning response to piezo impulses at various delays  Use least-squares to determine the combination of piezo impulses required to cancel out the Lorentz force detuning  Linear problem  Invert Response Matrix using standard matrix algebra

14. Adaptive Compensation  Extension to feed-forward adaptive compensation is straightforward  After each pulse determine the residual detuning  Calculate the incremental change required to cancel out that detuning  Update the waveform

15. Fermilab HTS  First single- cavity system developed for Fermilab HTS  System used for QA testing of blade-tuners for CM2 cavities  Also used to stabilize cavity resonance during long-term heat load studies  System in routine use for more than a year

16. S1-G at KEK  Single cavity system deployed to KEK during LFD studies of S1-G cryomodule  Successfully reduced LFD to less than 16 Hz in cavities equipped with  KEK Slide Jack Tuners  DESY/Saclay Tuners  INFN/FNAL Tuners

17. 325 MHz SSR1 Spoke Resonantor  Successfully reduced LFD in 325 MHz SSR1 spoke resonator from 3 kHz to 75 Hz at at 35 MV/m  Also stabilized resonant frequency against drifts due to pressure variations in 4K He bath

18. 8ms Pulse Test for Project X  Long Pulse Test in Fermilab HTS for proposed Project X  4ms fill, 4 ms flattop  Successfully reduced LFD from several kHz to better than 50 Hz  Very limited time available  Some stability problems observed  Compensation would not possible using ‘Standard’ half-sine pulse

19. Resonance Stabilization at NML  System was able to stabilize CCII resonance to  =16.8 Hz over 18.9 hour period during 4K commissioning of NML cyrosystem

20. SCRF Test Facility in NML  Eight-cavity system current near completion for NML CM1 at FNAL  Goal is to integrate LFD control into LLRF system

21. Summary  Procedures developed for routine pulsed operation that allow  Correction of forward/reflected baseband waveforms for cross-contamination  Accurate measurement of cavity detuning during each pulse  Characterization of detuning impulse response to the piezo  Automated determination of compensating piezo waveform  Combined procedures provide adaptive feed- forward compensation of Lorentz Force Detuning  Tests in HTS and S1-G show that detuning in ILC style cavities can be routinely reduced from many hundreds of Hz to a few tens of Hz or even better