Recycler Damper High Frequency Stability

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Recycler Damper High Frequency Stability

• Jim Crisp
• crisp_at_fnal.gov

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RR Damper Cartoon
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RR Damper Features

• Two bpms separated by 90 used to simulate
  optimum betatron phase
• split tube bpms 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/Ds
• 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

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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)

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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

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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

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BPM-Preamp-Sum/Difference

• 10KHz to 150MHz

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Anti-aliasing Filter

• 70MHz LPF
• (corrected for 15nsec delay)

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ADC sampling

• ADC sample rate 4 x 53MHz 212MHz

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CIC filter with decimate by 4

• Standard approach to bandwidth limit digital
  receivers
• Linear phase
• Decimate by 4 to insure FPGA can keep up

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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

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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
• 2.34db/100ft_at_1GHz
• Kicker cables LDF5-50A (7/8 heliax)
• 117 feet
• 1.31db/100ft_at_1GHz
• (Cable delays are used to make up part of the
  required 1 turn delay)

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Kicker frequency response

• 1.4 meter long stripline kicker
• About ½ kick at 65MHz
• Changes sign at 107MHz
• Linear phase

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Overall

• Need to measure amplifier
• Some phase error at upper end can be considered
  delay

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Beam phase response

• Betatron phase has opposite sign in upper/lower
  sidebands
• Time delay has same sign

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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

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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