1. Vasim Khan & Roger Jones
MAIN LINAC DDS DESIGN
Vasim Khan & Roger Jones

2. Outlook CLIC scheme Two Beam Acceleration Optimised parameters
What is wakefield
Main Linacs
Design constraints
Present structure
DDS design
Comparison
Forthcoming
V. Khan HEP group, The University of Manchester /41

3. CLIC scheme e- e+ collider C. M. Energy : 3 TeV
Normal conducting technology
Frequency : 12 GHz
Acc. Gradient : 100 MV/m
Luminosity : ~ cm-2 s-1
Novel technique : Two beam acceleration
Overall site length 48 km (compact ?)
V. Khan HEP group, The University of Manchester /41

4. CLIC parameters
Parameters
Designed value
unit
C.M Energy 3
TeV
Frequency
GHz
Acc. Gradient
100
MV/m
No. of cells per structure 24
luminosity
5.9 x 1034
cm-2 s-1
Luminosity in 1% of energy
2 x 1034
No. of particles per bunch
3.72 x 109
No. of bunches per pulse
312
Bunch length 44 μm
Transverse emittance IP
660, 20
nm rad
Beam size IP
40,0.9 nm
Crossing IP 20
mrad
Beam Power 14 MW
Total site length
48.4 km
Total site AC power
392
Overall wall plug-beam efficiency
7.1 %
V. Khan HEP group, The University of Manchester /41

5. CLIC complete layout
V. Khan HEP group, The University of Manchester /41

6. Two Beam Acceleration 140,000 main linac structures.
It is difficult to supply power using conventional RF source i.e. Klystron......it will require 10,000’s of such klystrons.
A low energy high current beam (drive beam) running parallel to the main beam.
Drive beam interacts with the impedance of the Power Extraction and Transfer Structures.
Drive beam is thus decelerated.
The decelerated energy is used to accelerate main beam.
V. Khan HEP group, The University of Manchester /41

7. Why ? 1) Linacs ? 2) Normal conducting ?
3) X-band frequency of 12 GHz ?
Synchrotron radiation [1] Energy loss per revolution [1]
[1] S.Y. Lee, Accelerator Physics.
Colliders
Particle
Beam energy
Circumference
∆E/rev.
circular
TeV km
LHC
p-p
7.0 27
6.0 keV
LEP
e- e+
0.1
26.7
2.8 MeV
CLIC*
1.5
106
* Assume if CLIC was a circular collider
V. Khan HEP group, The University of Manchester /41

8. Is there any energy loss in linear acceleration ?
In Linac we consider the power radiated to
the power supplied by an external source [1]
[1] S.Y. Lee, Accelerator Physics.
Colliders
Particle
Beam energy
Accelerator length
P/(dE/dt)
Linear
TeV km %
CLIC
e- e+
1.5 21
10-12
CLIC* 55 20
1.0
* Assume if CLIC was proposed to accelerate with accelerating gradient of ~2.75 GeV/m
V. Khan HEP group, The University of Manchester /41

9. Frequency scaling of rf parameters
Normal conducting ?
Need high gradient for a feasible site length
High gradient cavities will have high surface fields
Super conducting (SC) cavities can be operated up to ~ 40 MV/m
High gradient in SC cavities will quench the superconductivity.
Possible option is Normal Conducting (NC) cavities.
Frequency scaling of rf parameters
RF parameters
Requirement
Normal conducting
Super
conducting
RF surface resistance (Rs)
Low
Power dissipated (Pdis)
Quality factor (Q)
High
Shunt impedance per unit length (R’)
V. Khan HEP group, The University of Manchester /41

10. X-band (8-12 GHz)? Initial proposal was 150 MV/m @ 30 GHz
Operation with these parameters will suffer major breakdown issues
The optimisation procedure has resulted in 100 MV/m gradient with 12 & 14 GHz frequency option.
Lower frequency was chosen to utilise the expertise and technical know-how of the discontinued NLC/GLC project which was also proposed at 12 GHz.
V. Khan HEP group, The University of Manchester /41

11. What is wakefield ?
V. Khan HEP group, The University of Manchester /41

12. What is wakefield ? Fields excited by the ultra relativistic particles
Short range wake :tail of the bunch experiences field excited by the head of the bunch
Long range wake : trailing bunches experiences fields excited by the leading bunches
Transverse wake : luminosity dilution
Longitudinal : energy spread
V. Khan HEP group, The University of Manchester /41

13. Main Linac
V. Khan HEP group, The University of Manchester /41

14. Glossary 1 Monopole mode Dipole mode
V. Khan HEP group, The University of Manchester /41

15. Glossary 2
Synchronous mode : Most dominating mode in an accelerating cell, its phase vel. is in synchronous with speed of light
Bandwidth : Difference between the synchronous frequencies of the end cells (lowest dipole )
Large BW : 3.3 GHz
Small BW : 1 GHz
Moderate BW : 2.3 GHz
Heavy Damping : Q ~10
Moderate Damping : Q ~
V. Khan HEP group, The University of Manchester /41

16. Beam dynamics constraints [1],[2]
RF breakdown constraint [1],[2] 1) 2) Pulsed surface heating 3) Cost factor
Beam dynamics constraints [1],[2]
For a given structure, no. of particles per bunch N is decided by the <a>/λ and Δa/<a>
Maximum allowed wake on the first trailing bunch
Rest of the bunches should see a wake less than this wake(i.e. No recoherence).
Ref: [1]: A. Grudiev and W. Wuensch, Design of an x-band accelerating structure for
the CLIC main linacs, LINAC08 .
[2]: H. Braun, et al. , Updated CLIC Parameters, CLIC-Note 764, 2008.
V. Khan HEP group, The University of Manchester /41

17. Accelerating cells : Several designs
V. Khan HEP group, The University of Manchester /42

18. Wakefield suppression in CLIC main linacs
The present main accelerating structure (WDS) for the CLIC relies on linear tapering of cell parameters and heavy damping with a Q of ~10.
The wake-field suppression in this case entails locating the dielectric damping materials in relatively close proximity to the location of the accelerating cells.
To minimise the breakdown probability and reduce the pulse surface heating, we are looking into an alternative scheme for the main accelerating structures:
Detuning the first dipole band by forcing the cell parameters to have Gaussian spread in the frequencies
Considering the moderate damping Q~500
V. Khan HEP group, The University of Manchester /41

19. CLIC_G: Present baseline waveguide damped design
Structure
CLIC_G
Frequency (GHz) 12
Avg. Iris radius/wavelength <a>/λ
0.11
Input / Output iris radii (mm)
3.15, 2.35
Input / Output iris thickness (mm)
1.67, 1.0
Group velocity (% c)
1.66, 0.83
No. of cells per cavity 24
Bunch separation (rf cycles) 6
No. of bunches in a train
312
Ref: A. Grudiev, W. Wuensch, Design of an x-band accelerating structure for the CLIC main linacs, LINAC08
V. Khan HEP group, The University of Manchester /41

20. Damped and detuned design
Detuning: A smooth variation in the iris radii spreads the dipole frequencies. This spread does not allow wake to add coherently
Error function distribution to the iris radii varion results in a rapid decay of wakefield.
Due to limited number of cells in a structure (trunated Gaussian) 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
V. Khan HEP group, The University of Manchester /41

21. NLC/GLC DDS design Acceleration cells Beam tube Manifold HOM coupler
High power
rf coupler
HOM coupler
Beam tube
Acceleration cells
Manifold
V. Khan HEP group, The University of Manchester /41

22. Advantages Disadvantages More sensitive to machine tolerances
Moderate damping scheme: Breakdown probability is less
Pulse temperature rise is comparatively less
Manifolds can be used for beam position monitoring and cell alignments
Disadvantages
More sensitive to machine tolerances
Need bigger bandwidth for adequate detunig and hence more input power to achieve desired accelerating gradient
Interleaving neighbouring structure frequencies is necessary, hence structures are not identical which is not cost-efficient
V. Khan HEP group, The University of Manchester /41

23. Key parameters for designing an accelerating structure @ 12 GHz & 100 MV/m
Iris radii of the end cells
Iris thickness
<a>/λ
Group velocity
No. of cells per structure
Bunch spacing
Bunch charge
No. of bunches in a train => pulse length
V. Khan HEP group, The University of Manchester /41

24. Uncoupled (designed) distribution of Kdn/df for a four fold interleaved structure
Error function distribution
V. Khan HEP group, The University of Manchester /41

25. Eight fold interleaved structure
Finite no of modes leads to a recoherance at ~ 85 ns.
But for a damping Q of ~1000 the amplitude wake is still below 1V/pc/mm/m
Why not 3.3 GHz structure?
3.3 GHz structure does satisfies beam dynamics constraints but does not satisfies RF breakdown constraints.
V. Khan HEP group, The University of Manchester /41

26. Zero crossing scheme
Parameters closely tied to that of CLIC_G with two major changes
Gaussian distribution of cell parameters
Q= 500
V. Khan HEP group, The University of Manchester /41

27. CLIC_ZC structure #
Parameters
ZC1
ZC2
Unit 1
<a>/λ
0.102
0.1 - 2
IP/OP iris thickness
1.6 / 0.7
1.6/0.7 mm 3
IP / OP iris radii
2.99 / 2.13
2.87/2.13 4
IP / OP group velocity
1.49 / 0.83
1.45/.83 5
First / Last cell Q0
6366 / 6643
6408/6668 6
First / Last cell Shunt impedance
107 / 138
108/138
MΏ /m 7
Filling time
56.8
58.6 ns 8
IP Power (peak) 48 47 MW 9
RF-to-beam efficiency
27.09
26.11 % 10
Bunch population
3.0 x109
2.9 x 109 11
Esur (max)
285
231
MV/m 13
∆T max 20
25.2 K 14
14.07
14.36
MW(ns)^1/3/mm
V. Khan HEP group, The University of Manchester /41

28. Why not zero crossing scheme ?
Though RF breakdown constraints are satisfied it will be very challenging to achieve zero crossing scheme due to tight tolerances.
It may not be feasible to build a structure based on zero crossing scheme.
Possible option is a moderate bandwidth.
V. Khan HEP group, The University of Manchester /41

29. A 2.3 GHz Damped-detuned structure
Cell parameters
Cell # 1
Cell # 24
Iris radius (mm)
4.0
2.15
Iris thickness (mm)
0.7
Ellipticity
1.0
2.0 Q
4771
6355
R’/Q (kΩ/m)
11.64
20.09
vg/c (%)
2.13
0.9
∆f = 3.6 σ = 2.3 GHz
∆f/fc =13.75 %
<a>/λ=0.126
V. Khan HEP group, The University of Manchester /41

30. Typical DDS cell Accelerating mode (monopole mode) Manifold
Coupling slot
Accelerating mode
(monopole mode)
Dipole mode
Manifold mode
V. Khan HEP group, The University of Manchester /41

31. Spectral function -----(IFT) Wake function
24 cells
No interleaving
24 cells
No interleaving
∆fmin = 65 MHz
∆tmax =15.38 ns
∆s = 4.61 m
48cells
2-fold interleaving
∆fmin = 32.5 MHz
∆tmax =30.76 ns
∆s = 9.22 m
48cells
2-fold interleaving
V. Khan HEP group, The University of Manchester /41

32. Spectral function -----(IFT) Wake function
96 cells
4-fold interleaving
∆fmin = MHz
∆tmax = ns
∆s = m
96 cells
4-fold interleaving
192 cells
8-fold interleaving
192 cells
8-fold interleaving
∆fmin = 8.12 MHz
∆tmax =123 ns
∆s = m
V. Khan HEP group, The University of Manchester /41

33. CLIC_G vs CLIC_DDS
For CLIC_G structure <a>/λ=0.11, considering the beam dynamics constraint bunch population is 3.72 x 10^9 particles per bunch and the heavy damping can allow an inter bunch spacing as compact as ~0.5 ns. This leads to about 1 A beam current and rf –to-beam efficiency of ~28%.
For CLIC_DDS structure (2.3 GHz) <a>/λ=0.126, and has an advantage of populating bunches up to 4.5x10^9 particles but a moderate Q~500 will require an inter bunch spacing of 8 cycles (~ 0.67 ns).
Though the bunch spacing is increased in CLIC_DDS, the beam current is compensated by increasing the bunch population and hence the rf-to-beam efficiency of the structure is not affected alarmingly.
V. Khan HEP group, The University of Manchester /41

34. CLIC_G vs CLIC_DDS Parameters CLIC_G (Optimised) [1,2] CLIC_DDS
(Single structure)
CLIC_DDS*
(8-fold interleaved)
Bunch space (rf cycles/ns)
6/0.5
8/0.67
Limit on wake (V/pC/mm/m)
7.1
5.6
5.3
Number of bunches
312
Bunch population (109)
3.72
4.7
5.0
Pulse length (ns)
240.8
273
272.2
Fill time (ns)
62.9 42
40.8
Pin (MW)
63.8 72
75.8
Esur max. (MV/m)
245
232
224
Pulse temperature rise (K) 53 65
RF-beam-eff.
27.7
26.6
26.7
Figure of merit (a.u.)
9.1
8.41
8.29
[1] A. Grudiev, CLIC-ACE, JAN 08
[2] H. Braun, CLIC Note 764, 2008
* Averaged values of structure #1 & #8
V. Khan HEP group, The University of Manchester /41

35. ? CLIC_G vs CLIC_DDS CLIC_G CLIC_DDS Undamped Damped 1.56 1.55
@ 4.0 mm iris radius ?
Undamped
Damped
1.56
1.55
V. Khan HEP group, The University of Manchester /41

36. Circular
Square
Elliptical
Convex
Concave
V. Khan HEP group, The University of Manchester /41

37. Iris radius = 4. 0 mm
Iris thickness = 4.0 mm
Undamped cell with various geometries
Circular
Rectangular
Elliptical*
ε=10
ε=5
ε=3.33
ε=2.0
ε=1
Facc(GHz)
12.24
12.09
11.98
12.0
11.99
Eacc(V/m)
0.43
0.42
Hsur max /Eacc (mA/m)
3.64
4.86
4.71
4.54
4.29
3.75 3
Esur max /Eacc (mA/m)
2.27
2.33
2.28
V. Khan HEP group, The University of Manchester /41

38. Circular
Square
V. Khan HEP group, The University of Manchester /41

39. Surface magnetic field in different cell geometries
Circular
Rectangular
ε=10
ε=5
ε=3
ε=2
ε=1
Hsur max /Eacc
(mA/V)
V. Khan HEP group, The University of Manchester /42

40. Present status
4.35 mA/V
V. Khan HEP group, The University of Manchester /41

41. Next ?
Surface magnetic field is reduced, need to reduce surface electric field.
Efficiency calculations.
Dipole simulations, necessary changes in the geometry for critical coupling.
Wakefield calculations
Mechanical design with power couplers.
Hopefully will build one out of eight fold-interleaved structure in collaboration with CERN-KEK-SLAC
Thesis writing....
V. Khan HEP group, The University of Manchester /41

42. Acknowledgements
We would like to thank our collaborators for their involvement in discussions and many useful suggestions from
CERN : W. Wuensch, A. Grudiev, D. Schulte and R. Zennaro
KEK : T. Higo
SLAC : J. Wang and Z. Li
V. Khan HEP group, The University of Manchester /41

43. Thank you
Many of life’s failures are people who did not realise how close they were to success when they gave up Thomas Edison
V. Khan HEP group, The University of Manchester /41