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P. GoudketCockcroft All Hands Meeting - March 2007

ILC Crab Cavity CollaborationAmplitude and Phase Control Development

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

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

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

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Modes in the crab cavity

frequency

TM010accelerating mode

TM110hcrabbing mode

TM110v

TE111h

TM011Need to extract the fundamental mode

Higher order modes

Extraction of the lower order mode and the higher order modes is essential to minimise disruption of the beam.

v-verticalh-horizontal

TE111v

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0.00E+00

2.00E+01

4.00E+01

6.00E+01

8.00E+01

1.00E+02

1.20E+02

1.40E+02

0.0E+00 2.0E+09 4.0E+09 6.0E+09 8.0E+09 1.0E+10 1.2E+10 1.4E+10 1.6E+10 1.8E+10

Frequency (Hz)

R/Q

Electric

Magnetic

Monopole and dipole modes impedances

• MAFIA simulations carried out on the cavity have identified modes which may have a high coupling impedance with the beam.

• Apart from the fundamental monopole mode, dipole modes are the main concern.

0.0E+00

2.0E+04

4.0E+04

6.0E+04

8.0E+04

1.0E+05

1.2E+05

0 2 4 6 8 10 12 14 16 18 20

frequency / GHz

R/Q

/ O

hms/

m^2

Dipole modes from MAFIA

Monopole modes from MAFIA

Fundamental mode

Operating mode

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Aluminium crab cavity model• An aluminium

model of the crab cavity is currently being tested, both on a bead-pulling set-up and a stretched-wire set-up.

• The modular nature of the model makes it easy to change cavity configurations.

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Bead-pull theory• A perturbing object

inserted in the cavity will perturb the fields locally and may change the resonant conditions of the cavity.

• A change in frequency is proportional to the change in stored energy.

• The frequency shift is therefore proportional to the unperturbed electric and magnetic field strengths in the cavity.

U

vdEH

U

U

f

f v EH

4

22

e: dielectric constant of the perturbing object

m: permittivity of perturbing object

: shape factor of perturbing object

v: volume of perturbing object

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Bead-pull layout

• Bead-pulling allows the measurement of the electric and magnetic field strengths at the position of the bead.

• Non-spherical beads can distinguish between longitudinal and transverse field components.

• Dielectric beads allow the perturbation to only affect the electric field and not the magnetic field.

Coupler

Bead

VNA

offset

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Bead-pull results• The fundamental and

operating mode pass-bands have been studied so far.

• Analysis of the results shows good agreement with the theory.

• More measurements will be taken once potentially troublesome modes have been identified using the stretched-wire.

R/Q

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+03

2.78E+09 2.79E+09 2.80E+09 2.81E+09 2.82E+09 2.83E+09 2.84E+09 2.85E+09

MAFIA R/Q

Measured R/Q

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-100 0 100 200 300 400

Dielectric Bead

Metal bead

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Stretched-wire

• A pulse passing down the wire generates a TEM field pattern that simulates a bunch passing through the cavity. The wake-fields generated by the pulse feeds back onto the wire and can be measured in terms of S-parameters.

Wire

VNA

Port 1 Port 2

Launch cone

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Stretched-wire system design

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P. Goudket

S21 measurementsS21 (3-cell cavity)

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

2 3 4 5 6 7 8

Frequency (GHz)

S21

(dB

)

0mm

1mm

2mm

LOG(S21DUT/S21Ref)

-30

-25

-20

-15

-10

-5

0

5

3.8 3.85 3.9 3.95 4 4.05 4.1

Frequency (GHz)

S2

1 (

dB

)

LM 0mm

LM 1mm

LM 2mm

• The transmission of the signal through the device should be reflection-free except where there is a resonance.

• Moving the wire off-axis allows the study of dipole modes.• The area ‘under the curve’ is proportional to the loss factor of a

given resonance.

3.9GHz dipole mode pass-band2-8.5GHz frequency scan

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Impedance from stretched-wire results

• The S21 data from the measurement can be converted to impedance using various formulae.

3.8 3.85 3.9 3.95 4.05

200

400

600

800

1000

1200

1400

Z (Ohm)

F (Hz)

)sin()(2

)cos()Reference(

)DUT(

121

21

je

S

S j

• A formally exact formula can be used to derive the impedance from the wire measurements.

Formally exact method:

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Coupler model• A coupler model is

being designed to fit to the aluminium crab cavity model.

• It will allow the study of coupling factors, as well as being usable on the bead-pull and stretched-wire benches to evaluate the effect of the coupler on cavity fields.

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Future work• Improve and increase understanding of

measurement accuracy.• Fully characterise all modes of interest in

all possible crab cavity configurations.• Test the coupler design and compare to

simulations.• Act upon the information received to

improve the design in order to minimise the most troublesome modes.