T24_vg1.8_disk 11WNSDVG1.8

CLIC_G un-damped @ 11.424 GHzmeasurements versus simulations

A. GrudievCERN

1.07.2009

Acknowledgements

CERN:M. GerbauxR. ZennaroA. OlyuninW. Wuensch

SLAC:Z. Li

First cellHs/EaEs/Ea Sc/Ea

2

a [mm] 3.307

d [mm] 1.753

e 1.16

f [GHz] 11.433

Q(Cu) 6814

vg/c [%] 1.83

r’/Q [LinacΩ/m] 15198

Es/Ea 1.95

Hs/Ea [mA/V] 2.6

Sc/Ea2 [mA/V] 0.37

Middle cellHs/EaEs/Ea Sc/Ea

2

a [mm] 2.887

d [mm] 1.402

e 1.15

f [GHz] 11.432

Q(Cu) 6980

vg/c [%] 1.33

r’/Q [LinacΩ/m] 16960

Es/Ea 1.95

Hs/Ea [mA/V] 2.45

Sc/Ea2 [mA/V] 0.34

Last cellHs/EaEs/Ea Sc/Ea

2

a [mm] 2.467

d [mm] 1.05

e 1.13

f [GHz] 11.426

Q(Cu) 7157

vg/c [%] 0.92

r’/Q [LinacΩ/m] 18713

Es/Ea 1.9

Hs/Ea [mA/V] 2.3

Sc/Ea2 [mA/V] 0.28

6

Gradient in 24 regular cells

Number of regular cells: Nc 24Bunch population: N 3.72x109

Number of bunches: Nb 312 Bunch separation: Ncycl 6 rf cycles

Average unloaded of 100 MV/m Average loaded of 100 MV/m

0 4 8 12 16 20 24240

50

100

150

200

250

iris number

P [M

W] (

blac

k), E

s (gre

en),

Ea (r

ed) [

MV/

m],

T

[K] (

blue

), S

c*50

[MW

/mm

2 ] (m

agen

ta)

7.5 8.4

176

205

3.03.2

90

108

41.1

23.4

Pinload = 41.1 MW, Pout

load = 23.4 MW Eff = 0.0 % tr = 0.0 ns, tf = 0.0 ns, tp = 100.0 ns

0 4 8 12 16 20 240

50

100

150

200

250

iris number

P [M

W] (

blac

k), E

s (gre

en),

Ea (r

ed) [

MV/

m],

T

[K] (

blue

), S

c*50

[MW

/mm

2 ] (m

agen

ta)

15.0 16.8

206

240

4.1

4.5

105

126

56.4

32.2

Pinload = 56.4 MW, Pout

load = 14.7 MW Eff = 28.9 % tr = 20.7 ns, tf = 54.8 ns, tp = 238.8 ns

21' PI

QR

vP

QvdzdP

gg

Simulation setup 1 & 2HFSS-quad

HFSS simulation of ¼ of the structure:Surface conductivity (Cu): 58e6 S/mSurface approximation: ds=6 μm, Total number of tetrahedra: Ntetr = 1170348Mesh density: ~ 40000 tetr / ¼ cell

S3P-quadS3P simulation of ¼ of the structure made by Zenghai Li at SLAC-ACDSurface conductivity (Cu): 57e6 S/m different

HFSS v10.1

Simulation setup 3 HFSS-cells + couplers

HFSS simulation of ¼ of input coupler + segment of 5 deg. of the cells + ¼ of output coupler :Surface conductivity (Cu): 58e6 S/mSurface approximation: ds=1 μm, Total number of tetrahedra for cells: Ntetr = 506075Mesh density: ~ 350000 tetr / ¼ cell (10 times higher than in HFSS-quad setup)

HFSS v11.1

Measurement setup 1 (reflections)

Perfectload

Perfectload

VNAport1

VNAport2

1

2 3

4

Reflection = S11+S12

Frequency correction due to air (ε = 1.00059) Frequency in vacuum: f’ = f*sqrt(1.00059) ≈ f + 3.5 MHz @ X-band

Reflection: comparison

There is very small (~1MHz) or no difference in frequency between simulations and the air corrected measurements

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.44-45

-40

-35

-30

-25

-20

-15

-10

-5

0Input

f [GHz]

Ref

lect

ion

[dB

]

measurement (Vac)HFSS-cellsHFSS-quadS3P-quadmode launcher

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.44-45

-40

-35

-30

-25

-20

-15

-10

-5

0Output

f [GHz]R

efle

ctio

n [d

B]

measurement (Vac)HFSS-cellsHFSS-quadS3P-quadmode launcher

1

2 3

4

Measurement setup 2 (transmission)Perfect load

Perfect load

VNA port1

VNA port2Transmission = S13+S23

1

2 3

4

Perfect load

VNA port2VNA port1

Perfect load

Transmission: comparison

• There is small difference between HFSS and S3P simulation results due to different conductivity used in the simulations• Both simulation results show higher transmission than air corrected measurements by about 0.2 dB

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.44-3.6

-3.4

-3.2

-3

-2.8

-2.6

-2.4

f [GHz]

Tran

smis

ion

[dB

]

measurement (Vac)HFSS-cellsHFSS-quadS3P-quad

Some useful equationsnattenuatio ln 12

2 where SτePP inout

structure lossfreein energy stored -structurelossy in energy stored -

delay group timefilling - )arg(

factorquality average -

0

120

where

WW

dSd

PWt

PWQePP

inf

loss

Qt

inout

f

On the other hand

Finally

2

ftQ

Transmission: comparing group delay

There is no difference between both HFSS and S3P simulations and the air corrected measurements

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.4454

56

58

60

62

64

66

f [GHz]

d/d

[n

s]

measurement (Vac)HFSS-cellsS3P-quad

Transmission: comparing Q-factor • There is no difference in Q-factor (~7000) between HFSS and S3P simulations.• The measured Q-factor of about 6600 is lower than the simulated value by about 6 %.

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.445800

6000

6200

6400

6600

6800

7000

7200

f [GHz]

Q

measurement: (Vac)HFSS-cellsS3P-quad

Measurement setup 3 (bead pull)

Perfectload

Perfectload

VNAport1

VNAport2

1

2 3

4

E2 ~ S11-<S11>

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.42 GHz

-50 0 50-50

0

50f=11.421 GHz

-50 0 50-50

0

50f=11.422 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.423 GHz

-50 0 50-50

0

50f=11.424 GHz

-50 0 50-50

0

50f=11.425 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.426 GHz

-50 0 50-50

0

50f=11.427 GHz

-50 0 50-50

0

50f=11.428 GHz

-50 0 50-50

0

50

ReEz [kV/m]

ImE

z [k

V/m

]

f=11.429 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.43 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.431 GHz

Bead pull in complex plane

-0.05 0 0.05-0.05

0

0.05

ImS

11

f=11.415 GHz

-0.05 0 0.05-0.05

0

0.05

f=11.416 GHz

-0.05 0 0.05-0.05

0

0.05

f=11.417 GHz

-0.05 0 0.05-0.05

0

0.05

ImS

11

f=11.418 GHz

-0.05 0 0.05-0.05

0

0.05

f=11.419 GHz

-0.05 0 0.05-0.05

0

0.05

f=11.42 GHz

-0.05 0 0.05-0.05

0

0.05

ImS

11

f=11.421 GHz

-0.05 0 0.05-0.05

0

0.05

f=11.422 GHz

-0.05 0 0.05-0.05

0

0.05

f=11.423 GHz

-0.05 0 0.05-0.05

0

0.05

ReS11

ImS

11

f=11.424 GHz

-0.05 0 0.05-0.05

0

0.05

ReS11

f=11.425 GHz

-0.05 0 0.05-0.05

0

0.05

ReS11

Measurements: S11-<S11> HFSS-cells: E

0 100 2000

20

40

|Ez|

[kV

/m]

f=11.42 GHz

0 100 2000

20

40

f=11.421 GHz

0 100 2000

20

40

f=11.422 GHz

0 100 2000

20

40

|Ez|

[kV

/m]

f=11.423 GHz

0 100 2000

20

40

f=11.424 GHz

0 100 2000

20

40

f=11.425 GHz

0 100 2000

20

40

|Ez|

[kV

/m]

f=11.426 GHz

0 100 2000

20

40

f=11.427 GHz

0 100 2000

20

40

f=11.428 GHz

0 100 2000

20

40

z [mm]

|Ez|

[kV

/m]

f=11.429 GHz

0 100 2000

20

40

z [mm]

f=11.43 GHz

0 100 2000

20

40

z [mm]

f=11.431 GHz

200 400 6000

0.1

0.2

|Ez|

[a.u

.]

f=11.415 GHz

200 400 6000

0.1

0.2

f=11.416 GHz

200 400 6000

0.1

0.2

f=11.417 GHz

200 400 6000

0.1

0.2

|Ez|

[a.u

.]

f=11.418 GHz

200 400 6000

0.1

0.2

f=11.419 GHz

200 400 6000

0.1

0.2

f=11.42 GHz

200 400 6000

0.1

0.2

|Ez|

[a.u

.]

f=11.421 GHz

200 400 6000

0.1

0.2

f=11.422 GHz

200 400 6000

0.1

0.2

f=11.423 GHz

200 400 6000

0.1

0.2

z [a.u.]

|Ez|

[a.u

.]

f=11.424 GHz

200 400 6000

0.1

0.2

z [a.u.]

f=11.425 GHz

200 400 6000

0.1

0.2

z [a.u.]

Bead pull: field magnitudeMeasurements: |sqrt(S11-<S11>)| HFSS-cells: |E|

Field distribution at different frequencies

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

1.2

z [mm]

|Ez|

[a.u

.]

HFSS-cells: f=11.42 GHzmeasurement: f=11.418 GHz

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

1.2

z [mm]

|Ez|

[a.u

.]

HFSS-cells: f=11.424 GHzmeasurement: f=11.421 GHz

120o rf phase advance per cell frequency11.424 GHz

Best match frequency11.420 GHz

RF phase advance per cell at different frequencies

0 5 10 15 20 25-8

-6

-4

-2

0

2

4

niris

dphi

[deg

]

measurement: f=11.421 GHzHFSS-cells: f=11.424 GHzS3P-quad: f=11.424 GHz

120o rf phase advance per cell frequency: 11.424 GHz

Best match frequency:11.420 GHz

0 5 10 15 20 25-10

-8

-6

-4

-2

0

2

4

niris

dphi

[deg

]

measurement: f=11.418 GHzHFSS-cells: f=11.42 GHz

Summary table for T24_vg1.8_disk

S12 Pout/Pin

τ=0.5ln (Pout/Pin)

tf=dφ/dω [ns]

tf=W0/Pin [ns]

Q=ωtf/2τQ=ωW/(Pin-Pout)

Q=ωW/Ploss

Pin100 24 cells[MW]

Measurements (Vac)

0.715 0.511 0.336 60.9 - 6600 - -

HFSS ¼ 0.732 0.536 0.312 - 58.4 6720 7010 7010

HFSS InCoupOutCoupCells 24+2

0.7310.998750.998890.733

0.5340.99750.99780.537

0.3130.00130.00110.311

60.7 <- <-59.9

59.80.460.3659.0

696012700118006910

694013000123006880

664013200123006580 42.2

3-cells model

0.569-0.533

0.282-0.315

- 54.8-59.37

6974-6764

6980 41.1

S3P (SLAC)

0.730 0.533 0.315 60.8 6927(σ=57e6)6988(σ=58e6)

42.4

Summary on comparison• Simulation results of HFSS and S3P show very good agreement • Q-factor

• All 3 different ways of calculating Q-factor: S3P, HFSS-S-parameter solver and HFSS-eigenmode solver give very close values of about 7000

• The measurements of the T24_vg1.8_disk structure made at CERN show 6 % lower Q-factor of 6600

• RF phase advance• Both HFSS and S3P simulations and air corrected measurements simulations

show 120o rf phase advance frequency of 11.424 GHz which is the design frequency

• Good agreement (± 0.5 MHz) between simulations and measurements demonstrates extremely high (sub-micron) precision of machining. For example, it is equivalent to ± 0.6 μm tolerance on the outer wall radius RF phase advance

• Structure matching• There is a design error in structure matching of about 4 MHz. The match

frequency is 11.420 GHz . To some extent this is also in agreement with the measurements

HFSS S-par solver: v10.1 versus v11.1

Simulation setup 4 HFSS-cells + couplers

HFSS simulation of ¼ of input coupler + segment of the cells made in HFSS by 5 deg. Sweep (3D geometry created in HFSS)+ ¼ of output coupler :Surface conductivity (Cu): 58e6 S/mSurface approximation: ds=1 μm,

HFSS v11.1 HFSS v10.1versus

Reflection

4 MHz 4 MHz

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.44-45

-40

-35

-30

-25

-20

-15

-10

-5

0Input

f [GHz]

Ref

lect

ion

[dB

]

HFSS10HFSS11S3P

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.44-45

-40

-35

-30

-25

-20

-15

-10

-5

0Output

f [GHz]R

efle

ctio

n [d

B]

HFSS10HFSS11S3P

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.44-3.2

-3.1

-3

-2.9

-2.8

-2.7

-2.6

-2.5

-2.4

f [GHz]

Tran

smis

ion

[dB

]

HFSS10HFSS11S3P

Transmission4 MHz

Group delay and Q-factor

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.4454

56

58

60

62

64

66

f [GHz]

d/d

[n

s]

HFSS10HFSS11S3P

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.446400

6500

6600

6700

6800

6900

7000

7100

7200

f [GHz]Q

HFSS10HFSS11S3P

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.42 GHz

-50 0 50-50

0

50f=11.421 GHz

-50 0 50-50

0

50f=11.422 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.423 GHz

-50 0 50-50

0

50f=11.424 GHz

-50 0 50-50

0

50f=11.425 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.426 GHz

-50 0 50-50

0

50f=11.427 GHz

-50 0 50-50

0

50f=11.428 GHz

-50 0 50-50

0

50

ReEz [kV/m]

ImE

z [k

V/m

]

f=11.429 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.43 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.431 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.42 GHz

-50 0 50-50

0

50f=11.421 GHz

-50 0 50-50

0

50f=11.422 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.423 GHz

-50 0 50-50

0

50f=11.424 GHz

-50 0 50-50

0

50f=11.425 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.426 GHz

-50 0 50-50

0

50f=11.427 GHz

-50 0 50-50

0

50f=11.428 GHz

-50 0 50-50

0

50

ReEz [kV/m]

ImE

z [k

V/m

]

f=11.429 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.43 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.431 GHz

RF phase advance per cellHFSS v10.1 HFSS v11.1

Summary on HFSS• It seems that there is a bug in HFSS v11. • The results of the simulations using HFSS v11 are shifted up in frequency by 4 MHz with respect to the results of the simulations using HFSS v10 or S3P • Use HFSS-S-parameter solver VERSION 10 or S3P