1
DDS limits and perspectives
Alessandro D’Elia on behalf of UMAN Collaboration
2
Damped and detuned design
• Detuning: A smooth variation in the iris radii spreads the dipole frequencies. This spread does not allow wake to add in phase
• Error function distribution to the iris radii variation results in a rapid decay of wakefield.
• Due to limited number of cells in a structure wakefield recoheres.
• Damping: The recoherence of the wakefield is suppressed by means of a damping waveguide like structure (manifold).
• Interleaving neighbouring structure frequencies help enhance the wake suppression
3
VDL
Why a Detuned Damped Structure (DDS) for CLIC
4
• Huge reduction of the absorbing loads: just 4x2 loads per structure
• Inbuilt Wakefield Monitors, Beam Position Monitors that can be used as remote measurements of cell alignments
• Huge reduction of the outer diameter of the machined disks
5
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
Consequences on wake function
Cell shape optimization for fields
DDS1_C DDS2_E
6
RF Properties of CLIC_DDS_A in comparison with CLIC_G
Parameters Units CLIC_DDS_A 8 x DDS_A 8 x DDS (Circular cells) CLIC_G
Fc (Amplitude) - 1.29 x 1024 * 3.4 x 105 * 6573 * 1.06 **
Frms (Amplitude) - 1.25 x 1027 * 2.8 x 107 * 5 x 106 * 5.9 **
Fworst (Amplitude) - 1.32 x 1028 * 7.5 x 108 * 1.55 x 108 * 25.3 **
Pulse length ns 276.5 - - 240.8
Peak input power (Pin) MW 70.8 - - 63.8
No. of bunches - 312 - - 312
Bunch population 109 4.2 - - 3.72
Max Esurf MV/m 220 - - 245
T K 51 - - 53, 47
SC W/m2 6.75 - - 5.4
bXm-2 1.36 x 1034 - - 1.22 x 1034
RF-to-beam efficiency % 23.5 - - 27.7
RF cycles - 8 - - 6
Cost - -
* 312 bunches, only first dipole band** 120 bunches, quarter structure GdfidL wake
7
A new approach: a Hybrid Structure for CLIC_DDS_B
WGD_Structure
+DDS_Structure
=
Hybrid Structure
8
Study of the wake functionThe problem
15 16 17 18 19 200
0.2
0.4
0.6
0.8
1
Freq (GHz)
Am
plitu
de (a
. u.)
RectangleGaussian
Product Re(Z)
F
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-1
100
101
102
time (ns)A
mpl
itude
(%)
Convolution WakefieldFFT(Rectangle)FFT(Gaussian)
571MHz; F=2GHZ
Question: How big must be F in order to have acceptable wake damping starting from 0.5ns?
9
Study of the wake function
Wt16-7V/[pC mm m], considering that W(0)170-180V/[pC mm m], the maximum acceptable bump must be 4%
F2.9GHz and 0.830GHz
0 1 2 3 4 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)FFT(Gaussian)
F=2GHZ
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)FFT(Gaussian)F=2.5GHZ
0 1 2 3 4 510
-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)FFT(Gaussian)
F=2.9GHZ
10
0 0.5 1 1.5 210
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
What about a “Sinc” wake?
0 0.5 1 1.5 210
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
Wake uncoupledWake coupled
This is the wakefield considering only the first dipole band
2Kdn/dfReal(Zx)
11
0 0.5 1 1.5 210
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
GdfidL “Full Wake”
1st Dipole wake from GdfidL
The presence of the higher order bands makes the scenario even less comfortable
Conclusion: It is not possible to control the position of the zeros along the wake, a smooth function of the
impedance is needed
What about a “Sinc” wake?
12
Can other types of distributions improve the wake decay?
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution Wakefield
FFT(Exp[-(x2/22)2)]FFT(Rectangle)
15 16 17 18 19
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Freq (GHz)
Am
plitu
de (a
. u.)
Rectangle
Exp[-(x2/22)2]
Product Re(Z)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)FFT(Gaussian)
906MHz F=2.9GHZ
830MHz
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Wakefield for Gaussian
Wakefield for Exp[-(x2/22)2]
13
Can other types of distributions improve the wake decay?
967MHz F=2.9GHZ
1.036GHz
0 1 2 3 4 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)
FFT(sech2[x2/2])
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)
FFT(sech1.5[x2/2])
14 15 16 17 18 19 200
0.2
0.4
0.6
0.8
1
Freq (GHz)
Am
plitu
de (a
. u.)
Rectangle
sech1.5[x2/2]
Product Re(Z)
14 15 16 17 18 19 200
0.2
0.4
0.6
0.8
1
Freq (GHz)
Am
plitu
de (a
. u.)
Rectangle
sech2[x2/2]
Product Re(Z)
14
Can other types of distributions improve the wake decay?
=1GHz
926MHz
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)
FFT(sech1.5[x2/2])
14 15 16 17 18 19 200
0.2
0.4
0.6
0.8
1
Freq (GHz)
Am
plitu
de (a
. u.)
Rectangle
sech1.5[x2/2]
Product Re(Z)
14 15 16 17 18 190
0.2
0.4
0.6
0.8
1
Freq (GHz)
Am
plitu
de (a
. u.)
Rectangle
Exp[-(x2/22)2]
Product Re(Z)
F=2.5GHZ
0 1 2 3 4 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)
FFT(Exp[-(x2/22)2])
15
What about 0.67ns?
F=2GHZ
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)
FFT(sech1.5[x2/2])
14 15 16 17 18 190
0.2
0.4
0.6
0.8
1
Freq (GHz)
Am
plitu
de (a
. u.)
Rectangle
sech1.5[x2/2]
Product Re(Z)
0 1 2 3 4 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)FFT(Gaussian)
0 1 2 3 4 510
-2
10-1
100
101
102
time (ns)
Am
plitu
de (%
)
Convolution WakefieldFFT(Rectangle)
FFT(Exp[-x4/(24)])
16
How big is the bandwidth we may achieve?
2 2.5 3 3.52.3
2.4
2.5
2.6
2.7
2.8
SlotW (mm)
Ban
dwid
th (G
Hz)
Assuming SlotW constant throughout the full structure
1.5 2 2.5 3 3.50
200
400
600
800
1000
1200
1400
SlotW (mm)
Avo
ided
cro
ssin
g (M
Hz)
CLIC_DDS_ACLIC_P
We must consider that 400-500<Av. Cross.<800-900 in order to get Qs in the order of 500-600 which will preserve the fsyn distribution
NB: The BW has been evaluated considering the difference between 1st Reg. Cell and Last Reg. Cell, i.e. Cell#27, but the total number of the cells is 26 (26 cells 27 irises); then the real BW will slightly decrease in the real structure
Geometric Parameters
a (mm) 4.04-1.94
L (mm) 8.3316
t (mm) 4-0.7
eps 2
WGH (mm) 5
WGW (mm) 6
17
Bandwidth coupled and uncoupled
5 10 15 20 2515.5
16
16.5
17
17.5
18
18.5
# of cell
Fsyn
(GH
z)
Coupled (from GdfidL)Uncoupled - Uncoupled 27 cells: F= 2.685GHz
- Uncoupled 26 cells (not shown): F= 2.47GHz- Coupled (GdfidL): F= 2.363GHz
2 2.5 3 3.52.3
2.4
2.5
2.6
2.7
2.8
SlotW (mm)
Ban
dwid
th (G
Hz)
From theoretical distribution to real structure one must take into account a reduction of ~200MHz in the BW
Av. Cross~600MHz
18
0 0.2 0.4 0.6 0.8 110
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
What is the bandwidth of the real coupled structure?
GdfidL
Reconstructed wake (only 1st Dipole band)
Uncoupled wake with 25 peaks (F=2.314GHz)
0 1 2 3 4
100
101
102
s (m)
wak
e
The uncoupled wake with 25 frequencies (black dashed curve, F=2.314GHz) falls faster than the 1st dipole band reconstructed wake from GdfidL (red dashed curve): is there any strange effect from uncoupled to coupled that further reduce the bandwidth?
19
Non Linear Fit to improve wake reconstruction
The procedure:• I take GdfidL wake as “objective” function of my
non linear regression• I use reconstruction formula as my fitting function • Fsyn are considered as given from Lorentzian fit of
the impedance peaks while Qdip and Kicks are the parameters to be optimized
• Initial guess for Qdip and kicks are from Lorentzian fit
20
Results (1)The agreement with GdfidL is quite good and, as expected, the new procedure produces a major correction at the beginning of the curve while for the rest there are no appreciable variation with the wake reconstructed using the data from Lorentzian fit.
0 0.2 0.4 0.6 0.8 110
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
GdfidLFrom LorentzianNon Linear Fit
0 5 10 15 20 25-40
-20
0
20
40
60
N
Kic
ks (V
[pC
mm
m])
Non Linear FitLorentzian
0 5 10 15 20 250
500
1000
1500
2000
2500
N
Qdi
p
Non Linear FitLorentzian <Qdip>=312
<Qdip>=512
=94=67
It is clear that the wake is reconstructed from unphysical values of kicks and Qdip. Constraints on the parameters are needed.
0 1 2 3 4 510
-2
100
102
104
s (m)
Wak
e (V
/[pC
mm
m])
GdfidLLorentzianNon Linear Fit
21
Results (2)
<Qdip>=312<Qdip>=337
=94=67
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
GdfidLFrom LorentzianNon Linear Fit
0 5 10 15 20 250
1
2
3
4
5
6
N
Kic
ks (V
/[pC
mm
m])
LorentzianNon Linear Fit
0 5 10 15 20 250
200
400
600
800
N
Qdi
p
LorentzianNon Linear Fit
With same constraints and an appropriate length of the wake, kicks and Qdip starts to converge.
22
First results for sech1.5
15.5 16 16.5 17 17.5 18 18.510
20
30
40
50
60
70
Freq (GHz)
2Kdn
/df (
V/[
pC m
m m
GH
z])
0 0.2 0.4 0.6 0.8 110
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
Uncoupled Wake for 26 CellsGdfidLBunch position (6 RF cycles)
2Kdn/df Very sharp deep, before 0.15m
Need to finalize the simulation to finalize the analysis
Very preliminary
23
Conclusions• With conventional DDS (DDS_A) it seems very difficult to meet beam
dynamics criteria• With hybrid DDS, using Gaussian distribution, it seems non realistic to
get damping within 6 RF cycles • With different distribution (in particular sech1.5) it is possible to relax the
constraint on the BW and this could allow to stay in the 0.5ns bunch spacing
• Play with Kdn/df would be interesting to see what happen and especially whether it is possible to increase the bandwidth by distributing differently the frequencies
• However the requirement of 0.5ns is quite tricky and we have not yet considered surface fields…
• I would not close totally the door to 8 RF cycles
24THANKS Igor
25
Additional slides
26
Physical interpretation of the resultConstraints:• First and last three peaks in the impedance are well separated then their Qdip and kicks are considered fixed• The rest of the kicks must be positive and spanning in a range from zero to roughly 10• The rest of the Qdip can span from zero to a maximum of 1500
<Qdip>=312<Qdip>=576
=94=67
Wake is still well approximated but kicks and especially Qdip do not seem correct. The constraints I gave are still not enough.
0 0.2 0.4 0.6 0.8 110
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
GdfidLFrom LorentzianNon Linear Fit
0 5 10 15 20 250
1
2
3
4
5
6
N
Kic
ks (V
/[pC
mm
m])
Non Linear FitLorentzian
0 5 10 15 20 250
200
400
600
800
1000
1200
N
Qdi
p
LorentzianNon Linear Fit
27
Extrapolation for longer wakeIf I extrapolate for a longer wake it is clear that Qdip and kicks evaluated from Non Linear Fit are not correct.
0 5 10 15 2010
-4
10-2
100
102
104
s (m)
Wak
e (V
/[pC
mm
m])
GdfidLLorentzianNon Linear Fit
0 1 2 3 4 510
-2
100
102
104
s (m)
Wak
e (V
/[pC
mm
m])
GdfidLLorentzianNon Linear Fit
0 0.2 0.4 0.6 0.8 110
-1
100
101
102
103
s (m)
Wak
e (V
/[pC
mm
m])
GdfidLLorentzianNon Linear Fit
I need more wake to improve Qdip calculation
28
Increasing the length of the wake: 10m
<Qdip>=315<Qdip>=312
=67=67
This makes me much more confident on the wake reconstruction
0 2 4 6 8 1010
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
GdfidLFrom LorentzianNon Linear Fit
0 5 10 15 20 250
1
2
3
4
5
N
Kic
ks (V
/[pC
mm
m])
10m5m
0 5 10 15 20 25100
200
300
400
500
600
700
N
Qdi
p
10m5m
29
Going back to the beginningQuestion was: can I evaluate the bandwidth reduction from uncoupled?
0 0.1 0.2 0.3 0.4 0.510
-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
Uncoupled 27 CellsCoupled from Non Linear FitUncoupled 26 CellsUncoupled 25 CellsCoupled from Lorentzian 0.1 0.12 0.14 0.16 0.18 0.2
10-1
100
101
102
s (m)
Wak
e (V
/[pC
mm
m])
Uncoupled 27 CellsCoupled from Non Linear FitUncoupled 26 CellsUncoupled 25 CellsCoupled from Lorentzian
From GdfidL
Uncoupled 25 Cells
Uncoupled 27 Cells
Uncoupled 25 Cells
Uncoupled 26 Cells
2Kdn/df
Answer: It seems Yes, with some minor approximation. In particular in this case it is clear that the major reduction comes from one peak which is missed. Then I estimate a reduction of ~230MHz and not of 322MHz if I choose ~2.75GHz, I should stay around 2.5GHz which is the minimum required for sech1.5 distribution.
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