f Fermilab July 6, 2005Recycler Damper Stability1 Recycler Damper High Frequency Stability Jim Crisp

f Fermilab July 6, 2005Recycler Damper Stability2 RR Damper Cartoon

f Fermilab July 6, 2005Recycler Damper Stability3 RR Damper Features Two bpm’s separated by 90° used to simulate optimum betatron phase “split tube” bpm’s and 150kohm preamps provide flat frequency response from 10KHz to 70MHz Use A-B to avoid problems at low intensity –Optimize gain for highest beam intensity One turn delay –The error from each pbar is applied to that pbar Digital filter –Used to set 1 turn delay and provide comb filter –12 bit 212MHz A/D’s Commercial 100watt solid state amplifiers –10KHz to 230MHz –580nRad max kick (0.58mm max linear betatron oscillation) 1.4meter long stripline kicker –response is 3db down at 50MHz 50MHz will cover the first 550 rotation harmonics Lowest betatron frequency ~35KHz

f Fermilab July 6, 2005Recycler Damper Stability4 Feedback Loop 1/e time constant ~1/open loop gain –100turns for 1urad/mm gain (1% correction/turn) (.5urad/mm should be sufficient – V. Balbekov)

f Fermilab July 6, 2005Recycler Damper Stability5 Stability Requirements GH = -1 is a problem The phase shift must be less than 180º when the open loop gain is greater than 1 –Desire 30 to 60º phase margin

f Fermilab July 6, 2005Recycler Damper Stability6 Damper Components Stability requirement applies to all system elements in series –BPM –Preamp –Sum/Difference –Anti aliasing filter 70MHz LPF –Digital filter Sampling effects CIC/decimation filter Notch filter –Amplifier –cables –Kicker –Beam response

f Fermilab July 6, 2005Recycler Damper Stability7 BPM-Preamp-Sum/Difference 10KHz to 150MHz

f Fermilab July 6, 2005Recycler Damper Stability8 Anti-aliasing Filter 70MHz LPF –(corrected for 15nsec delay)

f Fermilab July 6, 2005Recycler Damper Stability9 ADC sampling ADC sample rate 4 x 53MHz = 212MHz

f Fermilab July 6, 2005Recycler Damper Stability10 CIC filter with decimate by 4 Standard approach to bandwidth limit digital receivers –Linear phase Decimate by 4 to insure FPGA can keep up

f Fermilab July 6, 2005Recycler Damper Stability11 Digital notch filter Remove energy at rotation harmonics to limit emittance growth –Depth of notches about 65db for the 12 bit ADC (If all notches identical, the closed orbit error would be reduced by 65db) –Noise induced emittance growth ~0.5 pi-mm-mRad/Hr –±18º phase shift -0.5db at 0.4 and 0.6 times the rotation frequency

f Fermilab July 6, 2005Recycler Damper Stability12 Amplifiers/Cables Amplifier Research KMA2020 –100Watt –10KHz to 230MHz –Just received Amplifiers Tuesday, will measure ASAP BPM cables LDF4-50 (1/2” heliax) –228 to 445 feet Kicker cables LDF5-50A (7/8” heliax) –117 feet (Cable delays are used to make up part of the required 1 turn delay)

f Fermilab July 6, 2005Recycler Damper Stability13 Kicker frequency response 1.4 meter long stripline kicker –About ½ kick at 65MHz –Changes sign at 107MHz –Linear phase

f Fermilab July 6, 2005Recycler Damper Stability14 Overall Need to measure amplifier Some phase error at upper end can be considered delay

f Fermilab July 6, 2005Recycler Damper Stability15 Beam phase response Betatron phase has opposite sign in upper/lower sidebands –Time delay has same sign

f Fermilab July 6, 2005Recycler Damper Stability16 Beam Response Corrected for delays and phase advance –Betatron phase has opposite phase on upper/lower sidebands –Delay has same phase for upper/lower sidebands –All betatron sidebands will have the same gain/phase response shown below As the damper gain increases, instability will start at the edges of the distribution –Probably at the low or high end of the damper frequency range

f Fermilab July 6, 2005Recycler Damper Stability17 Status 7/6/05 Preamps are installed at 2 locations –Remaining 2 at next opportunity Power amplifiers arrived yesterday –Chassis should be out of the shop this week One digital filter board is stuffed and debugging has begun –Critical path Would like some proton time to measure/verify beam response