dds limits and perspectives alessandro d’elia on behalf of uman collaboration 1
TRANSCRIPT
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
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• 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
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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
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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
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A new approach: a Hybrid Structure for CLIC_DDS_B
WGD_Structure
+DDS_Structure
=
Hybrid Structure
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Study of the wake functionThe problem
15 16 17 18 19 200
0.2
0.4
0.6
0.8
1
Freq (GHz)
Am
pli
tud
e (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
itud
e (%
)
Convolution Wakefield
FFT(Rectangle)
FFT(Gaussian)
571MHz; F=2GHZ
Question: How big must be F in order to have acceptable wake damping starting from 0.5ns?
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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
plit
ude
(%)
Convolution Wakefield
FFT(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
plit
ude
(%)
Convolution Wakefield
FFT(Rectangle)FFT(Gaussian)F=2.5GHZ
0 1 2 3 4 510
-1
100
101
102
time (ns)
Am
plit
ude
(%)
Convolution Wakefield
FFT(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)
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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?
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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
plit
ude
(%)
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
plit
ude
(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
plit
ude
(%)
Convolution Wakefield
FFT(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
plit
ude
(%)
Wakefield for Gaussian
Wakefield for Exp[-(x2/22)2]
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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
plit
ude
(%)
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
plit
ude
(%)
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
plit
ude
(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
plit
ude
(a. u
.)
Rectangle
sech2[x2/2]
Product Re(Z)
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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
plit
ude
(%)
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
plit
ude
(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
plit
ude
(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
plit
ude
(%)
Convolution WakefieldFFT(Rectangle)
FFT(Exp[-(x2/22)2])
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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
plit
ude
(%)
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
plit
ude
(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
plit
ude
(%)
Convolution Wakefield
FFT(Rectangle)FFT(Gaussian)
0 1 2 3 4 510
-2
10-1
100
101
102
time (ns)
Am
plit
ude
(%)
Convolution Wakefield
FFT(Rectangle)
FFT(Exp[-x4/(24)])
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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)
Ba
nd
wid
th (
GH
z)
Assuming SlotW constant throughout the full structure
1.5 2 2.5 3 3.50
200
400
600
800
1000
1200
1400
SlotW (mm)
Av
oid
ed
cro
ss
ing
(M
Hz)
CLIC_DDS_A
CLIC_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
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Bandwidth coupled and uncoupled
5 10 15 20 2515.5
16
16.5
17
17.5
18
18.5
# of cell
Fs
yn
(G
Hz)
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)
Ba
nd
wid
th (
GH
z)
From theoretical distribution to real structure one must take into account a reduction of ~200MHz in the BW
Av. Cross~600MHz
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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?
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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
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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])
GdfidL
From LorentzianNon Linear Fit
0 5 10 15 20 25-40
-20
0
20
40
60
N
Kic
ks
(V
[pC
mm
m])
Non Linear Fit
Lorentzian
0 5 10 15 20 250
500
1000
1500
2000
2500
N
Qd
ip
Non Linear Fit
Lorentzian <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
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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])
GdfidL
From LorentzianNon Linear Fit
0 5 10 15 20 250
1
2
3
4
5
6
N
Kic
ks
(V
/[p
C m
m m
])
Lorentzian
Non Linear Fit
0 5 10 15 20 250
200
400
600
800
N
Qd
ip
Lorentzian
Non Linear Fit
With same constraints and an appropriate length of the wake, kicks and Qdip starts to converge.
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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
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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
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Additional slides
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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])
GdfidL
From LorentzianNon Linear Fit
0 5 10 15 20 250
1
2
3
4
5
6
N
Kic
ks
(V
/[p
C m
m m
])
Non Linear Fit
Lorentzian
0 5 10 15 20 250
200
400
600
800
1000
1200
N
Qd
ip
Lorentzian
Non Linear Fit
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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])
GdfidL
From LorentzianNon Linear Fit
0 5 10 15 20 250
1
2
3
4
5
N
Kic
ks
(V
/[p
C m
m m
])
10m
5m
0 5 10 15 20 25100
200
300
400
500
600
700
N
Qd
ip
10m
5m
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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.