Impedance measurements with the ILC prototype cavity

Dr G. Burt

Cockcroft Institute

Lancaster University

P. Goudket, P. McIntosh, A. Dexter, C. Beard, P. Ambattu

Modal Calculations in MAFIA

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0 5 10 15 20

frequency (GHz)

R/Q

' (O

hms)

Dipole

Monopole

Lower Order Modes, 2.8 GHz

Operating and Same Order modes at 3.9 GHz

Trapped 5th dipole passband at 8 GHz

1st Dipole passband

Narrowband dipole modes

seen up to 18 GHz

High dipole impedances seen at 10 GHz and 13 GHz

High impedance monopole modes are not

a problem

Crab Cavity Prototype• Model fabricated at DL

and used to evaluate:– Mode frequencies– Cavity coupling– HOM, LOM and SOM Qe

and R/Q

• Modular design allows evaluation of:– Up to 13 cells.– Including all mode

couplers.

Prototype Cell Shape

• The cells are not squashed and are cylindrically symmetric.

• Two small discs is inserted into each cell in order to polarise the cavity.

Perturbation TheorySlater’s theorem

• Slater’s paper [[i]] states, in a cavity, the fractional change in frequency is proportional to the fractional change in stored energy.

• This can be used to characterise a standing wave cavity by introducing a small perturbation to the cavity and observing the change in frequency as the perturbation is induced. The change in cavity energy by a perturbation to the electric field can be calculated to be equal to

•

• [i] L.C. Maier, J.C. Slater, Field Strength Measurements in Resonant Cavities, Journal of Applied Physics, 23 (1), 1952

U

U

f

f

U

E

f

f

4

2

Non-Resonant Perturbation Technique• A perturbing object

placed within a cavity will change the resonant frequency of that structure proportionally to the field on the surface of the perturbing object.

2mm radius bead

Frequency without bead:3.98539GHzFrequency with perturbing bead:3.98554GHz-> 150kHz frequency shift

CouplerBead

VNA

offset

By pulling a bead through the cavity we can map the fields within the cavity as the frequency perturbation is proportional to the fields at that position.

Different type of beads• 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.

•Metal beads are perturbed by both fields.

Frequency shift vs. Phase shift

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Offset (mm)

Fre

qu

ency

sh

ift

(GH

z)

Df from Dphi

Df

It is often a slow process to use frequency shifts to characterise a cavity so instead it is possible to work out the frequency shift from the phase shift at a fixed frequency.

However with large perturbations the frequency calculated from the phase shift can often be smaller than the actual frequency shift as the relation moves out of the linear region.

LOM measurementsMonopole modes can be measured by directly measuring the frequency shift (or phase) by pulling a metallic circular bead along the cavity axis as the Ez field strongly dominates in this region.

As can be seen we achieved good agreement with simulations for R/Q.0.01

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2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85

frequency (GHz)

R/Q

(O

hm

s)

MAFIA R/Q

Measured R/Q

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Bead position (mm)

sqrt

(df/f

)

Dipole Bead-pull results

• If we pull a dielectric bead along the axis we can find the transverse E field on axis

• We can then use this to separate the transverse E and B fields perturbing a metal bead. • Hence we can calculate the R/Q

from Panofsky Wenzel theorem.

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0

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bead position (mm)

ph

ase

sh

ift

(de

g)

Dielectric Bead

Metal bead

Needle measurements• Alternatively we can use

a metal needle to perturb the cavity.

Corrected phase

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0

1

0 50 100 150 200 250 300 350

Position (steps)

Ph

as

e (

de

g)

Corrected phase (deg)

• According to Pierce a needle will strongly perturb electric fields aligned with it and weakly perturb perpendicular electric fields and magnetic fields.

• The other fields will however cause small errors.

Higher Order Modes

• For the HOM’s, things become more complicated.

• The bead-pull doesn’t give you the sign of the field so that has to be known.

• The reflections at the end of the beam-pipe cause trapped modes.

Corrected phase (deg)

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1

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5

6

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Corrected phase (deg)

Wire Measurements Technique

A pulse travelling along a wire has a similar field profile to a relativistic bunch.

The wire can move off axis to induce dipole modes.

• Technique employed extensively on X-band structures at SLAC.• Bench measurement provides characterisation of:

– mode frequencies– kick factors– loss factors

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 reflections 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

Transmission Theory

Impedance MatchingA conical broadband impedance transformer and a series of quarter wave resonators were used to provide a good match between the DUT and the RF source.

There is some disagreement in the community whether good matching is required or not so we erred on the side of caution

Perturbation by the wire

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phase advance / degrees

no wireno wireno wireon axison axison axison axis

The presence of the wire however perturbs the fields of the cavity and will shift the frequency and R/Q. This makes this technique only applicable to dipole, quadropole and higher azimuthal order modes.

At larger wire offsets errors creep into the dipole measurements

Wire Measurements Technique

This technique is a fast method of measuring the impedance over a large bandwidth.

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0

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Frequency (GHz)

Am

pli

tud

e (

dB

)

2mm

1mm

0mm

LOM

Operating Dipole Mode

We use an on-axis measurement as our reference and off-axis measurements as the DUT.

By observing how the coupling impedance varies with offset we can ascertain the mode order.

Operating Mode Measurements

We investigated how the measurements varied with wire offset. As we can see the R/Q decreases at large offsets due to the wire perturbation. In addition there are large error bars at low offsets due to the percentage uncertainty in the wire position.

The coupling impedance was measured for 3 and 9 cell cavities and was in good agreement with bead-pulls and MAFIA simulations.

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0

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2000

3.7 3.75 3.8 3.85 3.9 3.95 4 4.05 4.1

Frequency (GHz)

Co

up

ling

Im

pe

da

nce

(O

hm

s)

Real

Imaginary

R/Q of the 3.9GHz dipole pi-mode

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200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Wire offset (mm)

R/Q

(O

hm

/cm

^2)

Monopole modes• The monopole modes resonant frequency was found to

alter sizably as the wire was moved off-axis causing to cause errors in nearby dipole modes as the reference and DUT transmission will differ.

S21 of monopole and dipole modes around 8GHz

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7.90E+09 7.92E+09 7.94E+09 7.96E+09 7.98E+09 8.00E+09 8.02E+09 8.04E+09

Frequency (Hz)

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1

0mm offest

0.2mm offset

0.5mm offset

1mm offset

Repeatability• The measurements were repeated several times over

several days in order to ascertain repeatability of the measurements.

It is believed that due to the construction of the cavity that as the cavity was moved about cell misalignments moved causing the impedance to change. If the cavities were kept still the measurements were fairly repeatable.

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f (GHz)

Z (

Oh

m/c

m^

2)

Z 21

Z 16

Z 14

Z 22

Z23 (1)

Z23 (2)

='1.0mm_7.9_8.1GH

Results

Full System Prototype

At present we have built and are measuring the prototypes of the UK SOM coupler and power coupler and the SLAC HOM and LOM couplers to verify the full system.

Coupler Measurements0

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1 1

1

1

1e

port

probe

Q Qprobe d

Qd

11probe L

probe

Q Q

22, 1 2, 2

221

4port port Le

probe

d d QQ

Q S

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frequency (GHz)

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1

The external Q of the couplers were measured using the transmission from a calibrated probe of known Qe.

This is more accurate for high Qe’s than a reflection measurement.

Power Coupler Prototype Measurements

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Penetration (cm)

Ext

erna

l Q (

105 )

40.0mm43.5mm

48.5mm

53.5mm40.0mm

43.5mm48.5mm

53.5mm

In the spring 2007 I made measurements of power coupler and SOM coupler prototypes in order to verify the codes.

3 cell cavities were used to preserve field flatness.

There was some issues with metallisation of the window which have now been rectified.

Dipole modes damping by SOM coupler

The SOM coupler used was not the

coupler modelled by SLAC. The CI SOM

coupler was manufactured

instead.

This is not the full external Q, just the contribution from the SOM. After adjustment

the operating mode Qe is 8.84E9

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3.8 4.3 4.8 5.3 5.8

Frequency (GHz)

Ex

tern

al Q

MWS Simulations

Measurements

LOM Coupler Prototype external Q measurements

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frequency (GHz)

Ext

ern

al Q

Measurements

Simulations

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LOM mode #

Ext

erna

l QSLAC Qe

Measured Qe

CI Qe

The LOM coupler was found to give good agreement with both MWS and Omega 3P simulations. However it doesn’t meet the damping requirements for the ILC.

HOM coupler

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frequency (GHz)

exte

rnal

Q

The HOM coupler is the most complex of all 4 couplers and a large amount of time was spent analysing it.

Modes up to 7.8 GHz were found. Modes not found assumed to flow out of the beam-pipes.

HOM Coupler

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3.88 3.9 3.92 3.94 3.96 3.98 4 4.02 4.04 4.06 4.08

frequency (GHz)

exte

rnal

Q

SLAC simulations

Horizontal Measurements

Vertical Measurements

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Frequency (GHz)

Ref

lect

ion

Coe

ffici

ent

The filter was made adjustable to investigate manufacturing errors. The gap sensitivity was found to be 0.135 MHz/ micron.

The measurements were found to give good agreement with the SLAC simulations

(courtesy of Z. Li and L. Xiao)

A few LHC crab cavity simulations

G. Burt, R. Calaga

Short Range Wakes

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s (cm)

Wz

(V/p

C)

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Bun

ch C

harg

e de

nsity

Wz (V/pC)

bunch

ECHO 2D was used to calculate the longitudinal short range wakes in Rama’s design for the LHC cavity. The transverse wake was calculated analytically.

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S (cm)

Wt

(V/p

C/m

)

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nch

ch

arg

e D

en

sity

Wt (V/pC/m)

bunch

Dipole HOMsThen MAFIA’s 2D eigensolver was used to look at the dipole modes up to 3 GHz. Some of these modes will be highly perturbed by the boundary conditions at the end of the beampipes.

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frequency (GHz)

R/Q

(O

hms)

Beam-pipe LOM coupler

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10

100

1000

10000

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Penetration into the cavity (mm)

Ext

ern

al Q

1st monopole

2nd monopole

The damping of the two LOM’s were investigated using a KEK-B style beam-pipe LOM coupler. The inner diameter was 10cm and the penetration was varied. This currently doesn’t have a notch filter and is just a basic investigation.

If we go for this design it means that we need a large beam-pipe to fit the coupler which will reduce the maximum voltage.

LOM coupler modelling

27mm

12mm

4mm

72mm

25mm

7mm

ILC Crab cavity Single cell Qe LOM=150

A LOM coupler can be coaxial hook type LOM coupler can get very low external Q’s.

Waveguide LOM couplers are also effective.

SOM Waveguide CouplerA waveguide SOM coupler was investigated and achieved a Qe of 4.5x103. The WG was positioned 40 mm from the cavity.

A scheme of a WG power coupler, two WG SOM/HOM couplers cut-off to the fundamental and a beam-pipe, coaxial or WG LOM coupler on the other side could be a potential damping scheme. The power coupler would have to also extract the other mode in the 1st dipole pass-band.