Cockcroft Institute LC-ABD plenary April 2007 ILC Crab Cavity Collaboration Cockcroft Institute : –Richard Carter (Lancaster University) –Amos Dexter (Lancaster

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LC-ABD plenary April 2007

ILC Crab Cavity Collaboration

• Cockcroft Institute :– Richard Carter (Lancaster University)– Amos Dexter (Lancaster University)– Graeme Burt (Lancaster University)– Imran Tahir (Lancaster University)– Philippe Goudket (ASTeC)– Peter McIntosh (ASTeC)– Alex Kalinin (ASTeC)– Carl Beard (ASTeC)– Lili Ma (ASTeC)– Roger Jones (Manchester University)

• FNAL– Leo Bellantoni– Mike Church– Tim Koeth– Timergali Khabiboulline– Nikolay Solyak

• SLAC– Chris Adolphson– Kwok Ko– Zenghai Li– Cho Ng

http://www.lancs.ac.uk/cockcroft-institute/default.htm

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Crab Cavity Function

The crab cavity is a deflection cavity operated with a 90o phase shift.

A particle at the centre of the bunch gets no transverse momentum kick and hence no deflection at the IP.

A particle at the front gets a transverse momentum that is equal and opposite to a particle at the back.

The quadrupoles change the rate of rotation of the bunch.



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RDR Crab Cavity Parameters

Crossing angle 14 mrad

Cavity frequency, GHz 3.9 GHz

Kick required at 0.5 GeV CM 1.32 MV

Anticipated operational gradient at 0.5 GeV CM 3.81 MV m-1

Max gradient achieved in 3 cell cavity MV m-1 7.5 MV m-1

RMS relative phase stability for 2% rms Luminosity drop 0.1

RMS amplitude stability for 2% rms Luminosity drop 1.2%

Potential X beam jitter at crab cavity, m 500 m

Potential Y beam jitter at crab cavity, m 35 m

For 500 GeV CM we might use 1 nine cell cavity or two 5 cell cavities



CockcroftInstitute Anticipated RF

system

~ 14 m

Cryostat

Reference Phase 2 References to and from symmetrically placed crab cavities on other beam

DSP Phase Control

RF Amplifier

Feedback loop

DSP Phase Control

RF Amplifier

Feedback loop luminosity

reference from IP

BPM

spent beam

kick referencefrom spent beam

IP

• Minimum requirement for 14 mrad crossing is 1 9 cell or 2 5 - cell cavities per linac• 2 9 – cells would provide full redundancy in case of failure• Need space for cryostat, input/output couplers, tuning mechanisms…

Reference Phase 1

Linac timing



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TM110 Dipole mode cavity

View from top

Magnetic fieldin green

Electric Fieldin red

Beam

• The electric and magnetic fields are 90o out of phase.• For a crab cavity the bunch centre is at the cell centre when E is max and B is zero.• A particle at the centre of the bunch sees no electric or magnetic field throughout .



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Beamloading• Longitudinal electric field on axis is zero for dipole mode

• Beamloading loading is zero for on axis bunches• Bunches pass cavity centre when B transverse = 0 hence of axis E = maximum• Crab cavities are loaded by off axis bunches• Dipole deflection cavities are not loaded by off axis bunches• Power requirement for 9 cells (500 GeV CoM) ~ a few kW

0

50

100

150

200

250

300

350

400

450

0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07

External Q

Dri

ve P

ow

er (

Wat

ts p

er c

ell) Plus 1mm offset

Minus 1mm offset

No offset



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Using amplifier to extract cavity energy

180 degree phase shift on forward power after bunch

0

5

10

15

20

25

30

35

-30000 -20000 -10000 0 10000 20000 30000

time (ns)

Am

plitu

de o

f ca

vity

vol

tage

Steady forward power after bunch

0

5

10

15

20

25

30

35

-30000 -20000 -10000 0 10000 20000 30000

Time (ns)

Am

plitu

de o

f ca

vity

vol

tage

For the crab cavity the bunches can supply or remove energy.

Whilst in principle the amplifier can be used to reduce cavity energy after shifting its phase by 180o this is undesirable when one is trying to control cavity phase. It is desirable to chose a low external Q so this never needs to happen.

Bunch goes throughcavity at time t =0



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Modelling of cavity amplitude with microphonicsOscillatory bunch offset of 1 mm and random arrival phase of 1 degree

amplitude

0

50000

100000

150000

200000

250000

300000

350000

0 2000000 4000000 6000000 8000000 10000000cycles

Vo

ltag

e

Drive frequency in GHz = 3.9 GHzCentre cavity frequency in GHz = 3.9 GHzCavity Q factor = 1.0E+09External Q factor = 3.0E+06Cavity R over Q (2xFNAL=53 per cell) = 53 ohmsEnergy point ILC crab~0.0284J per cell) = 0.0284 JAmplitude set point = 301670 VMaximum Amplifier Power per cell = 300 WMaximum voltage set point (no beam) = 617740 VMaximum beam offset = 1.0 mmMaximum bunch phase error = 1.0 degBeam offset frequency = 2kHzBunch charge (ILC=3.2e-9) = 3.2E-09 CRF cycles between bunches = 1200Delay for control system in cycles = 3900Bunch length = 1 msCavity frequency shift from microphonics = 600 HzCavity vibration frequency = 230 HzInitial vibration phase (degrees) = 20 deg

PI controller with 1 ms delaycpr = 2.5e-6 Qe

cir = 1.0e-10 Qe

cpi = 2.5e-6 Qe

cii = 1.0e-10 Qe



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Modelling of cavity drive with microphonics

Out of phase Drive Amplitude

-150000

-100000

-50000

0

50000

100000

150000

200000

0 2000000 4000000 6000000 8000000 10000000

cycles

vo

ltag

e

In Phase Drive Amplitude

0

50000

100000

150000

200000

250000

300000

350000

400000

0 2000000 4000000 6000000 8000000 10000000

Cycles

Vo

ltag

e

follows microphonics

follows beam offset



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Modelling of cavity drive power with microphonics

Drive Power

0

50

100

150

200

250

300

350

400

450

500

0 2000000 4000000 6000000 8000000 10000000cycles

Wa

tts

• A single klystron can’t easily do this but solid state amplifiers can.

• To work with a Klystron we must lower the external Q



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Modelling of cavity phase with microphonics

Cavity Phase

-0.010

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0 2000000 4000000 6000000 8000000 10000000

cycles

deg

rees

Oscillatory bunch offset of 1 mm and random arrival phase of 1 degree

Modelling suggests that we might be able to control the phase of the cavity to within 6 milli-degrees of the measured phase error with respect to a local reference.



CockcroftInstituteWire Measurement

Technique


Technique employed extensively on X-band structures at SLAC.

Bench measurement provides characterization of:

- mode frequencies

- kick factors

- loss factors


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Wire Theory


A wire through a uniform reference tube can be regarded as a transmission line characterised by Ro , Lo and Co

The impedance Zll is large close to eachcavity mode . One measures the phase lag of a wave passing along the wire forthe cavity (DUT) with respect to the plain tube (Ref) then determines Zll and hence

kloss from the equations opposite.

A wire through the cavity under investigation is modelled with an additional series impedance Zll / l

As is measured as a function of frequency one obtains a loss factor at each frequency where Zll is large i.e.

for each mode.

dfZReU

V

Q

Rk ll

storedloss

mode

2

244

o

ll

Z

Zj

1

sinj

cos

jexp

S

S

REF,

DUT,

1

212

12


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Measurements


0

200

400

600

800

1000

1200

1400

1600

1800

3.8 3.85 3.9 3.95 4 4.05 4.1

Frequency (GHz)

Cou

plin

g Im

peda

nce

(Ohm

s)

1mm wire offset2mm wire offset

The coupling impedance has been calculated for a 3 cell cavity in order to investigate systematic errors in the measurements.

Measurements are underway to measure the loss factors of the dominant modes in the crab cavity.


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Long Range Wakefields


The long range wakes are found by summing over all modes and all bunches

2

// 2mod

2 cos exp2loss

all es allbunches

r sW k s

a Q

2mod

2 sin exp2loss

all es allbunches

c r sW k s

a Q


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Prototype Coupler


1 221

1 2

2

1S

A prototype Coupler has been constructed with replaceable tips and variable cavity separation to measure the external Q for a variety of coupler configurations.

A probe coupler will be matched to the ohmic Q of the cavity and calibrated using S11, with the loaded Q being measured using the bandwidth. Then the external Q can be measured from


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Placet


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.04 -0.02 0 0.02 0.04

Percentage change in frequency

Offs

et (

nm

)

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

0 50 100 150 200

Bunch number

Offs

et a

t th

e IP

(n

m)

The crab cavity has now been inserted into PLACET and bunches have been tracked through the final focus, with and without crab cavities.

The results give good agreement with the previous analytical results, and show little emittance growth.


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Phase Control Development

The phase control work at is focusing on the use of a 1.3GHz digital phase detector with fast 16 bit ADC and DAC conversion.

The digital phase detector offers an absolute measurement without calibration. They may eventually be used alongside phase quadrature measurements with double balanced mixers at an intermediate frequency for enhanced resolution. Used in quadrature double balanced mixers give both phase and amplitude.

A diode detector being used for amplitude measurements at the moment.

Vector modulation available to 4 GHzDegrees per Volt of a digital phase detector can be amplified to overcome ADC noise. Ultimate resolution is 5 milli-degree rms for 100kHz bandwidth

Digital Phase Detector Calibration Chart



CockcroftInstitute Phase Control Implementation for single

Cavity


Vector Modulator

I Q

D/A D/A

DSP

A/D

1.3 GHz Digital Phase

Detector

/3 Frequency Divider

/3 Frequency Divider

Oscilloscope

3.9 GHz Oscillator

10 MHz Reference

Amp

Spectrum Analyzer

Cavity

D/A

A randomly vibrating tuning stub simulates microphonics in a warm cavity


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16 bit ADC Sample Rate = 105MSPS, Latency = 130ns

16 bit DAC Sample Rate = 40MSPS, Settling time = 10ns

Have potential to react to a phase error

of 5 mdeg in 2-3 s.

Development of 16 bit DAC & ADC Boards


ADC 1

ADC 2

ADC 3

Digital phase detector

Gain = 100

Gain = 1

3.6o full scale

360o full scale

Diode Detector

DSP

RF

LO DAC 3

DAC 2

DAC 1 I

Q

Oscilloscope

360o = 1V

vector modulator

RF out / 3

/ 3

RF in

RF


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Status of measurement precision

Precision of the measurement is determined by looking at the jitter on a DAC output using digital amplification inside DSP, when a controller in the DSP is used to phase lock a low Q cavity.

Programmed basic control software in DSP and have demonstrated phase locking of warm cavity to better than 0.01 degrees rms within bandwidth of 50kHz.

Have yet to implement FPGAs hence slow read & write.

Read time by DSP CPU~300 ns

Write time to DAC ~200 ns.

Still using in built functions to get sine and cosine for vector modulator hence processing is a little slow.

Steady State pk-pk phase jitter = +/- 15 mdeg



CockcroftInstitute Phase

synchronisation I Position along cable

Far location

Near location time

Synchronisation when return pulse arrives at time when outward pulse is sent

adjust effective position of far location with a phase shifter

180o

0o

• If cavities are stabilized with respect to local references to ± 0.01 degrees we then seek synchronisation between local references to 0.06 degrees at 3.9 GHz = 43 fs

• Optical systems have been developed elsewhere that achieve this.

• Initial plans are to see what can be achieved with coax and s.o.a. RF components.

master oscillator

phase shifter

loop filter

directional coupler

Phase shifter

loop filter

directional coupler

digital phase detector


coax link

synchronous output

synchronous output

Interferometer line length adjustment Precision reflector

simple synchronisation scheme



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Synchronisation II

synchronous output

synchronous output

1.3 GHz master

oscillator

phase shifter

loop filter

3 dB directional coupler

phase shifter

loop filter

3dB directional coupler



~ 50 metre coax link

interferometer line length adjustment

precision reflector

D/A DSP A/D

vectormod.

vectormod.

D/A DSP A/D digital phase detector


Cavity Control Cavity Control

3.9 GHz master

oscillator

Load

phase shifter

• managing reflection on the interferometer is the biggest challenge

divide or mix to 1.3 GHz

divide or mix to 1.3 GHz

Note that the phase detectors for each

system should be as close as possible to their cavity output couplers.



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Vertical Cryostat Phase Control Tests

Local reference and controller

Local reference and controller

Phase measurement

Line to synchronise the local references must have its length continuously measured to with an accuracy of a few microns



Documents

Cockcroft Institute LC-ABD plenary April 2007 ILC Crab Cavity Collaboration Cockcroft Institute : –Richard Carter (Lancaster University) –Amos Dexter (Lancaster