A Multi-TeV Compact e+e- Linear Collider

I. Wilson for the CLIC Study Team.

CERN, 1211 Geneva 23, Switzerland.

**Abstract.** The CLIC study of a high energy (0.5 - 5 TeV), high
luminosity (10^34^ - 10^35^ cm^-2^ sec^-1^) e^±^ linear collider is
presented. Beam acceleration using high frequency (30 GHz)
normal-conducting structures operating at high accelerating fields (150
MV/m) significantly reduces the length and, in consequence, the cost of
the linac. Based on new beam and linac parameters derived from a
recently developed set of general scaling laws for linear colliders, the
beam stability is shown to be similar to lower frequency designs in
spite of the strong wake-field dependency on frequency. The drive beam
generation scheme for RF power production by the so-called \"Two Beam
Acceleration (TBA)\" method is described. It uses a thermionic gun and a
fully-loaded normal-conducting linac operating at low frequency (937
MHz) to generate and accelerate the drive beam bunches, and RF
multiplication by funnelling in compressor rings to produce the desired
bunch structure. Recent 30 GHz hardware developments and results from
the CLIC Test Facility (CTF), assessing the feasibility of the scheme,
are described.

# INTRODUCTION

The Compact Linear Collider (CLIC) covers a centre-of-mass energy range
for e^±^ collisions of 0.5 - 5 TeV \[1\] with a maximum energy well
above those presently being proposed for any other linear collider
\[2\]. It has been optimised for a 3 TeV e^±^ colliding beam energy to
meet post-LHC physics requirements \[3\] but can be built in stages
without major modifications. An overall layout of the complex is shown
in Fig.1. In order to limit the overall length, high accelerating fields
are mandatory and these can only be obtained with conventional
structures by operating at a high frequency.

![](media/image1.wmf)

**Figure 1.** Overall layout of the CLIC complex for a centre-of-mass
energy of 3 TeV.

![](media/image2.wmf)The choice of 30 GHz is considered to be close to
the limit beyond which standard technology for the fabrication of
normal-conducting travelling-wave structures can no longer be used
\[4\]. The RF power to feed the accelerating structures is extracted by
transfer structures from high-intensity/low-energy drive beams running
parallel to the main beam (Fig. 2). A single tunnel, housing both linacs
and the various beam transfer lines without any modulators or klystrons,
results in a very simple, cost effective and easily extendable
arrangement (Fig. 3).

**Figure 2.** One main beam and drive beam module.

![](media/image3.wmf){width="3.520138888888889in"
height="3.520138888888889in"}

**Figure 3.** Tunnel cross-section.

# MAIN PARAMETERS

The main beam and linac parameters are listed in Table 1 for various
colliding beam energies. The luminosity *L* normalised to the RF power,
*P*~RF~, depends on a small number of parameters in both low and high
beamstrahlung regimes:

$\frac{L_{\Upsilon\text{<<}1}}{P_{\text{RF}}} \propto \frac{\delta_{B}^{\frac{1}{2}}}{U_{f}}\frac{\eta_{b}^{\text{RF}}}{\varepsilon_{\text{ny}}^{\frac{1}{2}}}$
and
$\frac{L_{\Upsilon\text{>>}1}}{P_{\text{RF}}} \propto \frac{\delta_{B}^{\frac{3}{2}}}{U_{f}^{\frac{1}{2}}\beta_{y}^{\frac{1}{2}}}\frac{\eta_{b}^{\text{RF}}}{\sigma_{z}^{\frac{1}{2}}\varepsilon_{\text{ny}}^{\frac{1}{2}}}$
(1)

where δ~B~, is the mean energy loss, η^RF^~b~ the RF to beam efficiency
and *U*~f~, σ~z~, β~y~, ε\*~ny~ the beam energy, bunch length, vertical
beta function and vertical normalised beam emittance at the I.P
respectively \[5\].

**TABLE 1: Main beam and linac parameters**

  ------------------------------ ---------- ---------- ----------- -----------
  **Beam param. at I.P.**        **0.5      **1 TeV**  **3 TeV**   **5 TeV**
                                 TeV**                             

  Luminosity (10^34^cm^-1^s^-1^) 1.4        2.7        10.0        10.0

  Mean energy loss (%)           4.4        11.2       31          37

  Photons /electrons             0.7        1.1        2.3         3.2

  Coherent pairs per crossing    700        3×10^6^    6.8×10^8^   1.8×10^9^

  Rep. Rate (Hz)                 200        150        100         50

  10^9^e^±^ / bunch              4          4          4           4

  Bunches / pulse                154        154        154         154

  Bunch spacing (cm)             20         20         20          20

  H/V ε~n~ (10^-8^ rad.m)        200/2      130/2      68/2        78/2

  Beam size (H/V) (nm)           202/2.5    115/1.75   43/1        31/0.78

  Bunch length (μm)              30         30         30          25

  Accel.gradient (MV/m)          150        150        150         172

  Two linac length (km)          5          10         27.5        40

  Accelerating Sections          6940       14140      42940       62564

  Power / section (MW)           229        229        229         301

  Number of 50 MW klystrons      364        364        364         364

  Klystron pulse length (μs)     16.7       33.3       92          134

  RF to beam effic. (%)          24.4       24.4       24.4        21.3

  AC to beam effic. (%)          9.8        9.8        9.8         8.5

  AC power (MW)                  100        150        300         290
  ------------------------------ ---------- ---------- ----------- -----------

The parameters have been deduced from general scaling laws \[5\]
covering more than a decade in frequency. These scaling laws, which
agree with optimised linear collider designs, show that the beam blow-up
during acceleration can be made independent of frequency for equivalent
beam trajectory correction techniques.

![](media/image4.wmf){width="3.126388888888889in"
height="2.479861111111111in"}

**FIGURE 4.** Luminosity distribution with energy.

As a consequence and in spite of the strong dependence of wakefields on
frequency, CLIC whilst operating at a high frequency but with a low
charge per bunch *N*, a short bunch length σ~z~ , a strong focussing
optics and a high accelerating gradient *G*, preserves the vertical
emittance as well as low frequency linacs. The RF to beam transfer
efficiency is optimised by using a large number of bunches and by
choosing an optimum accelerating section length. In spite of the reduced
charge per bunch and the high gradient, excellent RF to beam efficiency
is obtained because the time between bunches is shorter and the shunt
impedance of the accelerating structures is higher.

Up to 1 TeV, where the beamstrahlung parameter *Υ *\<1, the beam
parameters are chosen to have a small δ~B~. To limit the power
consumption above 1 TeV, ε~ny~ is reduced and *Υ* allowed to be \>\>1.
In this regime (see Eq.1) high frequency linacs are very favourable
because σ~z~ is small. As a consequence, even with *Υ* \>\>1, neither
the *L* spectrum (Fig. 4), nor the number of emitted gammas which
increase the background in the detector, significantly deteriorate with
energy \[1\] (see Table 1).

MAIN LINAC

The effects of the strong 30 GHz wakefields (W~T~) can be kept moderate
by choosing *N* to be small (4 10^9^ at all energies) and σ~z~ at the
lower limit that results from the momentum spread acceptance of the
final focus. With a high gradient *G* and strong focusing, the single
bunch blow-up ∆ε~ny~ at all energies can be kept below ≈100 % (Fig. 5)
\[6\]. To obtain the values of *L* given in Table 1 assumes a very small
injected ε~ny~ of 1×10^-8^ rad.m. Limiting the overall ∆ε~ny~ relies in
part on the use of bumps which are created locally at 5-10 positions
along the linac by mis-aligning a few upstream cavities. The effects of
these bumps are used to minimise the local ε~ny~ (Fig.5). Without these
bumps, dispersive effects are $$`<!-- -->`{=html}10 times weaker than
*W*~T~ effects. The average lattice β-function starts from ≈ 4-5 m and
is scaled approx. as (energy)^0.5^. The FODO lattice is made up of
sectors with equi-spaced quadrupoles of the same length and normalised
strength, with matching insertions between sectors. The RF cavities and
quadrupoles are pre-aligned to 10 a a nd 50 μm respectively using a
stretched-wire positioning system. The off-set misalignments of the beam
position monitors (BPMs) are measured as follows \[7\]. A section of 12
quadrupoles is switched off, and with the beam centred in the two end
BPMs of this section, the relative mis-alignment of the other monitors
are measured with an accuracy of 0.1μm. The beam trajectory and ground
motion effects are corrected by a 1-to-1 correction. BNS damping is
achieved by running off-crest of the RF-wave by 6^o^ to 10^o^. Multiple
bunches are required to obtain high luminosities.

![](media/image5.wmf){width="4.409722222222222in" height="3.19375in"}

**FIGURE 5.** Emittance variation along the main linac.

The multi-bunch emittance blow-up ∆ε~ny~ is ≈ 20%. To make the 154-bunch
train stable requires a strong reduction of the transverse wakefields
that are induced by the beam in the accelerating structures.

Each cell of the 150-cell Tapered Damped Structure (TDS) \[8\] is damped
by its own set of four radial waveguides (Fig. 6) giving a *Q* of 16 for
the lowest dipole mode. A simple linear taper of the iris dimension
provides a de-tuning frequency spread of 2 GHz (5.4%). The waveguides
are terminated with short silicon carbide loads \[9\].

Calculations of the transverse wakefields in this structure indicate a
short-range level of about 1000 V/(pC⋅mm⋅m) decreasing to less than 1 %
at the second bunch and with a long time level below 0.1 %. The
simulated transverse wakefield behaviour is shown in Fig.7.

![](media/image6.wmf){width="2.1215277777777777in"
height="2.1638888888888888in"}

##### 

##### FIGURE 6 (a). One disc of TDS structure

##### 

##### FIGURE 6 (b). Cut-away view of TDS

A 15 GHz scale model of this structure has been tested in the ASSET Test
Facility at SLAC, the measured wakefield levels shown in Fig. 8 are in
excellent agreement with the theoretical predictions \[10\]. The 7.6 GHz
signal at the 1% level is not related to the structure but to the beam
pipe / structure transition.

![](media/image8.png){width="5.353472222222222in"
height="3.578472222222222in"}

**FIGURE 7.** Calculated transverse wakefield behaviour of the CLIC TDS

![](media/image9.png){width="4.739583333333333in"
height="3.7083333333333335in"}

**FIGURE 8.** Comparison of measured ASSET wakefield levels and theory.

THE RF POWER SOURCE

The overall layout of the CLIC RF power source scheme for a 3 TeV
centre-of-mass collider is shown in Fig.9. The RF power for each 624 m
section of the main linac is provided by a secondary low-energy
high-intensity electron beam which runs parallel to the main linac. The
power is generated by passing this electron beam through
energy-extracting RF structures (transfer structures) in the so-called
"Drive Beam Decelerator".

For the 3 TeV c.m. collider there are 44 drive beams (22 per linac).
Each drive beam has an energy of 1.18 GeV and consists of 1952 bunches
with a spacing of 2 cm and a maximum charge per bunch of 16 nC. These 22
drive beams, spaced at intervals of 1.248 km, are produced as one long
pulse by one of the two drive beam generators. By sending this drive
beam train towards the on-coming main beam, different time slices of the
pulse can be used to power separate sections of the main linac (see Fig.
1). This drive beam is generated as follows \[11\]. All the bunches (for
22 drive beams) are first generated and accelerated with a spacing of 64
cm as one long continuous train in a normal-conducting fully-loaded
937 MHz linac operating at a gradient of 3.9 MV/m. This 7.5 A 92 μs
continuous beam can be accelerated with an RF/beam efficiency ≈ 97%.

![](media/image10.wmf)

#### FIGURE 9. Overall layout of the CLIC RF power source for a 3 TeV centre-of-mass collider.

After acceleration the continuous train of 42944 bunches is split up
into 352 trains of 122 bunches using the combined action of a delay line
and a grouping of bunches in odd and even RF buckets. These trains are
then combined in a 78 m circumference ring by interleaving four
successive bunch trains over four turns to obtain a distance between
bunches at this stage of 8 cm.

#### ![](media/image11.png)

#### FIGURE 10. Cross-sectional view of a model CLIC PETS structure.

A second combination using the same mechanism is subsequently made in a
similar, larger 312 m circumference ring, yielding a final distance
between bunches of 2 cm. The power-extracting and transfer structures
(PETS) consist of 4 periodically-loaded rectangular waveguides coupled
to a circular beam pipe. Each 80 cm long structure provides 458 MW of 30
GHz RF power, enough to feed two accelerating structures. For stability
in the drive beam decelerator, these structures have to be damped to
reduce long-range transverse wakefield effect. A cross-sectional view of
a model of one of these PETS structures is shown in Fig.10.

the beam delivery and INTERACTION POINT

Studies of the beam delivery section consisting of a final-focus
chromatic correction section and a collimation section for the 3 TeV
collider have only just started and for the moment there is no
consistent design. A large crossing angle (20 mrad total) is required
\[12\] to suppress the multi-bunch kink instability created by parasitic
collisions away from the main interaction point (IP), and to allow a
large enough exit hole for the coherent pairs. This however means that
crab-cavities will have to be used to avoid a reduction in luminosity.

Although the final-focus design is at a very preliminary stage, an
optics has been found (see Fig.11) which already looks quite promising
\[13\]. 80% of the ideal luminosity is obtained for a 1% full-width flat
energy spread of the beams. The luminosity is calculated by convoluting
two tracked distributions. The rms spot sizes in both planes are 20-30%
larger than expected from the simple calculation using the emittance and
the beta function at the IP. Peak beta functions reach 1000 km. The
length per side is 3.1 km. Recent studies done at SLAC \[14\] suggest
that this length can probably be reduced significantly without
sacrificing performance by making the chromatic correction of the final
quadrupoles as local as possible. A preliminary design for 3 TeV
suggests that the length per side would be around 420 m.

The feasibility of maintaining 1nm beam sizes in collision in the
presence of ground movement and component jitter has to be investigated.
The use of position feedback systems within the 130 ns pulse are being
considered \[15\].

The consequences of the large mean energy loss (31%) and energy spread
(100%) which are produced by the very strong beam-beam forces at the IP
in the vertical plane (even when the beams miss each other by 10-20σ)
must be carefully studied. Extraction of a spent beam with 100% energy
spread and with a large beam divergence is a concern and will make
bending and focussing without beam losses particularly challenging.

The large number of coherent pairs produced at 3 TeV (6.8×10^8^) is also
a concern. The total energy carried by the pairs is about 40 Joules per
bunch crossing and extracting the particles without producing losses in
the detector will be a challenge. The worry is also that background
levels in the detector may dramatically increase due to the sheer number
of pairs produced.

![](media/image12.png){width="4.545138888888889in"
height="3.325in"}**FIGURE 11.** Final focus optics for a 3 TeV collider.

**TEST FACILITIES**

The first CLIC Test Facility (CTF1) operated from 1990 to 1995 and
demonstrated the feasibility of two‑beam power generation. It produced
76 MW of 30 GHz RF power from a low-energy high-intensity beam and
generated on-axis gradients in the 30 GHz structures of 125 MV/m.

A new test facility (CTF2) \[16\] is now being operated (see Fig.12).
The 30 GHz part of this facility is equipped with a few-microns
precision active-alignment system. The 48-bunch 450 nC drive beam train
is generated by a laser-driven S-band RF gun with a Cs~2~Te photocathode
(PC). It is accelerated to 40 MeV by two travelling-wave sections (HCS)
operating at two slightly different frequencies to provide beam loading
compensation along the train. After bunch compression in a magnetic
chicane, the bunch train passes through four power extraction and
transfer structures (PETS) each of which powers one 30 GHz accelerating
section (CAS) (except the third which powers two) with 16 ns long
pulses. The single probe beam bunch is generated by an RF gun with a
CsI+Ge PC. It is pre-accelerated to 50 MeV at S-band before being
injected into the 30 GHz accelerating linac. The drive beam RF gun has
produced a single bunch charge of 112 nC and a maximum charge of 755 nC
in 48 bunches. The maximum charge transmitted through the 30 GHz modules
is 450 nC. The highest accelerating gradient obtained is 59 MV/m and the
energy of an 0.7 nC probe beam has been increased by 55 MeV.

![](media/image13.wmf)

###### FIGURE 12. Layout of CTF2

Unexpected surface damage was found at these field levels and further
studies are needed to find the cause. The tests were made under
particularly bad vacuum conditions which for the moment makes vacuum a
prime suspect.

Extremely high gradients were obtained \[17\] by powering a 30 GHz
single-cell resonant cavity directly by the drive beam. The cavity
operated without breakdown at a peak accelerating gradient of 290 MV/m.
When pushed further, the cavity started to breakdown at surface-field
levels around 500 MV/m. The breakdown manifested itself as a field
extinction of the decaying pulse at different times in the pulse. At the
end of the test when the cavity was breaking down continuously, surface
field levels as high as 750 MV/m were obtained.

A new facility (CTF3) is under study \[18\] (see Fig.13), which would
test all major parts of the CLIC RF power scheme. To reduce costs, it is
based on the use of 3 GHz klystrons and modulators from the LEP injector
Linac (LIL). The drive beam is generated by a thermionic gun and is
accelerated by twenty 1.3 m long fully-loaded 3 GHz structures operating
at 7 MV/m with an RF to beam efficiency of 96%. The power is supplied by
ten 30 MW klystrons and compressed by a factor 2.3 to give a peak power
at each structure of 69 MW. The beam pulse is 1.4 μs long with an
average current of 3.5 A. The bunches are initially spaced by 20 cm (two
3 GHz buckets) but after two stages of frequency multiplication they
have a final spacing of 2 cm. This bunch train with a maximum charge of
2.3 nC per bunch is then decelerated by four 0.8 m long transfer
structures in the 30 GHz drive beam decelerator from an initial energy
of 184 MeV to a final energy of 125 MeV. Each transfer structure
provides 458 MW. The main beam is accelerated from 150 MeV to 510 MeV by
eight 30 GHz accelerating structures operating at a gradient of 150
MV/m.

![](media/image14.wmf)

**FIGURE 13.** CTF3 schematic layout.

**REFERENCES**

\[1\] J.P.Delahaye and 26 co-authors, Proc. PAC'99, New York, and
CERN/PS 99-05, 1999.

\[2\] Int. Linear Collider Technical Review Committee Report, ed. G.
Loew, SLAC-R-95-471, 1995.

\[3\] J. Ellis, E. Keil, G. Rolandi, CERN-EP/98-03, 1998.

\[4\] W. Schnell, CERN-LEP-RF/86-06, 1986.

\[5\] J.P.Delahaye and 3 co-authors*,*CERN/PS/97-51,1997.

\[6\] D. Schulte, Proc. EPAC'98, Stockholm, Sweden, and CERN/PS
98-018(LP), 1998.

\[7\] D. Schulte and T. Raubenheimer, Proc. PAC'99, New York, and
CERN/PS 99-24, 1999.

\[8\] M.Dehler, I. Wilson and W. Wuensch, CERN/PS 98-040.

\[9\] M. Luong, I. Wilson and W. Wuensch, , Proc. PAC'99, New York, and
CERN/PS 99-20, 1999.

\[10\] C. Adolphsen and M. Ross, SLAC, Private communication.

\[11\] H.Braun and 16 co-authors, CLIC Note 364 and CERN Yellow report
99-06 (Sept).

\[12\] O. Napoly, CLIC Note 414, CERN-SL-99-054 AP (Aug. 99).

\[13\] F. Zimmermann, Proc. LC99 (Frascati) October 1999.

\[14\] P. Raimondi and A. Seryi, SLAC-PUB-8612 (Aug. 2000).

\[15\] D. Schulte, CLIC Note 454 and CERN/PS 2000-051 (Aug. 2000).

\[16\] R. Bossart and 15 co-authors, CERN/PS 98-60, 1998.

\[17\] W. Wuensch and 3 co-authors, CERN/PS 2000-045 (Aug. 2000).

\[18\] The CLIC study team, CERN/PS 99-47 LP (July 99).