Post on 18-Dec-2015
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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 dielectric 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
N
XmXmmpCVWt
9
1
104///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
4
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
A 3.3 GHz structure
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
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)
1 3.15 9.9 1.67 1.63 17.45
7 2.97 9.86 1.5 1.42 17.64
13 2.75 9.79 1.34 1.2 17.89
19 2.54 9.75 1.18 1.0 18.1
24 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 %
7
Modified CLIC_G structure
UncoupledUncoupled
Coupled
Coupled
Q = 500
Q = 500
Undamped Undamped
8
Envelope Wake-fieldAmplitude Wake-field
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∆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).
CLIC_ZC structure
Coupled
UncoupledUndamped
Q = 500
Q = 500
10
Envelope Wake-field
Amplitude Wake-field
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
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
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
A 2.3 GHz Damped-detuned structure
∆f = 3.6 σ = 2.3 GHz∆f/fc =13.75 %<a>/λ=0.126
Cell # 1
Solid (dashed)curves coupled (uncoupled) modes
Avoided crossing
Uncoupled 2nd mode
Uncoupled 1st mode
Uncoupled manifold mode
Coupled 3rd mode
Light line
Cell # 13
Avoided crossing
Uncoupled 2nd mode
Uncoupled 1st mode
Uncoupled manifold mode
Coupled 3rd mode
Light line
Cell # 24
Avoided crossing
Uncoupled 2nd mode
Uncoupled 1st mode
Uncoupled manifold mode
Coupled 3rd mode
Light line
Spectral function
96 cells4-fold interleaving
192 cells8-fold interleaving
24 cellsNo interleaving
48cells2-fold interleaving
96 cells4-fold interleaving
192 cells8-fold interleaving
24 cellsNo interleaving
48cells2-fold interleaving
∆fmin = 65 MHz∆tmax =15.38 ns∆s = 4.61 m
∆fmin = 32.5 MHz∆tmax =30.76 ns∆s = 9.22 m
∆fmin = 16.25 MHz∆tmax = 61.52 ns∆s = 18.46 m
∆fmin = 8.12 MHz∆tmax =123 ns∆s = 36.92 m
Efficiency calculations
A 1.19
GHz 11.9942
6101.61072.3
I19-9
For CLIC_G structure <a>/λ=0.11, considering the beam dynamics constraint bunch population is 3.72 x 10^9 particles per bunch and the heavy damping can allow an inter bunch spacing as compact as ~0.5 ns. This leads to about 1 A beam current and rf –to-beam efficiency of ~28%.
For CLIC_DDS structure (2.3 GHz) <a>/λ=0.126, and has an advantage of populating bunches up to 4.5x10^9 particles but a moderate Q~500 will require an inter bunch spacing of 8 cycles (~ 0.67 ns).
A 1.13
GHz 11.9942
8101.6104.75
I19-9
V/pc/mm/m 1.71072.3150
10410010W
9
9limitT
V/pc/mm/m 5.6104.75150
10410010W
9
9limitT
Though the bunch spacing is increased in CLIC_DDS, the beam current is compensated by increasing the bunch population and hence the rf-to-beam efficiency of the structure is not affected alarmingly.
A 31.1I @ 23.4%
tLEaccIη b
CLIC_DDS
fillrbin tttPypulseenerg
beamenergy
p
rfillrfillbp
τT
ns 2462
pp1t
2
pp1ttttτ
0.5637.77
21.12
P
Ppp
.5MW47P
ULout
Lout
in
te)(approxima ns 23t
ns 40t
ns 208.111.9942
3128t
r
fill
b
Corrected formula for effective pulse length [1]
UnloadedUnloaded
1.19AI @ 27.7%ηCLIC_G
[1] A. Grudiev, CLIC-ACE, JAN 08
Allowed limit = 260 MV/m
Allowed limit = 56 K
Parameters CLIC_G (Optimised)
[1,2]
CLIC_DDS(Non-
optimised)
Bunch space (rf cycles/ns) 6/0.5 8/0.67
Limit on wake (V/pC/mm/m) 7.1 5.6
Number of bunches 312 312
Bunch population (109) 3.72 4.5
Pulse length (ns) 240.8 271
Fill time (ns) 62.9 40
Pin (MW) 63.8 74.5
Esur max. (MV/m) 245 249
Pulse temperature rise (K) 53 53
Rf-beam-eff. 27.7 24.3
[1] A. Grudiev, CLIC-ACE, JAN 08[2] CLIC Note 764