INVESITGATION OF AN ALTERNATE INVESITGATION OF AN ALTERNATE MEANS OF WAKEFIELD MEANS OF WAKEFIELD

SUPPRESSION IN CLIC MAIN LINACSSUPPRESSION IN CLIC MAIN LINACS

CLIC_DDSCLIC_DDS

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

2

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.

Constraints RF breakdown 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).

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Ref: A. Grudiev and W. Wuensch, Design of an x-band accelerating structure for the CLIC main linacs, LINAC08

Overview of present WDS structure

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

444th 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

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

Comparison between uncoupled and coupled calculations: 8 fold structure

644th 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 breakdown constraints.

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?

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 %

744th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

Modified CLIC_G structure

UncoupledUncoupled

Coupled

Coupled

Q = 500

Q = 500

Undamped Undamped

8

Envelope Wake-field Amplitude Wake-field

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

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).

944th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

CLIC_ZC structure

Coupled

UncoupledUndamped

Q = 500

Q = 500

10

Envelope Wake-field

Amplitude Wake-field

Interleaved cells & SRMS

Q = 50024 cells Q = 500

192 cells

1144th 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*

* Ref: R.M. Jones, et al, 2002, SLAC-PUB-9407, LINAC-02

A typical geometry : cell # 1

r2

h

r1

h1b

rc

a

a+a1

a1

a2

L

E-field in a CLIC_DDS single cell with quarter symmetry

Manifold

Coupling slotCell mode

Manifold mode

π phaseω/2π = 17.41 GHz

0 phaseω/2π = 14.37 GHz

Uncoupled (designed) distribution of Kdn/df for a four fold interleaved structure

Kdn/df

dn/df

Mode separation

In order to provide adequate sampling of the uncoupled Kdn/df distribution cell frequencies of the neighbouring structures are interleaved. Thus a four-fold structure (4xN where N = 24) is envisaged.

An erf distribution of the cell frequencies (lowest dipole) with cell number is employed.

Spectral functionAs the manifold to cell coupling is relatively strong there is a shift in the coupled mode frequencies compared to uncoupled modes which changes the character of the modes. For this reason we use spectral function method to calculate envelope of wakefield.

The modal Qs are calculated using Lorentzian fits to the spectral function.

Interleaved structure

Non- interleaved structure

Modal Qs

Mean Q

Non-interleaved structure

Non-interleaved structure

Interleaved structure

Interleaved structure

Envelope wakefield of the present CLIC_DDS structure: Q~500

Envelope wakefield with an artificially imposed Q = 300

Uncoupled mode

Q = 500

Q = 300

Cell # 1

• Iris radius = 4.0 mm• Iris thickness = 4.0 mm , • ellipticity = 1• Q = 4771• R’/Q = 1,1640 Ω/m• vg/c = 2.13 %c• ~ dipole frequencies (GHz)• 0 mode π mode 1 16.63 15.89 2 18.08 24.58 3 19.46 25.84

Cell # 24

• Iris radius = 2.3 mm• Iris thickness = 0.7 mm, • ellipticity = 2• Q = 6355• R’/Q = 20,090 Ω/m• vg/c = 0.9 %c• ~ dipole frequencies (GHz)• 0 mode π mode 1 13.02 18.18 2 18.74 20.19 3 20.43 21.49

A 2.3 GHz Damped-detuned structure

Details: delf, sig, etc.

3 disp curves+avoi. Cross.

F0,fpi,fx,fsyn vs # : represent by line

A 31.1I @ 23.4% tLEaccI

η b

fillrbin tttPypulseenerg

beamenergy

A 1.13

GHz 11.99428

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V/pc/mm/m 5.6104.7515010410010W 9

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pp1t2pp1ttttτ

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b

Corrected formula for effective pulse length

Unloaded

Unloaded 249.3 52.3

Some explanation about bunch spacing and population.

Plot for nb

Some more detail on eff. Cal.

Compare eff. With clic_g

Put allowed surface field values

24 cell structureSpectral function

2 kdn/df : coupled mode

2 kdn/df : uncoupled mode

Spectral function

4-fold interleaving96 cell structure

8-fold interleaving192 cell structure

Replace by new plots

Cal. Q’s of first few modes

Wake-function : Inverse Fourier Transform of spectral function

4-fold interleaving96 cell structure

8-fold interleaving192 cell structure

No interleaving24 cell structure

Replace by new plots

Next ?• Optimisation of the manifold geometry to achieve minimum possible Q (100-200).• Optimisation of the dipole bandwidth keeping in mind the constraints on the surface

fields.• Increasing the bunch spacing to 8 or 10 cycles to satisfy the beam dynamics constraints

on the wakefield, in this case efficiency of the overall collider will have to be compromised.

• Considering all the above optimisation procedure the first trailing bunch is still expected to see a higher envelop-wakefield than allowed. In this case a zero-crossing scheme of the amplitude of wake will be employed.

Conclusion• The present CLIC_DDS structure has similar structure specifications like that of CLIC_G for lowest dipole bandwidth (~ 1 GHz) and bunch spacing (6 cycles).• Interleaving the neighbouring structure frequencies helps in reducing the average envelope wakefield by a factor of appr. 2 for first 4m.•The envelope wakefield for the first 3 bunches with four fold interleaving and an enforced Q = 300 is above the acceptable limit.