Transcript INVESITGATION OF AN ALTERNATE MEANS OF WAKEFIELD SUPPRESSION IN CLIC MAIN LINACS CLIC_DDS

INVESITGATION OF AN ALTERNATE
MEANS OF WAKEFIELD
SUPPRESSION IN CLIC MAIN LINACS
CLIC_DDS
Wakefield suppression in CLIC main linacs
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.
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
Constraints
RF breakdown constraint
1)
E
max
sur
 260MV / m
2) Pulsed surface heating
T max  56 K
3) Cost factor
Pin 3  p Cin  18MW 3 ns mm
Beam dynamics constraints
1)
2)
For a given structure, no. of particles
per bunch N is decided by the <a>/λ
and Δa/<a>
Maximum allowed wake on the first
trailing bunch
6.667V / pC / mm / mX 4 X 109
Wt1 
N
Rest of the bunches should see a
wake less than this wake(i.e. No
recoherence).
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
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
4
A 3.3 GHz structure
Red:
Uncoupled
Blue: Coupled
Wt(0)=110 V/pc/mm/m
Wt1~ 2 V/pc/mm/m
Black:
Uncoupled
Red: coupled
Solid curves: First dipole
Dashed curves: second
dipole
Red: Uncoupled
Blue: Coupled
Comparison between uncoupled and
coupled calculations: 8 fold structure
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?
3.3 GHz structure does satisfies beam dynamics constraints but does not
satisfies RF breakdown constraints.
Cell parameters of a modified CLIC_G structure:
Gaussian distribution
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
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
Coupled
Undampe
d
Uncoupled
Envelope Wake-field
Uncoupled Coupled
Undampe
d
Amplitude Wakefield
Q = 500
Q=
500
8
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).
Cell parameters of seven cells of CLIC_ZC structure having Gaussian
distribution
Uncoupled values:
Cell #
a (mm)
b (mm)
t (mm)
Vg/c (%)
f1 (GHz)
<a>/λ=0.102
1
2.99
9.88
1.6
1.49
17.57
∆f = 0.83 GHz
4
2.84
9.83
1.4
1.38
17.72
∆f = 3σ
8
2.72
9.80
1.3
1.29
17.85
∆f/favg= 4.56%
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
∆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%.
CLIC_ZC structure
Coupled
Q = 500
Undampe
d
Uncoupled
Envelope Wake-field
Q = 500
Amplitude Wakefield
10
A typical geometry : cell # 1
b
r2
rc
a2
a1
h
a
r1
L
a+a1
h1
E-field in a CLIC_DDS single cell with quarter symmetry
Manifold
Manifold
mode
Coupling slot
0 phase
ω/2π = 14.37 GHz
Cell mode
π phase
ω/2π = 17.41 GHz
Uncoupled (designed) distribution of Kdn/df
for a four fold interleaved structure
An erf distribution of
the cell frequencies
(lowest dipole) with
cell
number
is
employed.
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.
Kdn/df
dn/df
Mode separation
As 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.
Noninterleaved
structure
Spectral function
Interleaved structure
Modal Qs
The modal Qs are
calculated
using
Lorentzian fits to the
spectral function.
Mean Q
Non-interleaved structure
Envelope wakefield
of
the
present
CLIC_DDS
structure: Q~500
Interleaved structure
Envelope wakefield
with an artificially
imposed Q = 300
Non-interleaved structure
Interleaved structure
A 2.3 GHz Damped-detuned structure
Cell # 1
•
•
•
•
•
•
Cell # 24
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
•
•
•
•
•
•
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
∆f = 3.6 σ = 2.3 GHz
∆f/fc =13.75 %
<a>/λ=0.126
Cell # 1
Coupled 3rd mode
Uncoupled 2nd mode
Uncoupled 1st
mode
Avoided crossing
Uncoupled manifold mode
Light line
Solid (dashed)curves coupled (uncoupled) modes
Coupled 3rd mode
Uncoupled 2nd mode
Uncoupled 1st
mode
Avoided crossing
Uncoupled manifold mode
Light line
Cell # 13
Cell # 24
Uncoupled 2nd mode
Coupled 3rd mode
Uncoupled 1st
mode
Avoided crossing
Uncoupled manifold mode
Light line
fx
fsyn
Red=f0
Blue=fpi
Red dashed=fsyn
Black= fx
fpi
f0
Spectral function
24 cells
No interleaving
96 cells
4-fold interleaving
48cells
2-fold interleaving
192 cells
8-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
48cells
2-fold interleaving
24 cells
No interleaving
∆fmin = 16.25 MHz
∆tmax = 61.52 ns
∆s = 18.46 m
96 cells
4-fold interleaving
∆fmin = 8.12 MHz
∆tmax =123 ns
∆s = 36.92 m
192 cells
8-fold interleaving
Efficiency calculations
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 –tobeam efficiency of ~28%.
I
3.72 10 1.6 10
6
11.9942 GHz
9
-19
 1.19 A
WTlimit

10 100  4 10 9
150  3.72 10
9
 7.1 V/pc/mm/m
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).
4.75 10 9 1.6 10 -19
I
 1.13 A
8
11.9942 GHz
WTlimit

10 100  4 10 9
150  4.75 10
9
 5.6 V/pc/mm/m
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.
Unloaded
Unloaded
Allowed limit = 260 MV/m
Allowed limit = 56 K
Corrected formula for effective pulse length [1]

1  pp  t 1  pp    246 ns
τ p  t b  t fill  t r   t fill

r
2
2  


ηCLIC_DDS 
beamenergy I  Eacc  L t b

pulseenergy Pin tb  t r  t fill

tb 
L
Pout
t fill
pp 
T  τ p
8  312
 208.1 ns
11.9942
 40 ns
Pin  74.5MW

 23.4% @ I  1.13 A
[1] A. Grudiev, CLIC-ACE, JAN 08
UL
Pout

21.12
 0.56
37.77
t r  23 ns (approxima te)
ηCLIC_G  27.7% @ I  1.19A
Parameters
CLIC_G
(Optimised)
[1,2]
CLIC_DDS
(Nonoptimised)
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
27.7
24.3
Bunch space (rf cycles/ns)
Rf-beam-eff.
[1] A. Grudiev, CLIC-ACE, JAN 08
[2] CLIC Note 764
192 cell
First 12 Q’s