Wakefield suppression in the CLIC main accelerating structures Vasim Khan & Roger Jones.
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Transcript of Wakefield suppression in the CLIC main accelerating structures Vasim Khan & Roger Jones.
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Wakefield suppression in CLIC main linacs
We are looking into an alternative scheme in order to suppress the wake-field in 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
1/12/2008
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 damping materials in relatively close proximity to the location of the accelerating cells.
44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
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Constraints RF constraint
1)
2) Pulsed surface heating
3) Cost factor
Beam dynamics constraints
1) For a given structure, no. of particles per bunch N is decided by the <a>/λ and Δa/<a>
2) Maximum allowed wake on the first trailing bunch
Rest of the bunches should see a wake less than this wake(i.e. No recoherence).
mMVEsur /260max
KT 56max
mmnsMWCP inpin33 18
N
XmXmmpCVWt
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1
104///667.6
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
Ref: A. Grudiev and W. Wuensch, Design of an x-band accelerating structure for the CLIC main linacs, LINAC08
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Overview of present WDS structure
Structure CLIC_GFrequency (GHz) 12
Avg. Iris radius/wavelength <a>/λ 0.11
Input / Output iris radii (mm) 3.15, 2.35Input / Output iris thickness (mm) 1.67, 1.0
Group velocity (% c) 1.66, 0.83No. of cells per cavity 24
Bunch separation (rf cycles) 6No. of bunches in a train 312
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
Lowest dipole band: ∆f ~ 1GHz Q~ 10
Ref: A. Grudiev, W. Wuensch, Design of an x-band accelerating structure for the CLIC main linacs, LINAC08
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A detuned structure
In order to keep the beam current same as that of CLIC_G structure and in turn the efficiency ,we assume bunch spacing of 6 cycles (appr. 0.5 ns) .
For a moderate Q it naturally requires a structure of large bandwidth to suppress the wakefield sufficiently.
It is observed that for a Gaussian distribution of cell parameters and a bandwidth of 3.3 GHz wakefield is sufficiently suppressed.
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
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Input required: Synchronous frequencies of end cells (fi) Width of Gaussian distribution(σ) Kick factor (K)
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Dispersion curves for 3 cells
2
2 2 2 2 2 2
1 cos 1 cos sin1 10TM TE TE TM
rTM rTE rTM rTE
k k k k
f f f f f f
2 20
2 20
TE
f fk
f f
2 202 2
0TM
f fk
f f
0
2 20
2 f ffr
f f
First cell a =4.95 mm
Mid cella =3.95 mm
Last cella= 2.15 mm
TE
TMTM
TE
TM
TE
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
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Comparison between uncoupled and coupled calculations
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
Black: UncoupledRed: coupled
Solid curves: First dipoleDashed curves: second dipoleRed: UncoupledBlue: Coupled
Red: UncoupledBlue: Coupled
Wt(0)=110 V/pc/mm/mWt1~ 2 V/pc/mm/m
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Comparison between uncoupled and coupled calculations: 8 fold structure
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
3.3 GHz structure does satisfies beam dynamics constraints but does not satisfies RF constraints.In this case:
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?
5~maxaccsur EE
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Cell a (mm) b (mm) t (mm) Vg/c (%) f1 (GHz)
1st 3.15 9.9 1.67 1.63 17.45
Ref 1 2.97 9.86 1.5 1.42 17.64
Ref 2 2.75 9.79 1.34 1.2 17.89
Ref 3 2.54 9.75 1.18 1.0 18.1
24th 2.35 9.71 1.0 0.86 18.27
Cell parameters of a modified CLIC_G structure: Gaussian distribution
Uncoupled values:<a>/λ=0.11∆f = 0.82 GHz∆f = 3σ i.e.(σ=0.27 GHz)∆f/favg= 4.5 %
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
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Modified CLIC_G structure
UncoupledUncoupled
Coupled
Coupled
Q = 500Q = 500
Undamped Undamped
Envelope Wake-field Amplitude Wake-field
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
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Cell # a (mm) b (mm) t (mm) Vg/c (%) f1 (GHz)
1 2.99 9.88 1.6 1.49 17.57
4 2.84 9.83 1.4 1.38 17.72
8 2.72 9.80 1.3 1.29 17.85
12 2.61 9.78 1.2 1.18 17.96
16 2.51 9.75 1.1 1.06 18.07
20 2.37 9.73 0.96 0.98 18.2
24 2.13 9.68 0.7 0.83 18.4
Cell parameters of seven cells of CLIC_ZC structure having Gaussian distribution
Uncoupled values:<a>/λ=0.102∆f = 0.83 GHz∆f = 3σ i.e.(σ=0.27 GHz)∆f/favg= 4.56%
∆a1=160µm and ∆a24= 220µm. The first trailing bunch is at 73% of the peak value (Wmax=180 V/pC/mm/m). ∆f=110 MHz. There is a considerable difference in the actual wake-field experienced by the bunch, which is 1.7 % of peak value which was otherwise 27%.
Zero crossing of wake-field
We adjust the mode frequencies to force the bunches to be located at the zero crossing in the wake-field. We adjust the zero crossing by systematically shifting the cell parameters (aperture and cavity radius).
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
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CLIC_ZC structure
Coupled
CoupledUncoupled
Uncoupled
Undamped Undamped
Q = 500 Q = 500
Envelope Wake-field
Amplitude Wake-field
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
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Interleaved cells & SRMS
Q = 50024 cells Q = 500
192 cells
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
SRMS= 33 V/pC/mm/mSRMS= 7 V/pC/mm/m
SRMS>1 BBU is likely to occur
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Beam dynamics simulation:
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
PLACETBeam is injected with realistic offsets from the electrical centre of the cavity.An injection offset of a σy results in ~ 70% emittance dilution at the nominal bunch spacing.
Injection offsetRed: σy
Black: 3σy/4Blue: σy/2Green: σy/4
8 fold interleaved structureQ=500
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CLIC_ZC structure# Parameters ZC1 ZC2(initial) Unit1 <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 mm
4 IP / OP group velocity 1.49 / 0.83 1.45/.83 mm
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 29 28.8 %
10 Bunch population 3.0X109 2.9X109 -
11 Esur (max) 275 221 MV/m
12 Eacc (avg) 100 100 MV/m
13 ∆T max 15 14.0 K
14 15 14.3 MW(ns)^1/3/mm
15 Luminosity (in1%) 9.6X1033 8.9 X1033 m-2
16 FOM 9.2 8.8 a.u. (% 1034/109)
inpin CP 3
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
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Fundamental mode properties: CLIC_ZC
1/12/2008
Bsur max (A/mX10^3)Esur max (MV/m)Eacc (MV/m)Pin (MW)∆T (K)
Dashed curves:Unloaded conditions
Solid curves: Beam loaded conditions
44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
Summary With a Gaussian detuning of cell parameters and Q=500, wake-field envelope is
damped but it is not sufficiently damped hence we look in to the actual wake felt by the bunch i.e. wake amplitude.
Varying the elasticity of the cells surface fields can be minimise to satisfy RF constraints: (Esur max in particular).
171/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
Next ? We are looking in to realistic tolerances to satisfy the zero crossing condition for a Q~500.
Introduce damping wave-guide (manifold) to the present structure.
A bandwidth of ~2GHz with a damping Q of ~ 200, in this case we expect wake-field to suppress sufficiently for a bunch spacing of 6 to 8 cycles to satisfy beam dynamics constraint but surface fields will be an issue to take care of.
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Thank you
1/12/2008 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008
We have benefited from valuable discussions with W. Wuensch and A. Grudiev regarding the recent structures and with D. Schulte, B. Dalenaand A. Latina on the beam dynamics code PLACET.
Acknowledgements