wakefield suppression in the clic main accelerating structures vasim khan & roger jones

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

9

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


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.


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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

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First cell a =4.95 mm

Mid cella =3.95 mm

Last cella= 2.15 mm

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TMTM

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Comparison between uncoupled and coupled calculations


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


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 %


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Modified CLIC_G structure

UncoupledUncoupled

Coupled

Coupled

Q = 500Q = 500

Undamped Undamped

Envelope Wake-field Amplitude Wake-field


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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).


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CLIC_ZC structure

Coupled

CoupledUncoupled

Uncoupled

Undamped Undamped

Q = 500 Q = 500

Envelope Wake-field

Amplitude Wake-field


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Interleaved cells & SRMS

Q = 50024 cells Q = 500

192 cells


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:


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


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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).


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


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

wakefield suppression in the clic main accelerating structures vasim khan & roger jones

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