1. Alternate Means of Wakefield Suppression in CLIC Main Linac
Roger M. Jones Contribution from
Cockcroft Institute and The University of Manchester
X-Band Structures and Beam Dynamics Workshop 1st – 4th December 2008 The Cockcroft Institute, Daresbury

2. Overview of FP7 Wakefield Suppression Kickoff Meeting
Integration of Task 9.2 within NC WP 9
Overall methodology and main goal
Possible goals and milestones
Very brief overview of past achievements
Review of some benefits of manifold damped and detuning wakefield suppression
Achievements and prospects for CLIC structure to date

3. FP7 Wakefield Suppression -Staff
Roger M. Jones (Univ. of Manchester faculty)
Alessandro D’Elia (Dec 2008, Univ. of Manchester PDRA based at CERN)
Vasim Khan (Ph.D. student, Sept 2007)
Collaborators: W. Wuensch, A. Grudiev (CERN)
A. D’Elia, CI/Univ. of Manchester PDRA based at CERN (former CERN Fellow).
V. Khan, CI/Univ. of Manchester Ph.D. student pictured at EPAC 08

4. Integration of Task 9.2 within NC WP 9
E. Jensen, EuCARD Kickoff CERN, 5 Dec 2008
R.M. Jones attended as Univ. Manchester rep of EuCARD Governing Board
J-P Delahaye, XB08 Workshop, Cockcroft Inst., UK, 1 Dec 2008

5. Integration of Task 9.2 within NC WP 9
Abstract of the planned activity
This work package will explore HOM damping in single multi-cell cavities and in groups of thereof. The features of both the long-range and short-range wake-fields will be explored. The consequences of the short-range wake-field on cavity alignment will be delineated. For the long-range wake-fields, trapped modes in particular will be focused upon. Global scattering matrix analysis will be employed in addition to current electromagnetic codes. The frequency sensitivity of the modes will be explored by exploiting a circuit analysis of the electromagnetic field and this will enable the sensitivity of the wake-field to fabrication errors to be evaluated over the complete collider.
At the University of Manchester and the Cockcroft Institute we are actively involved in simulating higher order modes of accelerating cavities and experimentally determining the structure of these modes with a purpose built stretched wire measurement set-up. We are actively involved in using intensive computer codes coupled with cascading of individual sections in order to rapidly compute the modal structure.

6. Integration of Task 9.2 within NC WP 9
List of Goals and Milestones
Goal 1. Develop a circuit model and a generalized scattering matrix technique to obtain accurate calculations on the global electromagnetic field from small segments thereof. This is a study of mode excitation.
Milestones
1.1 Sep 09: Write report on circuit model and globalised scattering matrix technique. This will include an analysis of the partitioning of dipole modes in CLIC structures
1.2 Apr 110: Produce a report for the design of damping and detuning a CLIC module
Goal 2. Make an accurate simulation of the wake-fields and HOMS. This is expected to be broadly verified with initial experiments on CTF3 and more precisely verified with an experiment at the SLAC FACET facility and stretched wire measurements.
2.1 Apr 10: Experiments on the measurement of HOMs on CTF3. This will enable the predicted features of HOM damping to be verified although only the broad characteristics of the modes are expected to be measurable.
2.2 Aug 10: Perform additional measurements on the wake-field at the SLAC FACET facility. This will facilitate a detailed comparison between the predicted decrement in the wake envelope and experimentally determined values. ASSET typically is accurate to better than 0.01 V/pC/mm/m.

7. Integration of Task 9.2 within NC WP 9
2.3 Sept 10: Write up a report on the experimental measurement of modes.
2.4 April 11: Conduct wire measurement on CLIC cavities to verify the distribution of frequencies and kick factors
Goal 3. Undertake beam dynamics simulations with Placet. These simulations will take into account both the long-range and short-range wake-fields. Simulations will be performed both with the baseline design and with relaxed fabrication tolerances. In addition to the standard wake-field the influence of x-y coupling of wake-fields from possible cavity distorsions will also be investigated.
Milestones
3.1 April 11: Initial result on baseline beam dynamics simulations
3.2 June 11: Results on beam dynamics simulations with relaxed tolerances and initial simulations on transverse mode coupling
3.3 August 11: Report on beam dynamics simulations including long and short range wakefields.
3.3 Sept 11: Report on beam dynamics simulations including transverse mode coupling
Major goal: Design and measure wakefield suppression in module

8. Wealth of Experience on Detuned Structure and Manifold Wakefield Suppression
More than one and half decades of experience in this area

9. Circuit Model of DDS
**Wakefield damping in a pair of X-band accelerators for linear colliders.R.M. Jones , et al, Phys.Rev.ST Accel.Beams 9:102001,2006.

10. Wealth of Experience on Detuned Structure and Manifold Wakefield Suppression
DDS3
DDS1
H60VG4SL17A/B
RDDS1
1. SLAC-PUB 7287 (1996), 2. SLAC-PUB 8174 (1999)
3. Wakefield damping in a pair of X-band accelerators for linear colliders.R.M. Jones , et al, Phys.Rev.ST Accel.Beams 9:102001,2006.

12. Determination of Modes in Structure via Stretched Wire Measurement
Measurement of RDDS1

13. Determination of Cell Offset From Energy Radiated Through Manifolds

14. Summary of Manifold Suppression of Wakefields in Detuned Structures

15. Beam Dynamics and Relaxed Tolerances
Emittance we incorporate random frequency errors into a set of 50 accelerating structures and randomly distribute them along the entire linac. In all cases the beam is injected into the linac with an offset of approximately one y, with an energy of 5 GeV and the progress of the beam is monitored as it traverses the entire linac.
The final emittance dilution, together with the rms of the sum wake-field, is illustrated for small changes in the bunch spacing.
The particular simulation illustrated includes a cell-to-cell frequency error with an rms value of 20 MHz. We chose this rather large frequency error in order to gain an understanding of the impact of relaxed
Emittance dilution (illustrated by the red dashed curve) versus the percentage change in the bunch spacing.
Also shown is the corresponding rms of the sum wake-field (by the solid blue curve).
**Wakefield damping in a pair of X-band accelerators for linear colliders.R.M. Jones , et al, Phys.Rev.ST Accel.Beams 9:102001,2006.

16. Summary of Manifold Wakefield Suppression
Detuning along with moderate damping has been shown to be well-predicted by the circuit model.
Interleaving of successive structures allows the detuning to be effective.
Manifold wakefield suppression has added benefits:
Serves as built-in beam diagnostic
Allows internal alignment of cells to be obtained from manifold radiation
Serves as vacuum pump-outs.

17. Achievements and Prospects for CLIC Structure
CAD of Conceptual Design for Alternate CLIC Moderately Damped Structure (Q ~ 500)
Current CLIC Baseline Design Heavily Damped Structure (Q ~ 10)

18. 2. Parameters of WDS-120 protos @14.4Wu
Alexej Grudiev (CERN)
Structure number
maxFoM
2(minCost) 4 6
CLIC_14Wu
RF phase advance per cell: Δφ [o]
120
Average iris radius/wavelength: <a>/λ
0.115
0.105
0.125
0.12
Input/Output iris radii: a1,2 [mm]
3.33, 2.4
2.85, 2.4
3.84, 2.4
3.87, 2.13
Input/Output iris thickness: d1,2 [mm]
3.33, 0.83
1.5, 0.83
1.83, 0.83
2.00, 0.83
2.66, 0.83
Group velocity: vg(1,2)/c [%]
1.44, 1.0
1.28, 1.0
1.93, 1.0
2.93, 1.0
2.39, 0.65
N. of cells, structure length: Nc, l [mm]
12, 112
23, 204
25, 221
24, 212
24, 229
Bunch separation: Ns [rf cycles] 7
Number of bunches in a train: Nb
278
106 83 77
Pulse length, rise time: τp , τr [ns]
188.2, 17.3
126.9, 17.7
115.1, 17.3
101.5, 17.6
160, 30
Input power: Pin [MW], P/C1,2 [GW/m]
54, 2.6, 2.4
61, 3.4, 2.6
73, 3.5, 2.7
87, 3.6
76, 3.1, 2.7
Max. surface field: Esurfmax [MV/m]
262
274
277
323
Max. temperature rise: ΔTmax [K] 55 30
23 (const) 37
Efficiency: η [%]
25.9
19.0
18.4
19.3
21.5
Luminosity per bunch X-ing: Lb× [m-2]
2.4×1034
2.0×1034
2.8×1034
2.6×1034
Bunch population: N
5.3×109
4.2×109
6.5×109
5.8×109
Figure of merit: ηLb× /N [a.u.]
11.6
8.8
8.3
9.5

19. Application to CLIC Structure
Bunch spacing is 6/7 cycles (depending on specific design) and this corresponds to / ns at a wavelength of 25 mm (0/2 = GHz).
C.f. NLC/JLC in which 0/2= GHz and the bunch spacing was 1.4/2.8 ns –i.e. CLIC is ~ 3 times smaller in bunch spacing
Thus, it is clear the detuning must demand a more rapid fall-off in the wake-field.
In practise the bandwidth of the Gaussian needs to be increased.
C.f. NLC/JLC in which we investigated a bandwidth in terms of sigma: 4/5 sigma. We also investigated various bandwidths (in the range >9 % to <12 %)
Ambitious/demanding requirements!

20. Ref: Jones et. al, 2003, SLAC-PUB 9467
Band Partitioning
Band partitioning of kick factors in 206 cell DDS1 X-band structure (facc= GHz). Largest kick factors located in the first band. Third and sixth bands although, an order of magnitude smaller, must also be be detuned along with the 1st band.
CLIC design facc = GHz shifts the dipole bands up in frequency.
The partitioning of bands changes with phase advance. Choosing a phase advance close to pi per cell results in a diminution of the kick factor of the first band and and enhancement of the 2nd and 3rd bands. A similar effect occurs close to pi/2.
Kick factors versus phase advance for cells with an iris radius of ~ 4.23 mm.
Ref: Jones et. al, 2003, SLAC-PUB 9467

21. Current CLIC Baseline Accelerating Structure
HOM damping waveguides
GHz, 2π/3 so mm period
Alignment
High electric field and power
flow region - breakdown
Magnetic field concentration –
pulsed surface heating
Cooling
Vacuum pumping
Short range wakefields
Beam and rf
EPAC, 26 June 2008
W. Wuensch, CERN 21

22. Alternate Design CLIC Accelerating Structure
RDDS structure illustrates the essential features of the conceptual design
Each of the cells is tapered –iris reduces with an Erf-like distribution
HOM manifold running alongside main structure remove dipole radiation and damp at remote location (4 in total)
Each of the HOM manifolds can be instrumented to allow: 1) Beam Position Monitoring 2) Cell alignments to be inferred
High power
rf coupler
HOM coupler
Beam tube
Acceleration cells
Manifold

23. Wake-field Suppression in CLIC Main Linac -Initial design
Circuit model provides rapid determination of optimal wakefield suppression results in a bandwidth of 3.6 (3.36 GHz) and f/ fc =20%.
Leftmost indicates the modal distribution and rightmost the coupled and uncoupled wakefield
Four-fold interleaving of successive structures results in excellent wake-field suppression at the location of each bunch
Meets CLIC beam dynamics requirements!
However, breakdown considerations require a redesign with additional constraints imposed
Uncoupled
dn/df
Kdn/df
Coupled
Kick Factor Weighted Density Function
Envelope of Wakefield for Single 25-Cell Structure (Q ~ ∞)
Wakefield for 8-Fold Interleaved Structure (Q ~ ∞)
Envelope of Wakefield for 4-Fold Interleaved Structure (Finite Q )

24. Wake-field Suppression in CLIC Main Linac -Modified design
Electrical breakdown considerations at a CLIC gradient of 100 MV/m restricts the group velocity of the fundamental mode
This forces the initial and final iris radii to be restricted and enforces a severe restriction on the bandwidth of the accompanying dipole modes.
The envelope of the wake-field is not sufficiently suppressed.
The option of forcing the bunches to be located at the zero-crossing is explored
Beam dynamics study with PLACET in progress
Results of initial study shown
Parameters of detuned CLIC structure CLIC_ZC
Envelope of Wakefield for Single 24-Cell Structure (Q ~ 500)
Envelope of Wakefield for 4-Fold Interleaved Structures
Wakefield for 4-Fold Interleaved CLIC_ZC Structure
See Khan & Jones, Proc. EPAC 2008 and LINAC 2008

25. Summary
Analytical truncated Gaussian is a useful design tool to predict wakefield suppression.
Initial design provides a well-damped wakefield.
Including the constraints imposed by breakdown forces a consideration of zero-point crossing.
Beam dynamics study including systematic and random errors in progress –will provide detailed answer.
Manifold damping provides useful characteristics of built-in BPM together with a direct indication of internal alignments

26. Overall Goals
Provide proof-of-principle of manifold damped and detuned design and structure test at CTF3
Overall properties of wakefield suppression to be tested in modules at CTF3 (SLAC FACET?)
Provide typical tolerances/alignments for practical multi-structure operation (from PLACET beam dynamics simulations) –CLIC!
N.b. this structure has the potential for a significantly smaller pulse temperature rise than the present baseline design for CLIC