1. LLRF regulation of CC2 operated at 4˚K Gustavo Cancelo for the AD, TD & CD LLRF team

2. Objectives of this talk Show good regulation results operating CC2 at NML (pulsed mode). – Validate the combined RF plus active resonant control approach. – Validate the fixed feed forward plus PI (proportional + integral) closed loop control, by comparison to only FF and P. – Raise awareness that the good numbers are obtained at the cost of RF power overhead and a control system working on the linear region of the RF klystron. Show some “integrated microphonic” numbers. Show that have good working LLRF systems and we keep improving them. – Some LLRF components can be used or adapted for Project X R&D. – New LLRF equipment is also needed.

3. CC2 operated in pulsed mode (800µs flattop) Feedforward ON & Feedback OFF Feedforward & Feedback ON RF amplitude and phase look flat, but how flat are they?

4. FF LLRF Control +++ r + + - + ++ d= n= x y e u K Resonance control:FF (piezo) v P: plant. C: controller. FF: feed forward control. r: reference. e: error. u: control drive. d: load disturbance. x: process states. n: measurement noise. y: observed output. LLRF control regulates measured error signals. The beam will see measurement noise that the regulator won’t see. P: CC2 This four transfer functions are particularly important Beam LFD Microphonics Transmitter noise d Receiver noise ADC noise Master Osc.

5. CC2 detuning CC2 has been operated at 4.5˚K and shows large detuning fluctuations of up to ±500 Hz. The oscillations mainly come from cryogenic pressure fluctuations.

6. Proportional control closed loop gain K P =20 The stability of the gradients is greatly improved by the PI control and higher gains. – rms values of10 -4 for amplitude and 0.01 degrees for phase after the first 20 or 30μs of the flattop. During the first few tens of microseconds, a small overshoot or undershoot is observed for very large cavity detuning. The integral part of the PI control rejects large low frequency disturbances and has 0 steady state error and a settling time of few tens of microseconds. Proportional + integral control closed loop gain K P =100, Ki=6.2 million r/s Vertical scale x30 times smaller σ=10 -4 σ=0.01 degrees overshoot ~300 RF pulses plotted together

7. Gradient overshoot The overshoot shows a strong correlation with the amplitude of the detuning. CC2 gradient amplitude follows a square law and the phase a tangent law as a function of the detuning.

8. Forward and reflected power The PI control is an effective regulator as long as there is enough RF power available and the RF operates in the linear region. A cavity detuned by 500Hz (~2 half bandwidths) requires 4 times more power. Pfor/Pref crosstalk Pref not zero because QL not matched

9. Piezo tuners and RF control 7 hr run combining both piezo and RF control. The piezo is used to track and compensate low frequency fluctuations of pulse to pulse detuning. These fluctuations are attributed to cryogenic pressure fluctuations. The piezo is not compensating LFD at this point. During the run, the pressure fluctuates 0.34% rms with a dominant noise component of 3.7 minutes. Piezo OFFPiezo ON σ = 272 Hzσ = 51 Hz

10. RF regulation with piezo ON The peak to peak overshoot is 4 x 10 -4 for amplitude and 0.04 degrees for phase, that is 10 to 15 times smaller than with piezo OFF. The rms regulation for the rest of the flattop is smaller than 2 x 10 -5 and 0.001 degrees respectively Zoomed in

11. Integrated microphonics Since we sample at 1 Hz, the microphonic spectrum is folded many times around the 0.5 Hz Nyquist frequency. A~30 minute run shows an rms of 30Hz Calculated as the difference in cavity detuning at the end two consecutive pulses

12. Summary and (near) future work Excellent field regulation achieved with RF and resonance (piezo) control. – RF and resonance control can work together. RF power must be available for control. For Project X the RF disturbances will be of the same nature but with different values and order of importance. We have good working LLRF systems and we keep improving them. Near future work – Study the performance of the PI control near klystron saturation. – For that we need to lower the high voltage and operate the CC2 at high gradient. We count on active LFD compensation Resonant frequency tracking with piezo may be needed.