F Fermilab July 6, 2005Recycler Damper Stability1 Recycler Damper High Frequency Stability Jim Crisp [email protected]

July 6, 2005 Recycler Damper Stability 1

fFermilab

Recycler Damper High Frequency Stability

Jim Crisp

[email protected]


fFermilab

RR Damper Cartoon


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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


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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)

1sin201

100sin

2

det

det

Rad

m

mm

RadGfor

turnsG

N

kick

kick

D


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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

11

1

GHforHGH

G

X

X

GHXGXX

in

out

outinout


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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

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

0.00 0.01 0.10 1.00 10.00 100.00 1000.00

-180.00

-135.00

-90.00

-45.00

0.00

45.00

90.00wire - bpm - preamp - sum&diff


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Anti-aliasing Filter

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

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

0.10 1.00 10.00 100.00 1000.00

-180.00

-135.00

-90.00

-45.00

0.00

45.00

90.00

135.00

180.00


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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

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

0.10 1.00 10.00 100.00 1000.00

LPF, CIC2, and LPF*CIC2


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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

Notch Filter

.0

1.0

2.0

0 1 2

To ƒ

ampl

itude

-180

0

180

angl

e

nT

nTang

nTmag

z n

cos1

sinarctan

cos12

1


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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@1GHz

• Kicker cables LDF5-50A (7/8” heliax)– 117 feet – 1.31db/100ft@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 Kicker Gain

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300

frequency [MHz]

3nR

ad/V

at

dc

c

GeVPmgml

MHzfV

nRadl

l

Pg

l

V

xgainkicker

9.811.04.1

1079.2sin1

2'


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Overall

• Need to measure amplifier

• Some phase error at upper end can be considered delay

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

0.01 0.10 1.00 10.00 100.00 1000.00

Preamp, LPF, CIC2, kicker

-90.00

-45.00

0.00

45.00

90.00

0.01 0.10 1.00 10.00 100.00 1000.00

Preamp, LPF phase


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Beam phase response

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

dlyUdlyUU

dlyLdlyLL

sidebandlower

dlyo

sidebandupper

dlyo

harmonicsbetatron

dlyo

harmonicsrotation

dlyo

o

tfphasetftf

mnfromsidebandupper

tfphasetftf

mnfromsidebandlower

tuneofpartfractionalituneofpartintegerm

ttfnttfn

ttfttfnsignaldetector

tftermdrivingkicker

222cos

1

222cos

2cos2cos

2cos2cos

2cos


fFermilab

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

-110.00

-100.00

-90.00

-80.00

-70.00

0.4 0.405 0.41 0.415 0.42 0.425 0.43

-180.00

-90.00

0.00

90.00

180.00

-110.00

-100.00

-90.00

-80.00

-70.00

0.57 0.575 0.58 0.585 0.59 0.595 0.6

-180.00

-90.00

0.00

90.00

180.00


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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

Documents

F Fermilab July 6, 2005Recycler Damper Stability1 Recycler Damper High Frequency Stability Jim Crisp [email protected]