FINAL-FOCUS SCHEMES FOR CLIC AT 3 TEV
F. Zimmermann, H. Burkhardt, T. Risselada, F. Schmidt, CERN, Geneva, Switzerland,
H.-J. Schreiber, DESY Zeuthen, Germany
Abstract
We discuss benefits and drawbacks of two different finalfocus schemes for CLIC at 3 TeV centre-of-mass (c.m.)energy, by examining tolerances, tunability and potential
background for a 3.3-km long baseline final-focus system[1] and a shorter advanced design [2].

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1

INTRODUCTION

The length of the final-focus system may have a significant impact on the total extent of a 3-TeV CLIC. We here
compare the 3.3-km long baseline optics [1] with a morecompact system developed by Raimondi [2]. In particular,
we discuss performance, tolerances, collimation, and tunability of these two systems.

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2 OPTICS
The baseline optics was described in Ref. [1]. Beta functions and dispersion of the alternative compact optics aredepicted in Fig. 1.
The baseline optics [1] is a rather conventional, modular design, consisting of matching section, horizontal chromatic correction, vertical chromatic correction, and finaltransformer. Two pairs of sextupoles correct the doublet
chromaticity. The sextupoles of a pair are separated by an
optical −I transform, so that geometric aberrations cancel.
Following a proposal by Oide [3], the dispersion is nonzero
only at the second sextupole of each pair. This reduces thenumber of bending magnets, hence the synchrotron radiation, and also the chromo-geometric aberrations. Second
order dispersion is corrected by adjusting the ratio of bending angles in the two chromatic correction sections.
The second optics derives from the NLC 1-TeV final focus, developed by Raimondi and Seryi [2]. To limit the impact of synchrotron radiation, the sextupole strengths wereincreased by a factor 3.4 from the NLC design and all bending angles reduced accordingly. Upstream quadrupoles,sextupoles, and bending angles have been empirically finetuned for maximum luminosity, using a Monte-Carlo optimization. This optics is only 500 m long. The disper∗sion has a nonzero slope at the collision point (D x = 1.8mrad), and is maximum across the final doublet. Two sextupoles are located here. Three other sextupoles are positioned upstream of the main bending magnets. They cancel the geometric aberrations induced by the two chromatic
sextupoles. The free length between the exit face of the lastquadrupole and the collision point, l ∗ , is 4.3 m, comparedwith 2 m for the first optics. This leaves more space forthe detector and it would avoid placing final quadrupoles
inside the detector solenoid field.
Table 1 lists relevant parameters for the two systems.
The gradient of the last sextupole in the compact system
would correspond to a pole-tip field of about 2 T at 5 mm

Figure 1: Compact final focus scaled from the NLC design[2]. Beta-function values on the left axis are in units ofkm, dispersion values on the right are in m. The interaction
point (IP) is on the right.
Table 1: Beam and final-focus parameters.
opticsbaselinecompact
beam energy
1.5 TeVno. of bunches per second
15400
bunch population
4 × 10 9
ideal luminosity w/o pinch
4.56 × 10 34 cm−2 s−1
IP beta functions
8.0 (x), 0.15 (y) mm
IP normalized emittances
0.68(x), 0.02 (y) µm
full-width momentum spread
0.8–1.0%
demagnification factor
90 (x), 346 (y)peak vertical beta function
1000 km
200 kmpeak dispersion
10 cm5 cmtotal length3282 m548 mtotal bending length
705 m
276 m
total bending angle|θi |586 µrad 363 µrad
gradient of last quadrupole
450 T/m
388 T/m
gradient of 2nd last quadr.
184 T/m
135 T/mstrength of SD sextupole
1.29 m −3 20.1 m−3
strength of SF sextupole
2.70 m −3 5.6 m−3

3PERFORMANCE

Figures 2 and 3 display the luminosity simulated with andwithout synchrotron radation as a function of the beam energy spread for the two final-focus systems. The luminosity
was computed by convoluting tracked particles on a grid.
Figure 4 shows the corresponding rms beam sizes, for thecase with synchrotron radiation. All figures depict simulation results from MAD [4] and from Sixtrack90 [5]. The

latter is an operator-overloaded Fortran90 upgrade of Sixtrack [6], and is believed to represent higher-order chromatic effects more accurately than MAD.
The luminosity for nominal parameters (0.8% full energy spread) is about the same for the two optics. Figures 2 and 3 identify synchrotron radiation as the dominant
limitation, which reduces the luminosity to 65–75% of theideal value. The energy bandwidth of the compact system
is wider, and would allow maintaining a larger BNS damping at the end of the linac.
Residual optical aberrations were analyzed using automatic differentiation in Sixtrack90; see Table 2.
Figure 4: Horizontal and vertical rms beam sizes simulated
by Sixtrack90 [6] including synchrotron radiation vs. thefull-width momentum spread for the two optics.
of ideal luminosity, from 71% to 25% for the baseline, andfrom 66% to 31% for the compact optics. Jitter and drift
tolerances on vertical magnet positions and field strength
are similar as well.
Figure 5 shows that the transverse tails at the entrance
to the final quadrupole are much smaller for the compactsystem, thus reducing an important background source.
Figure 2: Luminosity, in units of the ideal geometric luminosity L0 , vs. the full-width momentum spread for thebaseline optics, as simulated by MAD [4] and Sixtrack90[6] with and without synchrotron radiation.

Figure 3: Relative luminosity vs. the full-width momentum
spread for the compact optics, as simulated by MAD [4]and Sixtrack90 [6] including random energy fluctuations
due to synchrotron radiation.

Figure 5: Beam halo at final-quadrupole entrance for baseline (top) and compact optics (bottom). The initial (uniform) distribution extends up to ±15σ x , ±70σy , and ±4%.

4 COLLIMATION ISSUES
Table 2: Residual aberrations ∆σ x(y) /σy(x),0 , which are
added in quadrature to the linear spot sizes σ y(x),0 .
Lie gen. ∆σx /σx0 Lie gen. ∆σy /σy042baselinex δ0.70y  δ20.41
2 3 2 2x δ0.43xy δ0.15x 2 δ 20.40y 2δ30.12 2
2compactxδ
0.42y δ0.91
22 2x δ0.41x y  δ0.31
The tunability of the two system is comparable: Varyingβx∗ from 10 mm to 2 mm, decreases the luminosity, in units

The beams in a linear collider must be collimated before
passing through the final doublet. The collimation depth
is determined from the conditions that (1) beam particles
and (2) synchrotron radiation photons should not hit any
magnet apertures on the incoming side of the IP. Figures
6 and 7 show synchrotron radiation fans emitted in the final doublet. The collimation depth for the baseline optics
should be less than 23σ x and 80σy and that for the compact
optics less than 14σx or 83σy . In the latter case the horizontal beam size σx includes both betatron and dispersive
components, of roughly equal size. The horizontal betatroncollimation depth required is about half that of the baseline.

CLIC 3 TeV (2000)

Figure 6: Synchrotron radiation fans across the final doublet for the baseline optics with beam envelopes of 23σ xand 80σy . Pictures refer to horizontal (top), vertical (center) and 45 ◦ plane (bottom). [Courtesy O. Napoly]
CLIC 3 TeV (2001)

Figure 8: Number of lost electrons per muon passing
through a detector with 7.5-m radius as a function of position along baseline final focus. Potential collimator locations are indicated. The IP is at 3282 m.
in order that one muon passes through the detector. At a
distance of 500 m from the IP, this number is about 10 4 .
Lowering the c.m. energy to 500 GeV increases the number of lost beam particles per muon by about an order ofmagnitude. The dependence on the distance is weak, inFig. 8. Thus, we do not expect a big difference between thebaseline optics and the shorter system. So far only muons
generated by the Bethe-Heitler process were considered,and no magnetized toroids or cylinders for muon suppression have yet been included in the final-focus tunnel.

5Figure 7: Synchrotron radiation fans for the compact optics
with beam envelopes of 14σ x and 83σy . [O. Napoly]
The collimators are combinations of short (0.5 radiationlength) spoilers, made from Be or C, and long (20 r.l.) absorbers. In order that the spoilers are not destroyed bya mis-steered bunch train, the transverse beam area σ x σymust be larger than (50–100 µm) 2 [9]. For the baseline
optics all beam sizes at high-beta points fall between these
two limits. The maximum beam sizes in the compact optics are on average a factor 2 smaller. Scaling parts of theNLC collimation design [10] for adequate beam sizes andnegligible emittance growth at 1.5 TeV beam energy, we estimate that a separate energy collimation section upstreamof the final focus is at least 2 km long. This number assumes that the 2nd set of absorbers as well as the betatroncollimation can be integrated into the final focus proper. A
complete stand-alone collimation system, as contemplated
for NLC, would occupy about 5–6 km, at 1.5 TeV.
A first assessment of muon background was made using
a simulation program developed for TESLA [11]. Figure
8 depicts the number of beam particles which must be collimated at various locations along the baseline final focus

CONCLUSION AND THANKS

The compact system [2] provides a larger l ∗ , a wider momentum bandwidth, and reduced beam tails. Tunability,tolerances and luminosity are comparable to the baselineoptics. The horizontal collimation depth is reduced byabout a factor of two, due to increased l ∗ and dispersion
across the final doublet. To which extent collimation canbe integrated into the two systems remains to be quantified.
We thank O. Napoly for producing Fig. 6, A.-S. Müller
for useful discussions and help with PAW, and G. Guignardfor a careful reading of the manuscript.

6REFERENCES[1] F. Zimmermann, et al., EPAC 2000, Vienna, p. 519.
[2] P. Raimondi and A. Seryi, EPAC 2000, Vienna, p. 492.
[3] K. Oide, HEACC’92, Hamburg, p. 2993 (1992).
[4] H. Grote and F. C. Iselin, CERN-SL-90-13-AP-REV.2.
[5] E. Forest and F. Schmidt, EPAC 2000, Vienna.
[6] F. Schmidt, CERN-SL-94-56-AP; D. P. Barber, G. Ripken
and F. Schmidt, DESY 87/036; G. Ripken, DESY-R1-71/1.
[7] O. Napoly, B. Dunham, EPAC 94, London, 1, 698 (1994).
[8] S. Fartoukh, O. Napoly, EPAC98, Stockholm (2000); S. Fartoukh, Ph.D. thesis, DAPNIA/SEA-97-02T (1997).
[9] S. Fartoukh, J.B. Jeanneret, J. Pancin, report in preparation.
[10] P. Tenenbaum et al., LINAC 2000 (2000).
[11] H.J.Schreiber, contribution to ECFA/DESY Workshop
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