grudiev 17.06.2009

T24_vg1.8_disk 11WNSDVG1.8

CLIC_G un-damped @ 11.424 GHzmeasurements versus simulations

(preliminary)

A. Grudiev17.06.2009

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 [

MW

] (b

lack

), E

s (

gre

en),

Ea (

red

) [M

V/m

],

T

[K

] (b

lue)

, 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, P

outload = 23.4 MW

Eff = 0.0 % tr = 0.0 ns, t

f = 0.0 ns, t

p = 100.0 ns

0 4 8 12 16 20 240

50

100

150

200

250

iris number

P [

MW

] (b

lack

), E

s (

gre

en),

Ea (

red

) [M

V/m

],

T

[K

] (b

lue)

, 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, P

outload = 14.7 MW

Eff = 28.9 % tr = 20.7 ns, t

f = 54.8 ns, t

p = 238.8 ns

2

1'PI

Q

R

vP

Qvdz

dP

gg

Simulation setup 1 & 2HFSS-quad

HFSS simulation of ¼ of the structure:Surface conductivity (Cu): 58e6 S/mSurface approximation: ds=5 μm, Total number of tetrahedra: Ntetr = 1024991Mesh density: ~ 35000 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 v11.1

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)

Reflection: comparison

• There is a shift up in frequency of ~3.5 MHz due to air correction in the measurements• The HFSS simulation results are about 4 MHz higher than air corrected measurements• The S3P simulation results are about 4-5 MHz lower than air corrected measurements• There is very small (~1MHz) or no difference between S3P 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

0

f [GHz]

Ref

lect

ion

[dB

]

input measurementoutput measurement

input measurement - Air corrected

output measurement - Air corrected

input HFSS-cellsoutput HFSS-cells

input HFSS-quad

output HFSS-quad

input S3P-quadoutput S3P-quad

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

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.44-4

-3.8

-3.6

-3.4

-3.2

-3

-2.8

-2.6

-2.4

-2.2

-2

f [GHz]

Tran

smis

ion

[dB

]

S3P-quad

HFSS-quadHFSS-cells

measurement: S13+S23

measurement: |S13|+|S23|

measurement: 2*S13measurement: 2*S23

measurement: Air corrected

Transmission: comparison • There is a shift up in frequency of ~3.5 MHz due to air correction in the measurements• The HFSS simulation results are about 4 MHz higher than air corrected measurements• The HFSS simulation results shows more transmission by about 0.3 dB at 11.424 GHz• The S3P simulation results shows less transmission than HFSS by about 0.15 dB at 11.424 GHz

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

W

W

d

Sd

P

Wt

P

WQePP

inf

loss

Q

t

inout

f

On the other hand

Finally

2

ftQ

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.4450

52

54

56

58

60

62

64

66

68

70

f [GHz]

d /

d

[ns

]

measurement

measurement: Air correctred

HFSS-quadHFSS-cells

S3P-quad

Transmission: comparing group delay

• There is a shift up in frequency of ~3.5 MHz due to air correction in the measurements• The HFSS simulation results are about 4 MHz higher than air corrected measurements• There is no difference between S3P simulations and the air corrected measurements

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

measurement: Air correctedHFSS-cells

S3P-quad

Measurement setup 3 (bead pull)

Perfectload

Perfectload

VNAport1

VNAport2

1

2 3

4

E2 ~ S11-<S11>

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>

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.421 GHz

-50 0 50-50

0

50f=11.422 GHz

-50 0 50-50

0

50f=11.423 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.424 GHz

-50 0 50-50

0

50f=11.425 GHz

-50 0 50-50

0

50f=11.426 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.427 GHz

-50 0 50-50

0

50f=11.428 GHz

-50 0 50-50

0

50f=11.429 GHz

-50 0 50-50

0

50

ReEz [kV/m]

ImE

z [k

V/m

]

f=11.43 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.431 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.432 GHz

HFSS-cells: E

0 100 2000

20

40

|Ez|

[kV

/m]

f=11.421 GHz

0 100 2000

20

40

f=11.422 GHz

0 100 2000

20

40

f=11.423 GHz

0 100 2000

20

40

|Ez|

[kV

/m]

f=11.424 GHz

0 100 2000

20

40

f=11.425 GHz

0 100 2000

20

40

f=11.426 GHz

0 100 2000

20

40

|Ez|

[kV

/m]

f=11.427 GHz

0 100 2000

20

40

f=11.428 GHz

0 100 2000

20

40

f=11.429 GHz

0 100 2000

20

40

z [mm]

|Ez|

[kV

/m]

f=11.43 GHz

0 100 2000

20

40

z [mm]

f=11.431 GHz

0 100 2000

20

40

z [mm]

f=11.432 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 120o phase advance per cell

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

z [mm]

|Ez|

[a.

u.]

HFSS-cells: f=11.428 GHz

measurement: f=11.421 GHz

0 5 10 15 20 25-126

-124

-122

-120

-118

-116

-114

iris number

d [

deg]

measurement: f=11.421 GHz, per cell

measurement: f=11.421 GHz, averageHFSS-cells: f=11.428 GHz, per cell

HFSS-cells: f=11.428 GHz, average

2 5 8 11 14 17 20 23-5-4-3-2-1012345T24_vg1.8 @ 11.424 GHz

cell number

[Pa

dv-

12

0]

(de

g)

S3P simulation resultscourtesy of Zenghai Li

The best frequency fit for 120 deg average phase advance per cell is the same for S3P simulations and air corrected measurements: 11.424 GHz and is different for HFSS: 11.428 GHz

Field distribution at the best match• The best match frequency is 3-4 MHz lower than the 120 deg phase advance frequency both in HFSS simulation and measurement• The average phase advance per cell is about 3 deg/cell different at the best match frequency both for HFSS simulation and measurement• There is still residual standing wave even in the case of HFSS simulations where the match is about -40 dB

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

z [mm]

|Ez| [a

.u.]

HFSS-cells: f=11.424 GHz

measurement: f=11.418 GHz

0 5 10 15 20 25-124

-122

-120

-118

-116

-114

-112

-110

-108

iris number

d [

deg]

measurement: f=11.418 GHz, per cell

measurement: f=11.418 GHz, average

HFSS-cells: f=11.424 GHz, per cell

HFSS-cells: f=11.424 GHz, average

Power for <Eacc> = 100 MV/m

11.42 11.422 11.424 11.426 11.428 11.43 11.43240

45

50

55

60

65

70

75

f [GHz]

P[M

W]

for

<E

acc>

=10

0MV

/m

S3P

HFSS

Summary table for T24_vg1.8_diskparameters at 11.424 GHz if not stated otherwise

S12 Pout/Pin

τ=0.5ln (Pout/Pin)

tf=dφ/dω [ns]

tf=W0/Pin [ns] Q=ωtf/2τ Q=ωW

/PlossPin100 24 cells[MW]

Measurements

0.7077 0.5008 0.3457 63.11 - 6600 -

HFSS ¼ 0.741 0.549 0.2998 58.67 58.65 7025 7006

HFSS InCoupOutCoupCells 24+2

0.74120.998750.998890.743

0.54940.99750.99780.552

0.29940.00130.00110.297

58.590.4600.36257.77

702012700118006980

700513200123007001 42.1 @

11.428 GHz

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

Conclusions• There is no difference between HFSS simulations of ¼ of the structure and HFSS simulation of couplers + cells despite a factor 10 difference in the mesh density. This demonstrates that numerical convergence has been reached• All 3 different ways of calculating Q-factor: S3P, HFSS-S-parameter solver and HFSS-eigenmode solver give very close values of 6990, 7020 and 6980, respectively• The measurements of the T24_vg1.8_disk structure made at CERN show 6 % lower Q-factor of 6600• The difference in the simulated transmission between HFSS-S-parameter and S3P comes from the “geometrical” type of error which is equivalent to a difference of 4 MHz in the frequency for the 120 deg phase advance per cell• S3P simulations show 120 deg phase advance frequency of 11.424 GHZ. This is the frequency used in design of the cells using HFSS-eigenmode solver meaning that HFSS-eigenmode solver and S3P agrees and that the systematic error of 4 MHz in the case of T24_vg1.8_disk geometry comes from the HFSS-S-parameter solver• The 120 deg phase advance frequency in the air corrected measurement is 11.424 GHz which is the same as design frequency with the accuracy of ± 0.5 MHz. This demonstrates extremely high (sub-micron) precision of machining. For example, it is equivalent to ± 0.6 μm tolerance on the outer wall radius

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

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

0

f [GHz]

Ref

lect

ion

[dB

]

input measurementoutput measurement

input measurement - Air corrected

output measurement - Air corrected

input HFSS-cellsoutput HFSS-cells

input HFSS-quad

output HFSS-quad

input S3P-quadoutput S3P-quad

HFSS v11.1

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

0

f [GHz]

Ref

lect

ion

[dB

]

input measurementoutput measurement

input measurement - Air corrected

output measurement - Air corrected

input HFSS-cellsoutput HFSS-cells

input HFSS-quad

output HFSS-quad

input S3P-quadoutput S3P-quad

HFSS v10.1

Transmission

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.44-4

-3.8

-3.6

-3.4

-3.2

-3

-2.8

-2.6

-2.4

-2.2

-2

f [GHz]

Tra

nsm

isio

n [d

B]

S3P-quad

HFSS-quadHFSS-cells

measurement: S13+S23

measurement: |S13|+|S23|

measurement: 2*S13measurement: 2*S23

measurement: Air corrected

HFSS v11.1

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.44-4

-3.8

-3.6

-3.4

-3.2

-3

-2.8

-2.6

-2.4

-2.2

-2

f [GHz]

Tran

smis

ion

[dB

]

S3P-quad

HFSS-quadHFSS-cells

measurement: S13+S23

measurement: |S13|+|S23|

measurement: 2*S13measurement: 2*S23

measurement: Air corrected

HFSS v10.1

Group delay

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.4450

52

54

56

58

60

62

64

66

68

70

f [GHz]

dphi

/dw

[ns]

measurement

measurement: Air correctred

HFSS-quadHFSS-cells

S3P-quad

HFSS v11.1

11.4 11.405 11.41 11.415 11.42 11.425 11.43 11.435 11.4450

52

54

56

58

60

62

64

66

68

70

f [GHz]

dphi

/dw

[ns]

measurement

measurement: Air correctred

HFSS-quadHFSS-cells

S3P-quad

HFSS v10.1

Q-factor

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

measurement: Air correctedHFSS-cells

S3P-quad

HFSS v11.1

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

measurement: Air correctedHFSS-cells

S3P-quad

HFSS v10.1

Phase advance per cell

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.421 GHz

-50 0 50-50

0

50f=11.422 GHz

-50 0 50-50

0

50f=11.423 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.424 GHz

-50 0 50-50

0

50f=11.425 GHz

-50 0 50-50

0

50f=11.426 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.427 GHz

-50 0 50-50

0

50f=11.428 GHz

-50 0 50-50

0

50f=11.429 GHz

-50 0 50-50

0

50

ReEz [kV/m]

ImE

z [k

V/m

]

f=11.43 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.431 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.432 GHz

HFSS v11.1

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.421 GHz

-50 0 50-50

0

50f=11.422 GHz

-50 0 50-50

0

50f=11.423 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.424 GHz

-50 0 50-50

0

50f=11.425 GHz

-50 0 50-50

0

50f=11.426 GHz

-50 0 50-50

0

50

ImE

z [k

V/m

]

f=11.427 GHz

-50 0 50-50

0

50f=11.428 GHz

-50 0 50-50

0

50f=11.429 GHz

-50 0 50-50

0

50

ReEz [kV/m]

ImE

z [k

V/m

]

f=11.43 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.431 GHz

-50 0 50-50

0

50

ReEz [kV/m]

f=11.432 GHz

HFSS v10.1

Phase advance per cell

5 10 15 20 25-124

-122

-120

-118

-116

-114

-112

niris

dphi

[de

g]

measurement: f=11.421 GHz, per cell

measurement: f=11.421 GHz, averageHFSS-cells: f=11.424 GHz, per cell

HFSS-cells: f=11.424 GHz, average

HFSS v10.1

2 5 8 11 14 17 20 23-5-4-3-2-1012345T24_vg1.8 @ 11.424 GHz

cell number

[Pa

dv-

12

0]

(de

g)

S3P simulation resultscourtesy of Zenghai Li

Outlook• To cross-check above conclusions S-parameter frequency sweep calculated with S3P would be very useful• Similar study of the other structures (T18, TD18, TD24, …) would also help to understand the limitations of structure manufacturing as well as the structure design using HFSS-S-parameter solver

Recipes for structure matching• Use HFSS-S-parameter solver VERSION 10• Use S3P• …