INTRODUCTION
The CLIC design is based on a main linac, in which the beam is accelerated in normal
conducting X-band accelerating structures. The necessary RF power to feed these
structures is extracted from a drive beam in a chain of power extraction and transfer
structures (PETS) than runs in parallel to the main beam. In principle, the RF power
could also be produced by klystrons. In the past, this has indeed been proposed in the
JLC-X [jlc] and NLC [nlc] designs, which also used normal conducting X-band
accelerating structures but fed by klystrons. A clear advantage of a klystron based
design is that the basic RF unit prototypes can be tested more easily than for a drive
beam scheme. The production of the drive beam at the necessary high current is
relatively costly.
It appears necessary to highlight the implications that the choice of RF power source
has on the CLIC design at 500GeV. The drive beam based design is documented
elsewhere []. In this document the focus will be on the first exploration of the klystron
based design.
Currently, two strategies have been followed to determine the klystron based machine
parameters:
 In the first approach, the current CLIC 500GeV design is fully maintained,
except that the drive beam is replaced by klystrons as the main linac power
source. This choice minimises the design modifications. As will be described
below, the number of klystrons required is 1000, which appears very large.
 In the second approach, some optimisation of the CLIC parameters is
performed in order to reduce the number of klystrons. However, the structure
design strategy remains unaltered, i.e. strong damping of the higher order
transverse modes is used. In contrast, NLC and JLC-X considered only weak
damping and detuning. The total number of klystrons needed with the two
strategies appears to be very similar.
In our studies, no cost optimisation has been performed since no cost model is
currently available that is vetted by the CLIC cost working group.
KLYSTRON AND PULSE COMPRESSOR DESIGN
X-band Klystron Design
To be filled by Gerry
High-power X-band RF pulse compression system analysis
In the NLC/GLC design, the SLED II pulse compressor [1] was adopted as a part of
the RF power production station [2], as is shown in Fig. 1. The SLED II is a passive
waveguide circuit which stores RF energy in a pair of resonantly tuned delay lines for
several roundtrips, until a phase reversal in the input pulse causes it to be expelled in a
compressed pulse of increased power. The lines are iris coupled at one end to a power
directing hybrid and shorted at the other. To reduce losses and to enhance powerhandling capabilities, the delay lines are represented by overmoded waveguides.
Length of the each line is chosen in a way that the round trip time delay is equivalent
to the duration of the compressed pulse. In order to reduce the physical length of the
waveguides involved, it was suggested to use multimoded systems [3]. In these
systems, waveguide is utilized multiple times, often carrying different modes
simultaneously. Such a pulse compressor was build and tested at SLAC [4]. It
produced close to 550 MW of output RF power with a pulse width of 400 ns and a
repetition rate of 60 Hz. The measured breakdown trip rate trip at this peak power
level was about 7.510-7/pulse.
Figure 1: Schematic of the main linac RF sub-unit for the NLC/GLC.
In its original design, the SLED II is supposed to be operated with a factor 4
pulse compression (the ratio between the input and the output pulses durations). We
have analyzed power gain and efficiency of a similar system, but for different pulse
compression ratios. In our analysis we have used the following assumptions:
 Similar to NLC/GLC, the two combined 75MW  1600ns klystrons were
considered as an RF power source.
 The Ohmic losses per meter length of the delay line were scaled from 11.424 GHz
to 12 GHz for the same delay line circular waveguide aperture.
 For the waveguide distribution system, an RF transport efficiency of 0.92 was
taken, similar to the NLC/GLC design value.
 To estimate the calculated peak RF power production feasibility we have used the
semi-empirical approach [5], which to large extend allows to extrapolate the
existing experimental results: PC<550MW(TC/400ns)1/2, where TC is the
compressed pulse length and PC is an extrapolated RF peak power limit at a given
(7.510-7/pulse) breakdown trip rate.
The results of this analysis are summarized in Table 1.
Table 1: The SLED II RF pulse compressor performance
Compression factor
3
4
5
Pulse length (ns)
533
400
320
Delay line length (m)
40
30
24
Power gain
2.47
3.21
3.78
Efficiency
0.823
0.8
0.756
Peak power/structures (MW)
341
443
567
Power limit (MW)
476
550
614
6
267
20
4.21
0.702
630
673
7
228
17.1
4.56
0.651
684
730
PARAMETER CHOICE
Beam Dynamics Constraints
The beam parameters for CLIC at 500 GeV centre-of-mass have been optimised in a
similar fashion as for the 3 TeV version [2].
The basic parameters at the collision point are determined by the different
accelerator systems:
 The bunch charge N and length σz are mainly a function of the linac design.
The longitudinal single bunch wakefield makes the bunch length a function of
the charge σz(N) in order to limit the final beam energy spread.. The transverse
wakefield effects then limit N, via the wakefield kick which is propotional to
NWT(2σz).
 The horizontal emittance is mainly a function of the damping ring
performance, with some contributions from other systems.
 The vertical emittance depends on damping ring and the transport from the
damping ring to the interaction point.
 The effective vertical and horizontal beta functions are functions of the final
focus system and have lower limits.
Some parameters have been chosen to be more relaxed than for CLIC at 3 TeV:
 Larger horizontal emittance at the interaction point of 2.4 μm instead of 0.66
μm has been assumed to relax the damping ring design requirements.
 Larger beta-functions have been assumed at the collision point to relax the
beam delivery system requirements.
The bunch charge in the main linac has been chosen as for the 3 TeV case but taking
into account that the machine is significantly shorter. This has two main
consequences. First, this allows tolerating a constant local transverse wakefield kick,
even at lower gradients. In case of the 3 TeV design the wakefield kick had to be
reduced with the gradient since the length of the machine increased. Second, it allows
having a factor of about two larger local wakefield kick from one bunch to the next
than at 3 TeV. In addition, the requirement for the quality of the luminosity spectrum
at the interaction point has been made more stringent, in order to make the
degradation of the spectrum quality due to beam-beam effects and the unavoidable
initial state radiation comparable. As a figure of merit we use the luminosity delivered
within a band of 1% around the nominal centre-of-mass energy.
0.35
0.25
3 TeV, 100 MV/m
500 GeV, 100 MV/m
500 GeV, 50 MV/m
0.2
0.15
L
bx
/N [1025/bx/m 2]
0.3
0.1
0.05
0
0.06
0.08
0.1
0.12
0.14 0.16
<a>/ 
0.18
0.2
0.22
Figure 2: Luminosity per bunch crossing in 1% energy spectrum divided by the
bunch population Lbx/N versus average aperture to the wavelength ratio <a>/λ is
plotted.
In order to illustrate the difference between the two cases of 3 TeV and 500 GeV,
luminosity per bunch crossing in 1% energy spectrum divided by the bunch
population Lbx/N versus average aperture to the wavelength ratio <a>/λ is plotted in
Fig. 1 for 3 difference cases: 3 TeV, <Eacc> = 100 MV/m; 500 GeV, <Eacc> = 100
MV/m; and 500 GeV, <Eacc> = 50 MV/m. Black diamond curve represent the nominal
case where the optimum <a>/λ is 0.11. Using the nominal structures optimized for 3
TeV in the 500 GeV main linac would result in luminosity loss of about factor 6 from
0.3 to 0.05. This loss can be partially compensated by using accelerating structures
with larger aperture since for 500 GeV the optimum <a>/λ is close to 0.16. In
addition, Fig. 1 shows the difference in the Lbx/N for 500 GeV between 100 MV/m
and 50 MV/m accelerating gradients coming mainly from the linac length, red circles
and blue triangles, respectively.
RF constraints
The following three rf constraints have been used in the optimization:
1. Surface electric field: Esurfmax < 260 MV/m
2. Pulsed surface heating: ΔTmax < 56 K
3. Power: Pin /C∙τp1/3∙f <156 MW/mm/ns2/3
Here Esurfmax and ΔTmax refer to maximum surface electric field and maximum
pulsed surface heating temperature rise in the structure respectively. Pin, τp and f
denote input power, pulse length and frequency respectively. C is the circumference
of the first regular iris. These constraints are the same as used in the optimization of
the 3 TeV CLIC main linac accelerating structure [3,4]. This means that the structure
high gradient performance is as challenging to achieve as for the 3 TeV case. In
addition, two values for the rf phase advance per cell in the structure have been
investigated: 2π/3 and 5π/6.
Three TeV Design Constraints
In addition to the beam dynamics and rf constrains, there are a number of
constraints which has to be applied to the 500 GeV CLIC if it would be built as the
first stage of 3 TeV CLIC. There are several parameters fixed by the 3 TeV design:
bunch separation Ns of 6 rf cycles, rf pulse length tp of 242 ns and the structure active
length Ls of 230 mm. These parameters can only be changed by factor 2 since it is
related to the 3 TeV layout or to the rf frequency in the injectors. Finally the list of
different cases studied in this paper is presented below:
1. Ns = free; Ls > 200 mm; tp = free
2. Ns = 6; Ls = 230 mm; tp = 242 ns
3. Ns = 6; Ls = 480 mm; tp = 242 ns
4. Ns = 6; Ls = 480 mm; tp = 483 ns
where the first case represents 500 GeV CLIC optimum without taking into account 3
TeV design constraints. It is used as a reference to indicate how much the
performance is reduced due to the 3 TeV design constraints.
Optimisation Results
The 500 GeV CLIC main linac accelerating structure optimization has been
performed in a range of <Eacc> from 50 to 100 MV/m always at 12 GHz. The figure
of merit (FoM) ηLb×/N has been maximized as in [2,3], where η is RF-to-beam
efficiency. For fixed centre-of-mass collision energy this quantity is proportional to
the average luminosity divided by the average rf power which has to be provided for
acceleration. Unfortunately, no cost model was available for 500 GeV CLIC
optimization.
The results are presented in Fig. 2 where all 4 different combinations mentioned in
the previous section has been analyzed for two different values of rf phase advance
per cell and are marked as shown in the legend. In addition, two cases are presented
which correspond to the 500 GeV CLIC built using nominal 3 TeV structure (CLIC_G
[4]) at the nominal and double pulse lengths. Since the repletion rate is limited to
multiples of 50 Hz, the luminosity in 1% energy spectrum calculated at 50 Hz for all
the cases and normalized to the nominal luminosity in 1% energy spectrum at 3 TeV
of 2×1034 cm-2sec-1[1] is plotted in Fig. 2(bottom) as a luminosity reduction factor.
First Fig. 2(top) where FoM is presented clearly indicate that reduction of the gradient
allows to design a structure which is better adapted to the 500 GeV CLIC (larger
aperture). Second, in Fig. 2(bottom) there are two cases which are quite close to the
red solid line which is the best case achieved where no 3 TeV constraints were
applied. Let’s consider 3 cases indicated in Fig. 2 by arrows:
1. Nominal structure but not nominal pulse length. This means the layout must be
adapted. Luminosity is 3 times lower than nominal. Gradient is 80 MV/m.
2. Optimized structure of nominal length and nominal pulse length. This means
the layout is nominal. Luminosity reduction is only factor 2. Gradient is 80
MV/m.
3. Optimized structure of double length and double pulse length. The layout is not
nominal. Luminosity is the same as for 3 TeV case. Gradient is significantly
lower: 50 MV/m.
The fact that layout is not nominal in the cases 1 and 3 means that it has to be rebuilt
to a certain extent when upgrading from 500 GeV to 3 TeV. It is not necessary in the
case 2. Case 3 gives nominal luminosity but the significantly lower gradient and
consequently longer linac could have an impact on the cost which was not optimized
in the present study. Finally case 2 has been chosen as a baseline configuration for
500 GeV CLIC based on the drive beam 12 GHz rf power source. In the next section,
the performance of the structures presented in Fig. 2 is shown for the case of the
klystron based 12 RF power source.
5
10
4.5
9
4
8
Luminosity reduction factor
bx
L /N* [1023/bx/m 2]
3
2
3.5
3
2.5
2
1
1.5
1
6
5
4
1
3
2
1
0.5
0
50
7
60
70
80
<Eacc> [MV/m]
90
100
0
50
2
3
60
70
80
<Eacc> [MV/m]
90
100
2 /3: Ns =free, Ls >200mm, tp=free
2 /3: Ns =6, Ls =230mm,
2 /3: Ns =6, Ls =480mm,
tp=242ns
tp=242ns
2 /3: Ns =6, Ls =480mm, tp=483ns
CLIC-G, tp=242ns
CLIC-G, tp=483ns
5 /6: Ns =free, Ls >200mm, tp=free
5 /6: Ns =6, Ls =230mm, tp=242ns
5 /6: Ns =6, Ls =480mm,
5 /6: Ns =6, Ls =480mm,
tp=242ns
tp=483ns
Figure 3: FoM (top left) and luminosity reduction factor (top right) are presented for 10 different
sets of constraints described in the text and marked in the legend (bottom left).
Number of Klystrons
In Fig 3, compression efficiency and the corresponding power gain of the rf pulse
compression system are presented as described in Section Igor. The 12 GHz 75 MW
peak power klystron pulse length of 1600 ns is assumed. The points on the curves in
Fig. 3 correspond to different compressions. The smooth line assumes fractional
compression number which is impossible to achieve in practice. In this case, the pulse
length of the klystron must be adjusted.
Figure 4: Compression efficiency (blue) and power gain (red) versus pulse length.
Using the above parameters for the klystron and rf pulse compression system the
number of klystron which are necessary to feed 250 GeV is calculated using
following formula:
P klys
Pl p ea k
0.5 Ecm NN b
N klys  l


75MW GPC  75MW t p GPC  75MW
where, Ecm= 500 GeV centre-of-mass collision energy, N is the bunch population, Nb
is the number of bunches, GPC is the power gain which is the function of pulse length
tp. The parameters N, Nb, tp are taken for structures presented in fig. 2 and the
corresponding number of klystron is calculated for each structure. The results are
presented in Fig. 4.
Klystron based 500 GeV CLIC
7000
2/3: N s =free, L s >200mm, t p=free
Nklys
2/3: N s =6, L s =230mm, t p=242n
s
2/3: N s =6, L s =480mm, t p=242n
s
2/3: N s =6, L s =480mm, t p=483n
6000
CLIC% G, t p=242n
CLIC% G, t p=483n
5000
5/6: N s =free, L s >200mm, t p=free
5/6: N s =6, L s =230mm, t p=242n
5/6: N s =6, L s =480mm, t p=242n
4000
5/6: N s =6, L s =480mm, t p=483n
3000
2000
1000
50
55
60
65
70
75
80
<E a c c > [MV/m]
85
90
95
100
Figure 5: Number of klystron per linac for different structures which have been
presented in Fig. 2.
1.8
x 10
-3
Klystron based 500 GeV CLIC
2/3: N s =free, L s >200mm, t p=free
FoM
Nklys
2/3: N s =6, L s =230mm, t p =242n
2/3: N s =6, L s =480mm, t p =242n
1.6
2/3: N s =6, L s =480mm, t p =483n
CLIC% G, t p=242n
1.4
CLIC% G, t p=483n
5/6: N s =free, L s >200mm, t p =free
5/6: N s =6, L s =230mm, t p =242n
1.2
5/6: N s =6, L s =480mm, t p =242n
5/6: N s =6, L s =480mm, t p =483n
1
0.8
0.6
0.4
50
55
60
65
70
75
80
<E a c c > [MV/m]
85
90
95
100
Figure 6: Ratio of the Figure of Merit to the number of klystron per linac for different
structures which have been presented in Fig. 2.
The smallest number of klystrons can be achieved if the nominal 3 TeV CLIC
structure (CLIC_G) is used at 50 MV/m. Then only about 1200 klystrons per linac are
needed. But the corresponding luminosity in 1% of the energy spectrum is only
0.15x1034 [Hz/cm2] at the repetition rate of 50 Hz. This is unacceptably lower than the
nominal value of 1x1034 [Hz/cm2]. A compromise has to be found to balance the
number of klystrons (cost) and the luminosity (performance). To do this a ratio of the
FoM to the number of klystrons is plotted in the same way as before in Fig. 5. Three
structures with highest ration of FoM to the number of klystrons were picked up as an
example and the parameters are presented together with the parameters of the current
base line structure for 500 GeV CLIC base on the drive beam 12 GHz rf power source
(case 2 described in the previous section) in Table 1. All three structures should
operate at the pulse length close to the nominal pulse length of 242 ns. This seems to
be a value which is close to the optimum for a given klystron and pulse compression
system parameters. For this pulse length the pulse compression power gain GPC =
4.45 and the corresponding compression efficiency is 68%.
Table 1: Parameters of the nominal 500 GeV CLIC structure together with possible
structures for the klystron based 500 GeV CLIC.
Case
CLIC_502 1
2
3
80
50
57
50
rf phase advance: ∆φ[ ]
150
120
120
150
Average iris radius/wavelength: <a>/λ
0.145
0.145
0.145
0.16
N. of reg. cells, str. length: Nc, l [mm]
19, 229
56, 480
56, 480
45, 480
Bunch separation: Ns [rf cycles]
6
6
6
6
Average accelerating gradient: <Ea>
[MV/m]
o
-2
Luminosity per bunch X-ing: Lb× [m ]
0.57×10
Bunch population: N
6.8×10
Number of bunches in a train: Nb
9
34
34
0.33×10
9
34
0.38×10
9
0.5×10
34
5.1×10
5.49×10
6.63×10
354
374
382
339
Pulse length: τp [ns]
242
242
242
242
Input power: Pin [MW]
74.2
59
76
72
250
193
215.6
230
56
24.3
27.6
33
Efficiency: η [%]
39.6
50.7,
49.5
49.6
Figure of merit: ηLb× /N [a.u.]
3.3
3.24
3.41
3.74
1.0
0.62
0.73
0.85
Max. surface field: Esurf
max
[MV/m]
max
Max. temperature rise: ΔT
34
[K]
-2 -1
Luminosity @ 50 Hz [10 cm s ]
9
Number of klystrons per linac
3000
1865
2100
2249
In summary:
 Structures optimized for the maximum figure of merit have been analyzed
 Lowest number of klystron has been found for CLIC_G@50MV/m@240ns
which is about 2400 klystrons BUT the luminosity is 0.15x1034 [1/(cm2s)]
@50Hz
 Compromise Luminosity versus Nklys: (0.6 - 1)x1034 [1/(cm2s)] @50Hz
results in 3700 - 6000 klystrons
 Further optimization could improve luminosity but probably will not reduce
significantly number of klystrons
 To do this, cost model is needed which weights Nklys, gradient and
Luminosity in a proper way.
IMPACT ON THE CLIC DESIGN AND COST
Design Changes
Philippe:
Second tunnel
Main linac infrastructure
Cost Difference
Philippe:
Difference of cost between klystron-based and drive beam based approach
This chapter might be missing in the first version, i.e. before the CLIC cost is know.
CONCLUSION
REFERENCES
[jlc] JLC
[nlc] NLC
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Collider’, Proceedings of EPAC 2004, Lucerne, Switzerland.
[3] S. G. Tantawi et al., Phys. Rev. ST Accel. Beams 5, 2002.
[4] S. Tantawi et al., ‘High-power multimode X-band rf pulse compression system for future
linear colliders’, Phys. Rev. ST Accel. Beams, Vol. 8. 2005.
[5] A. Grudiev, W. Wuensch, ‘A New Local Field Quantity Describing the High Gradient Limit of
Accelerating Structures’, Proceedings of LINAC 2008, Victoria, British Columbia, Canada.
[B2] A. Grudiev et al., “Optimum Frequency and Gradient for the CLIC Main Linac”, EPAC’06,
Edinburgh, June 2006.
[B3] A. Grudiev et al., “Optimum Frequency and Gradient for the CLIC main linac accelerating
structure”, LINAC’08, Victoria BC, Canada, 2008.
[B4] A. Grudiev, W. Wuensch, “Design of X-band accelerating structure for the CLIC main linac”,
LINAC’08, Victoria BC, Canada, 2008.