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).
mMVEsur /260max
KT 56max
mmnsMWCP inpin33 18
NXmXmmpCVWt
9
1104///667.6
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
101.6104.75I19-9
V/pc/mm/m 5.6104.7515010410010W 9
9limitT
p
rfillrfillbp
τT
ns 2462
pp1t2pp1ttttτ
0.5637.7721.12
PP
pp
.5MW47P
ULout
Lout
in
(assumed) ns 23tns 40t
ns 208.111.9942
3128t
r
fill
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.