hybrid designs - directions and potential 1 alessandro delia, r. m. jones and v. khan

1

Hybrid designs - directions and potential

Alessandro D’Elia, R. M. Jones and V. Khan

2

Outline

1. Conventional DDS limitations2. A Hybrid Design as a possible CLIC_DDS_B3. Single cell studies4. Full structure designs and related wakefield

damping5. CLIC_G + Rect. Manifold studies6. Conclusions

3

CLIC_DDS_A: regular cell optimizationThe choice of the cell geometry is crucial to meet at the same time:1. Wakefield suppression2. Surface fields in the specs

CLIC_DDS_A- 8 Fold Interleaving

Cell shape optimization for fields

DDS1_C DDS2_E

CLIC_DDS_A-Single

4

A new approach: a Hybrid Structure for CLIC_DDS_B

WGD_Structure

+DDS_Structure

=

Hybrid Structure

5

First steps on the Hybrid Structure

Erf distribution of the dipolar frequencies as

in DDS

0 50 100 150 20012

14

16

18

20

22

24

(deg)Fr

eque

ncy

(GH

z)

Very high coupling

of first dipolar band from cell to manifold via slot as in WGDS

+

The Erf distribution of the dipolar modes prevent to these modes to add in phase and this will result in a rapid decay of the wakefield in the short time scale; a high coupling will help when the mode will start to recohere in a longer time scale

First three dipole bands are shown in the picture above; encircled is the avoided crossing region which is related to the coupling: here is ~1GHz in DDS_A was <200MHz

6

Some preliminary calculation

The following calculations refer to Str#3 (see Slide#39)

V/[p

c m

m m

]

s (m)

Damped (Q=270)Undamped (Q=6500)

No interleaving

V/[p

c m

m m

]

s (m)


2-Fold interleaving

V/[p

c m

m m

]

s (m)


2-Fold interleaving

7

Summary table for new CLIC structure prototypesStructure CLIC-G-CDR CLIC-G CLIC-M CLIC-N CLIC-O CLIC-PAverage loaded accelerating gradient [MV/m] 100

RF phase advance per cell [rad] 2π/3

Average iris radius to wavelength ratio 0.11 0.1152 0.1116 0.114 0.1196Input, Output iris radii [mm] 3.15, 2.35 3.41, 2.35 3.34, 2.24 3.6, 2.1 4.04, 1.94Input, Output iris thickness [mm] 1.67, 1.00

Input, Output group velocity [% of c] 1.65, 0.83 1.99, 0.83 1.89, 0.74 2.25, 0.64 2.94, 0.53First and last cell Q-factor (Cu) 5536, 5738

First and last cell shunt impedance [MΩ/m] 81, 103

Number of regular cells 26

Structure active length [mm] 230 217 Bunch spacing [ns] 0.5 ns

Filling time, rise time [ns] 67, 21 62.6, 22.4 57.4, 22.4 62.3, 25.7 62.4, 31.0 61.1, 38.9Number of bunches in the train 312 312 322 306 295 282Total pulse length [ns] 243.7 240.5 240.3 240.6 240.4 240.5Bunch population [109] 3.72 3.72 4.1 3.72 3.74 3.73 3.74Peak input power [MW] 61.3 60.0 65.2 63.3 60.4 60.7 62.5RF-to-beam efficiency [%] 28.5 27.9 29.2 27.3 27.3 26.1 24.3Maximum surface electric field [MV/m] 230 246 243 245 268 304Max. pulsed surface heating temperature rise [K] 45 45 43 43 48 59

Maximum Sc [MW/mm2] 5.4 5.3 5.2 5.1 4.2, 5.6 3.5, 6.9

P/C [MW/mm] 3.0 3.0 3.0 2.9 2.7, 2.0 2.46, 2.27

Luminosity per bunch X-ing [1034/m2 ] 1.22 1.32 1.22 1.21 1.24

Figure of Merit [1025%/m2] 9.15 9.42 8.93 8.46 8.03

8

Basic Cell ParametersFirst Cell Last Cell

a (mm) 4.04 1.94

L (mm) 8.3316 8.3316t (mm) 4 0.7

eps 2 2b (mm) 10.964 9.669

vg (%) 2.594 0.645

fsyn (GHz) 15.7411 18.5425

ksyn (V/[pc mm m]) 43.18 95.22

g=L-t

L

bt/2

eps*t/2=elip

First Cell Last Cell

9

Cell 1 with manifold

Geometric Parametersb (mm) 10.872-10.217

WGW (mm) 6

WGH (mm) 5

SlotH (mm) 2.5

Geometric Parametersb (mm) 10.217-10.372

WGW (mm) 6

WGH (mm) 5

SlotW (mm) 3.5

10

Proposed 1st CellWGW

SlotW

WGH

SlotH

Parameters

a (mm) 4.04

L (mm) 8.3316

t (mm) 4

eps 2

b (mm) 10.282

WGW (mm) 6

WGH (mm) 5

SlotW (mm) 3.5

SlotH (mm) 3

Htot (mm) 16.282

fsyn (GHz) 15.405

fdip@0 (GHz) 12.702

Htot

11

Last Cell with Manifold

Geometric Parameters

WGW (mm) 6

WGH (mm) 5

SlotH (mm) 3.709-4.299

Fsyn (GHz) 18.530-17.699

Vg (%) 0.629-0.469

12

Proposed 1st and Last cellsWGW

SlotW

WGH

SlotH

Parameters First Cell Last CellBig Av. Cross

Last CellBig Band

a (mm) 4.04 1.94 1.94

L (mm) 8.3316 8.3316 8.3316

t (mm) 4 0.7 0.7

eps 2 2 2

b (mm) 10.282 9.209 9.573

WGW (mm) 6 6 6

WGH (mm) 5 5 5

SlotW (mm) 3.5 3 1.5

SlotH (mm) 3 4.073 3.709

Htot (mm) 16.282 16.282 16.282

fsyn (GHz) 15.405 18.189 18.5305

fdip@0 (GHz) 12.702 13.037 12.697

Vg (%) 2.338 0.56 0.63

R/Q (k/m) 9.743 20.97 21.318

ksyn (V/[pC m mm]) 36.047 80.316 94.14

Htot

13

Procedure adopted to build the full structure

• Build 1st, Mid and Last Cells• Distribute the frequencies in Erf fashion• Optimize Erf sigma minimizing the wake on

the first trailing bunch• Use this sigma to distribute iris radii and

thicknesses• Tune the correct monopole frequency using

cavity radius

14

First, Last and Mid cell parameters (Big Band) WGW

SlotW

WGH

SlotH

Parameters First Cell Mid Cell (Cell#14)

Last Cell (Cell#27)*

a (mm) 4.04 2.99 1.94

L (mm) 8.3316 8.3316 8.3316

t (mm) 4 2.35 0.7

eps 2 2 2

b (mm) 10.282 9.793 9.573

WGW (mm) 6 6 6

WGH (mm) 5 5 5

SlotW (mm) 3.5 2.5 1.5

SlotH (mm) 3 3.489 3.709

Htot (mm) 16.282 16.282 16.282

fsyn (GHz) 15.405 17.103 18.5305

fdip@0 (GHz) 12.702 12.798 12.697

Vg (%) 2.338 1.313 0.63

R/Q (k/m) 9.743 15.002 21.318

ksyn (V/[pC m mm]) 36.047 72.25 94.14

Htot

* This is used only to optimize the Erf

15

From 3 cells to the full structureFrom First, Mid and Last cell fsyn’s and kicks, we enforce a Gaussian distribution of Kdn/df as a function of f (for the details, please refer to Vasim’s PhD thesis or Roger Jones papers). The wake is Kdn/df .

Kick DistributionFsyn Distribution

2 Kdn/df

Wake envelope

16

3.5 3.55 3.6 3.65 3.7 3.752

2.2

2.4

2.6

2.8

3

n (=f/)

Wak

e on

sec

ond

bunc

h (V

/[pC

mm

m])

Best n

Best n=3.64 =0.8587

17

Geometrical parameters of the cells from Erf

1.5 2 2.5 3 3.5 4 4.50

20

40

a (mm)

# of

Cel

l

0 5 10 15 20 25 300

5

# of Cell

a (m

m)

0 1 2 3 40

10

20

30

t (mm)

# of

Cel

l

0 5 10 15 20 25 300

2

4

# of Cell

t (m

m)

0 10 20 301

1.5

2

2.5

3

3.5

# of Cell

Slot

W (m

m)

datafitted curve

a26=2.0648

SlotW26=1.5769

t26=1.0409

b will be used to tune the cell and SlotH will change accordingly to have Htot constant

0 5 10 15 20 25 3010

-1

100

101

102

s (m)

wak

e

Reconstructed wakeWake limitGdifdL Wake

Wakefield Str#1 (Large Band)

0 0.5 1 1.5 2 2.5 3 3.510

0

101

102

s (m)

wak

e

Reconstructed wakeWake limitGdifdL Wake

0.05 0.1 0.15 0.2 0.25 0.310

0

101

102

s (m)

wak

e

18

V/[p

c m

m m

]

s (m)


“Uncoupled” Wake

NB: Reconstructed wake Only 1st Dipole band

Impedance Full Transverse Impedance (all dipoles)

Transverse Impedance (First two dipole bands)

19

0 5 10 15 20 250

500

1000

1500

2000

2500

3000

3500

Cell Number

Qdi

p

Peak Number

0 5 10 15 20 251

2

3

4

5

6

7

Cell Number

Kic

k (V

/[pC

mm

m])

Peak Number

20

First, Last and Mid cell parameters (Big Av. Cross.) WGW

SlotW

WGH

SlotH



a (mm) 4.04 2.99 1.94

L (mm) 8.3316 8.3316 8.3316

t (mm) 4 2.35 0.7

eps 2 2 2

b (mm) 10.282 9.528 9.209

WGW (mm) 6 6 6

WGH (mm) 5 5 5

SlotW (mm) 3.5 3.25 3

SlotH (mm) 3 3.754 4.073

Htot (mm) 16.282 16.282 16.282

fsyn (GHz) 15.405 16.8395 18.189

fdip@0 (GHz) 12.702 12.8635 13.037

Vg (%) 2.338 1.236 0.56

R/Q (k/m) 9.743 14.73 20.97

ksyn (V/[pC m mm]) 36.047 62.574 80.316

Htot


21

Wakefield Str#2 (Large Av. Crossing)

0 2 4 6 810

-2

10-1

100

101

102

s (m)

wak

e

GdfidLReconstructed wake (only 1st Dipole Band)

0.1 0.2 0.3 0.4 0.5 0.6 0.710

-2

100

102

s (m)

wak

e

V/[p

c mm

m]

s (m)


“Uncoupled” Wake

22

Impedance

Full Impedance

First Dipole Impedance

0 2 4 6 8 10 12 140

100

200

300

400

500

Samples

Qdi

p

0 2 4 6 8 10 12 140

5

10

15

Samples

Kic

k (V

/[pC

mm

m])

Peak Number

Peak Number

23

What’s wrong?

Design strategy is not correct to ensure Erf distribution on dipoles!!!

0 5 10 15 20 2515.5

16

16.5

17

17.5

18

18.5

19

Cell number

Fsyn

(GH

z)

Non Erf distribution

0 2 4 6 8 10 12 1415

15.5

16

16.5

17

17.5

18

18.5

Number of Cell

Fsyn

(GH

z)~ Erf distribution

Samples

Str#1Str#2

Peak NumberPeak Number

24

New strategy• Fix First, Mid and last cell• Optimize • Vary “a” and “t” accordingly to Erf with previous • Find out 7 fiducial values (4 + the 3 already found for 1st,

Mid and Last cell) in order to get fsyn vs “a/t/b”• Get the distribution of fsyn corrected by ksyn• Then optimize again of the distribution of fsyn• Known fsyn evaluated from Mathematica in the previous

point, go back to fsyn vs “a/t/b” to find the geometrical parameters of the full structure

25

Detailed Procedure

3.5 3.55 3.6 3.65 3.7 3.752

2.2

2.4

2.6

2.8

3

n (=f/)

Wak

e on

sec

ond

bunc

h (V

/[pC

mm

m])

in

15.5 16 16.5 17 17.5 18 18.50

2

4

6

HFSS Dipole Frequency (GHz)

a (m

m)

datafitted curve

15.5 16 16.5 17 17.5 18 18.50

2

4

6

Dipole Frequency (GHz)

a (m

m)

datafitted curve

Re-optimize Sigma

26

First, Last and Mid cell parameters (Str#3) WGW

SlotW

WGH

SlotH



a (mm) 4.04 2.99 1.94

L (mm) 8.3316 8.3316 8.3316

t (mm) 4 2.35 0.7

eps 2 2 2

b (mm) 10.5 9.63 9.209

WGW (mm) 6 6 6

WGH (mm) 5 5 5

SlotW (mm) 3 3 3

SlotH (mm) 2.782 3.652 4.073

Htot (mm) 16.282 16.282 16.282

fsyn (GHz) 15.579 16.965 18.189

fdip@0 (GHz) 12.697 12.852 13.037

Vg (%) 2.464 1.274 0.56

R/Q (k/m) 9.959 14.582 20.97

ksyn (V/[pC m mm]) 39.799 67.183 80.316

Htot


27

Optimized theoretical Fsyn vs Fsyn HFSS simulations for regular cells

5 10 15 20 2515.5

16

16.5

17

17.5

18

18.5

# of Cells

Fsyn

(GH

z)

HFSSTheoretical

Max F=5MHz

<F>=1MHz

28

Wakefield: Comparison Str#2 and Str#3

0 2 4 6 8 1010

-3

10-2

10-1

100

101

102

s (m)

wak

e

0 0.2 0.4 0.6 0.8 1 1.2

101

102

s (m)

wak

e

Str3Str2

290 2 4 6 8 1010

-2

10-1

100

101

102

s (m)

wak

e

Wakefield

GdfidLReconstructed wake (only 1st Dipole band)

0.5 1 1.5 2

100

101

102

s (m)w

ake

0 0.1 0.2 0.3 0.4

101

102

s (m)

wak

e

Impedance

Full Impedance


30

2 4 6 8 10 12 14 16100

120

140

160

180

200

220

240

260

280

Samples

Qdi

p

2 4 6 8 10 12 14 161

2

3

4

5

6

7

8

9

10

Samples

Kic

k (V

/[pC

mm

m])

Peak Number

Peak Number

31

Comparison: Str3 coupled and uncoupled

0 5 10 15 2010

-3

10-2

10-1

100

101

102

s (m)

wak

e

0 0.5 1 1.5 2

101

102

s (m)w

ake

Coupled (reconstructed wake from GdfidL)Uncoupled

It seems that the coupling changes the nature of the wake in the early meters

32

Is Q distribution playing a role?

2 4 6 8 10 12 14 1650

100

150

200

250

300

Peak number

Qdi

p

Real Qdip from GdfidLGaussian Distribution<Real Qdip from GdfidL>

0 5 10 15 2010

-8

10-6

10-4

10-2

100

102

104

s (m)

wak

e

0 0.5 1 1.5 2 2.5

100

101

102

s (m)

wak

e

0 0.5 1 1.5 210

0

101

102

s (m)

wak

e

Uncoupled Q distribution plays a marginal role

Coupled

Coupled

33

16 16.5 17 17.5 182

2.5

3

3.5

4

Freq (GHz)

Kic

k

datafitted curve

Let’s go back to Kdn/df (1)From Fsyn distribution we get dn/df, then we multiply by the kicks and we would expect to get a Gaussian-like distribution

Uncoupled-DDS_A

Coupled-DDS_A

16 16.5 17 17.5 180

5

10

15

20

25

Freq (GHz)

# of

Cel

ls

datafitted curve

16 16.5 17 17.5 180

50

100

150

200

Freq (GHz)

arb.

Uni

ts

dn/dfK2Kdn/df

16 16.5 17 17.5 18 18.50

5

10

15

20

25

Freq (GHz)

# of

Cel

ls

datafitted curve

16 16.5 17 17.5 18 18.50

1

2

3

4

5

6

Freq (GHz)

Kic

k

datafitted curve

16 16.5 17 17.5 18 18.50

20

40

60

80

100

120

Freq (GHz)

arb.

Uni

ts

dn/dfK2Kdn/df

34

Let’s go back to Kdn/df (2)

15.5 16 16.5 17 17.5 18 18.50

10

20

30

40

Freq (GHz)

arb.

Uni

ts

dn/dfK2Kdn/df

Uncoupled-Str3

Coupled-Str3

15 16 17 18 190

5

10

15

20

25

30

Freq (GHz)

# of

Cel

ls

datafitted curve

15.5 16 16.5 17 17.5 18 18.51.5

2

2.5

3

Freq (GHz)

Kic

k

datafitted curve

15.5 16 16.5 17 17.5 18 18.5-40

-20

0

20

40

60

80

100

120

Freq (GHz)

arb.

Uni

ts

dn/dfK2Kdn/df

16 16.5 17 17.5 180

5

10

15

Freq (GHz)

# of

Pea

ks

datafitted curve

16 16.5 17 17.5 18 18.50

2

4

6

8

10

Freq (GHz)

Kic

k

datafitted curve


35

0 2 4 6 8 10

100

s (m)

wak

e

What is the problem?

0 0.5 1 1.5 2 2.5

100

101

102

s (m)

wak

e

0 10 20 3015.5

16

16.5

17

17.5

18

18.5

Cell Number

Fsyn

(GH

z)0 5 10 15 20

15

16

17

18

19

Number of points

Fsyn

(GH

z)First Dipole Impedance Uncoupled

Uncoupled with all 27 Fsyn’sUncoupled with only 16 Fsyn’s

36

CLIC_G + Rect. manifold

• Linear tapering• Cell parameters: CLIC_G• Tapering: CLIC_G i.e. linear

37

WW=7.5 WH =6.5 Wpos=14.5

Wpos

WW

WH

40

H-H Boundary condition

HFSS single cell simulations

E-H Boundary condition

0 50 100 150 20010

12

14

16

18

20

(deg)

Freq

uenc

y (G

Hz)

H-H Boundary condition

0 50 100 150 20012

14

16

18

20

22

24

(deg)

Freq

uenc

y (G

Hz)

E-H Boundary conditionHybrid DDS

Hybrid “CLIC_G”

41

Conclusions• We have shown that an average Q<200 can be achieved

with this structure with a bandwidth ranging from 2.4-3GHz

• However strong coupling results in a change of the nature of dipole distribution

• The next step is to analyze the structure for a moderate damping (as in NLC, Q~400-500) in order to preserve the nature of Erf distribution

• We have shown that with a Q<600, with 2-fold interleaving a good damping can be anyway achieved

• Further studies are needed but the structure looks promising

42

Additional slides

hybrid designs - directions and potential 1 alessandro delia, r. m. jones and v. khan

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