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)
Damped (Q=600)Undamped (Q=6500)
2-Fold interleaving
V/[p
c m
m m
]
s (m)
Damped (Q=270)Undamped (Q=6500)
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
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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
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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)
Damped (Q=1350)Undamped (Q=6500)
“Uncoupled” Wake
NB: Reconstructed wake Only 1st Dipole band
Impedance Full Transverse Impedance (all dipoles)
Transverse Impedance (First two dipole bands)
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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
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 9.528 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
* This is used only to optimize the Erf
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)
Damped (Q=156)Undamped (Q=6500)
“Uncoupled” Wake
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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
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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
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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
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) 10.5 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
* This is used only to optimize the Erf
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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
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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
First Dipole 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
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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
First Dipole Impedance
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
38
39
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
43