Abstract A traditional Final Focus System based on dedicated chromaticity correction sections is presented as an alternative for CLIC Final Focus. The Scheme of the lattice is shown and tha luminosity bandwidth is calculated. A systematic tuning using Beam Based Alignment and sectupole knobs is perdormed. The complete comparison to the Local Chromaticity correction scheme is presented

A Latina

CERN R Tomas

H Garcia

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TRADITIONAL FINAL FOCUS SYSTEM FOR CLIC
H.Garcia∗, A.Latina, R.Tomas, CERN, Geneva 1211, Switzerland
Abstract
A traditional Final Focus System based on dedicated
chromaticity correction sections is presented as an alter-
native for CLIC Final Focus. The Scheme of the lattice is
shown and tha luminosity bandwidth is calculated. A sys-
tematic tuning using Beam Based Alignment and sectupole
knobs is perdormed. The complete comparison to the Local
Chromaticity correction scheme is presented.
INTRODUCTION
The main task of a linear collider Final Focus System
(FFS) [1] is to focus the beam to the small sizes required
at the interaction point (IP). To achieve this, the FFS forms
a large and almost parallel beam at the entrance of the Fi-
nal Doublet (FD), which contains two strong quadrupole
lenses. For the nominal energy, the beam size at the IP is
σ =
√
β∗ε, where ε is the beam emittance and β∗ is the be-
tatron function at the IP. However, a beam with an energy
spread σδ , the beam size is diluted by the chromaticity of
these strong lenses.
The chromaticity scales approximately like
ξ ∼ L∗+Lq/2β∗ , where L∗ is the distance from the IP
to the last quadrupole and Lq is the quadrupole length.
Thus the chromatic dilution of the beam size σδ
L∗+Lq/2
β∗
may be very large. The design of the Final Focus is
driven primarily by the necessity of compensating the
chromaticity of the FD.
There are two different approaches in order to compen-
sate the chromatic effect, the traditional scheme, based on
dedicated chromatic correction sections for each plane; and
the local correction scheme, based on the local correction
of the chromaticity. Here we are focused on the dedicated
scheme.
LATTICE LAYOUT
In the Traditional FFS, used in the SLC and FFTB in
SLAC, the chromaticity is compensated in dedicated chro-
matic correction sections (CCX and CCY) by sextupoles
placed in high dispersion and high beta regions. The geo-
metric aberrations generated by sextupoles are canceled by
using them in pairs with a minus identity transformation
between them. The advantage of this scheme is its sepa-
rated optics with strictly defined functions and straightfor-
ward cancellation of geometrical aberrations. This makes
the system relatively simple for design and analysis. The
most important disadvantage is that the chromaticity is not
∗ hector.garcia.morales@cern.ch
Parameter Units Value
Beam energy TeV 1.5
Last drift L∗ m 3.5
Nominal beam size σx/σy nm 40/1
Nominal beta function βx/βy mm 10/0.07
Nominal bunch length σz μm 44
Bunch population 3.7 · 109
Table 1: Key parameters of the CLIC Final Focus at the IP
 0
 250
 500
 750
 1000
 1250
 0  250  500  750  1000  1250  1500
 0
 0.01
 0.02
 0.03
 0.04
 0.05
β1
/2
(m
1/
2 )
η(
m
)
s(m)
βx
1/2
βy
1/2
η
Figure 1: Layout of the FFS with dedicated chromatic cor-
rection sections.
locally corrected. The consequence is an intrinsic limita-
tion on the bandwidth of the system due to the unavoidable
breakdown of the proper relations between the sextupoles
and the FD for different energies. Moreover the system is
very sensitive to any disturbance of the beam energy due
to synchrotron radiation. The bending magnets have to
be large and weak enough to minimize the additional en-
ergy spread due to synchrotron radiation. As a result the
Beam Delivery System becomes a significant fraction of
the length of the accelerator.
Using FFADA (Final Focus Automatic Design and Anal-
ysis) [5] we can generate a lattice for a Final Focus with the
desired parameters. The lattice layout for the 1.5 km long
FFS is shown in Fig. 1. We compare this lattice with two
other different lattices: the current lattice of the CLIC FFS
with local chromaticity correction scheme and a 3 km long
lattice proposed in [3].The lattice shown in Fig. 1 takes the
same parameters for the beam size at the IP and are shown
in Table 1.
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01 Circular and Linear Colliders
A03 Linear Colliders
 35
 40
 45
 50
 55
 60
 65
 70
 75
 80
 1  2  3  4  5
σ x
*  
(n
m
)
Maximum order considered
Trad 1.5km
Trad 3km
Local scheme
Figure 2: Horizontal beam size for order considered com-
puted by MAPCLASS.
 0.6
 0.8
 1
 1.2
 1.4
 1.6
 1.8
 2
 1  2  3  4  5
σ y
*  
(n
m
)
Maximum order considered
Trad 1.5km
Trad 3km
Local scheme
Figure 3: Vertical beam size for order considered computed
by MAPCLASS.
BEAM SIZES
The most important parameter that determines the final
luminosity of a collider is the beam size at the IP. Due to
strong nonlinearities, the beam size might be augmented
considerably. In Fig.2 and 3 we see the beam size order
by order computed in MAPCLASS [6]. The nonlineari-
ties are better corrected in the local scheme yielding to a
smaller final beam size at the IP. We can compare the MAP-
CLASS results to the beam sizes obtained after tracking us-
ing PLACET. Table 2 shows the results for both cases, with
and without synchrotron radiation effect. The agreement is
complete with the results obtained before.
LUMINOSITY
The luminosity in a linear collider can be expressed as
L = frepnbN
2
4πσ∗xσ∗y
HD (1)
where frep is the repetition frequency, nb the number
of bunches per pulse, N the number of particles per
bunch and σx,y the RMS horizontal and vertical spot size
Table 2: Beam sizes in nm and peak Luminosity for 1%
energy offset in units 1034cm−2 per BC.
Trad. 1.5km Trad 3.0km Local
rms σx 69.80 76.05 40.39
w/o sync. σy 1.39 1.24 1.11
rms σx 71.62 78.85 48.46
w sync. σy 3.22 1.47 2.69
w/o sync. Lpeak1% 1.51 1.52 2.24
w sync. Lpeak1% 1.25 1.37 1.71
 0
 2e+33
 4e+33
 6e+33
 8e+33
 1e+34
 1.2e+34
 1.4e+34
 1.6e+34
 1.8e+34
-1 -0.5  0  0.5  1
Lu
m
in
os
ity
 (
cm
-2
s-
1 )
dp (%)
Trad 1.5km
Trad 3.0km
Local
Figure 4: Absolute lumiosity for three different schemes:
Local scheme, 1.5km and 3.0km traditional schemes.
respectively. Finally, HD is the enhancement factor due to
the pinch effect, the mutual attraction of both beams close
to the IP.
In Fig. 4 we see the luminosity as a function of the rel-
ative momentum deviation dp = dEE . The local scheme
presents a higher peak luminosity due to the better com-
pensation of the nonlinearities. In Fig. 5 are represented the
normalized luminosities according to the peak luminosities
given in 4. In this case we can compare the bandwidth of
both schemes giving again a better performance of the lo-
cal scheme over both traditional schemes. The length of
the system seems to have no influence in the luminosity.
FFS TUNING
The biggest challenge faced by the BDS is the demon-
stration of the performance assuming realistic static and dy-
namic imperfections [7]. The diagnostics and the collima-
tion sections have been demonstrated to be robust against a
prealignment of 10 μm over 500 m. Standard orbit correc-
tion techniques, as the 1:1 correction and dispersion free
steering, guarantee the beam transport without blow-up in
these regions. However this techniques fail at the FFS due
to the very non-linear behavior of the system.
Proceedings of IPAC2012, New Orleans, Louisiana, USA TUPPR022
01 Circular and Linear Colliders
A03 Linear Colliders
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 0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0.9
 1
-1 -0.5  0  0.5  1
R
el
at
iv
e 
lu
m
in
os
ity
dp (%)
Trad 1.5km
Trad 3.0km
Local
Figure 5: Normalized lumiosity for three different
schemes: Local scheme, 1.5 km and 3.0 km traditional
schemes.
One-to-one correction (1:1)
The most straightforward beam-based alignment method
is one-to-one steering. The aim of this alignment procedure
is to steer the beam such that the transverse displacements
measured by the BPMs are minimized. The beam is steered
by using dipole correctors or by using quadrupole displace-
ments. A matrix describing the response of the trajectory
to corrector changes may be used to simultaneously adjust
all correctors, sometimes called few-to-few steering.
Dispersion Free Steering (DFS)
The principle of DFS consists of a simultaneous correc-
tion of the orbit and the dispersion using one of the standard
orbit correction algorithms. This guarantees that the beam
orbit is flat while at the same time minimizing the residual
dispersion. The beam position is measured with a set of
N BPMs. The orbit is corrected with a set of M dipole
magnets (correctors).
Multiknobs
A knob is a linear combination of variables that are able
to modify one property of the beam without changing the
others but this is only ensured if the knobs are orthogonal.
We use 10 different knobs corresponding to 5 sextupole po-
sition in x and y.
Tuning simulation
We simulate the tuning process using an algorithm de-
veloped in [8]. We use 110 different seeds with an initial
random misalignment of 10μm in all the elements of the
line and a BPM resolution of 10nm. The tracking simula-
tions are done in PLACET and luminosity is measured with
Guinea-Pig, being the luminosity the figure of merit of the
optimization.
The tuning simulation results are shown in Fig. for both
the local and traditional FFS. The performance of the tra-
ditional scheme is clearly better. Almost all the machines
keep half of the luminosity and 80% of them are above the
80% of the luminosity.
 0
 10
 20
 30
 40
 50
 60
 70
 80
 90
 100
 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1  1.1  1.2  1.3  1.4
%
 m
ac
hi
ne
s 
w
ith
 L
>
x 
ax
is
 v
al
ue
L/L0
Traditional BBA+Knobs First pass L0=3.51 10
34
Local BBA+Knobs Fifth pass L0=5.22 10
34
Figure 6: Luminosity performance for 100 statistical real-
izations of the Traditional and local CLIC FFS after tuning
using BBA+Knobs algortihm.
CONCLUSIONS
We have presented an alternative Final Focus System for
CLIC at
√
s = 3 TeV. We have reduced in a factor two the
leght of the previous traditional system without any signif-
icant luminosiry loss. We have seen that the general per-
formance is far from the performance of the current local
chromaticity correction scheme. Despite of the bad perfor-
mance we have demonstrated that the tuning process seems
to work much better for the traditional scheme due mainly
to the orthogonality of the knobs. An optimization of a√
s = 500 GeV lattice is ongoing expecting even better re-
sults due to more relaxed energy constraints that imposes a
multi-TeV collider.
ACKNOWLEDGMENTS
I want to thank Andrea Latina for his constant support
and help in the tuning process and Daniel Schulte for pro-
viding us the FFADA code.
REFERENCES
[1] T.O. Raubenheimer, F.Zimmermann, ”Final Focus systems in
linear colliders“, Rev.Mod.Phys. 77, 1, (2000).
[2] P.Raimondi, A.Seryi, ”Novel Final Focus Design for Future
Linear Colliders“, Phys.Rev.Lett. 86, 7, (2001)
[3] F.Zimmermann, R.Helm, J.Irwin, ”Optimization of the NLC
Final Focus System“, (1996)
[4] R.Brinkmann, ”Optimization of the Final Focus System for
Large Momentum Bandwidth“, DESY-M-90-14, (1990).
[5] O.Napoly, B.Dunham, "FFADA: Computer Design of Final
Focus Systems for Linear Colliders", EPAC’94 (1994).
[6] R.Tomàs, ”Nonlinear optimization of beam lines“, Phys.Rev.
STAB, 9, 081001, (2006).
[7] Y.Nosochkov, P.Raimondi, T.O.Raubenheimer, A.Seryi,
M.Woodley, “Tuning Knobs for the NLC Final Focus”,
EPAC’02 Paris (2002).
[8] A.Latina, ”A Novel Alignment Procedure for the Final Focus
of Future Linear Colliders“, LINAC10, (2010)
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01 Circular and Linear Colliders
A03 Linear Colliders


TRADITIONAL FINAL FOCUS SYSTEM FOR CLIC

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TRADITIONAL FINAL FOCUS SYSTEM FOR CLIC

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