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CER
N-A
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2018
CERN-ACC-2018-0018June 2018
[email protected]
About flat telescopic optics for the future operation of the
LHC
S. Fartoukh, N. Karastathis, L. Ponce, M. Solfaroli, R.
Tomas
Keywords: LHC and HL-LHC optics, ATS Scheme
Summary
This report discusses and motivates the possible deployment of
flat collision optics for the future operationof the LHC.
Performance reach estimates are presented, showing a possible
improvement of the peak lu-minosity by 20 % at constant beam
parameters in comparison with round optics, and a virtual
luminosityreaching 1.0 × 1035 cm−2s−1 assuming the availability,
inject-ability and ramp-ability up to 7.0 TeV ofthe full LIU beam
by the end of Run III. These estimates are supported by a certain
number of simulationresults, including beam-beam effects, and
operational aspects based on the first LHC machine
developmentsession which took place with probe beams and flat
optics in 2017. The main expected optics limitations,together with
possible mitigation measures, are also analyzed in details.
1 Introduction and main motivations
1.1 General description and considerationsOne key ingredient to
push the performance of a collider is the reduction of the
transverse beamsizes at the interaction point (IP), which are
directly given by the transverse beam emittances andby the value of
the β-functions at the IP, i.e. β∗x and β
∗y . In the LHC, collision optics are generally
considered as being “round” by default, i.e. with
β∗x = β∗y ≡ β∗ , (1)
while, in principle, flat collision optics can also be built,
i.e. with a β∗ aspect ratio not necessarilyequal to unity and
defined as follows:
r∗ ≡ β∗X/β∗|| , (2)
with β∗X and β∗|| representing the β
∗ values in the crossing and parallel separation planes,
respec-tively. To be competitive with round optics in terms of
performance, the geometric average of thesetwo β∗’s shall obviously
be preserved when flattening the optics at the IP:
β∗eq. ≡√β∗Xβ
∗|| ∼ cst . (3)
1
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Combining the two definitions of above, the β∗ value in each of
the two transverse planes can alsobe parametrized as follows: {
β∗X = β∗eq. ×
√r∗
β∗|| = β∗eq./√r∗
. (4)
As a result, when flattening a given optics at constant β∗eq.,
i.e. acting only on r∗, β∗ shall be further
pushed in one of the two transverse planes. The corresponding
peak β function is then increasedin proportion in the inner
triplet, compared to a round optics with the same equivalent β∗,
whichfurthermore justifies the usage of the ATS [1] techniques in
the case of flat optics. In order tomitigate the subsequent
reduction of mechanical aperture in the inner triplet, and ideally
to evenpreserve it, the crossing plane shall then be chosen as the
plane of the largest β∗, which leads to
r∗ ≥ 1 , (5)
according to the definition of this quantity given in Eq. (2).
More specifically for the LHC, due tothe race-track shape of the
beam screens equipping the existing inner triplets, in particular
orientedvertically in IR1 (ATLAS) and horizontally in IR5 (CMS),
and targeting flat collision optics withan aspect ratio much larger
than unity (typically in the range of r∗ ∼ 3 − 4 for the LHC,
seeSection 2.3), the crossing angle shall be chosen horizontal in
ATLAS and vertical in CMS, i.e.leading to a crossing configuration
which is exactly opposite to the present one with round optics(see
sketch in Fig. 1). In addition to the drastic modifications of the
optical functions in flat opticsconfiguration, which results, as we
will see later, to a substantial improvement in terms of
peakperformance (∼ +20% at constant beam parameters), a
re-orientation of the crossing planes inthe ATLAS and CMS
insertions is not without any other consequences, which are of
completelydifferent nature and are enumerated hereafter.
• Forward-Physics experiments - During the proton run, two
forward-physics experiments,namely AFP [3] and CT-PPS [4] hosted in
IR1 and IR5, respectively, are parasitically takingdata, using
dedicated detectors (roman pots) installed in between Q5 and Q6.
The concept ofboth experiments relies on the very modest dispersion
of ∼ 10 cm generated by the D1/D2separation/recombination dipoles
located in between Q3 and Q4. This small dispersion ishowever very
sensitive to any optics perturbations, in particular the magnitude
and orienta-tion of the crossing angle. When horizontal, the
crossing angle indeed impacts negativelyand substantially on this
quantity (at a level up to 30-40%), which increases in
proportionthe minimum mass observation threshold which is
accessible by the experiment. Whileoperating the LHC in round
optics mode (with V/H crossing in IR1/5) offers more advanta-geous
conditions for the AFP experiment, the situation becomes more
favorable to CT-PPSassuming a running mode with flat collision
optics (and H/V crossing in IR1/5).
• Triplet luminosity lifetime - It has been recently realized
(and already partially imple-mented) that dedicated crossing angle
gymnastics can potentially reduce the peak radiationdose deposited
at specific locations in the inner triplet, and therefore increase
its luminositylifetime [5]. Passing to flat optics for the third
exploitation period of the LHC, over the fullperiod or only a
fraction of it, more precisely alternating between a VH and HV
crossingscheme in ATLAS and CMS, will definitely help in this
direction, preserving as much aspossible the IR1 and IR5 triplets,
in their present functionality, or as spare magnets for IR2and IR8
in the HL-LHC era.
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Figure 1: Sketch for the beam footprint in the inner triplets of
IR1 (top) and IR5 (bottom), for round(left) and flat (right) optics
configurations [2]. The small circles on the left/right or
top/bottomsides of the (out-of-scale) beam-screens represent the
helium capillaries, reducing the mechanicalaperture of the inner
triplet by about 2× 5 mm in one of the two transverse planes.
1.2 Performance reachAfter some algebra on the well-known
expression of the geometric luminosity loss factor in thepresence
of a crossing angle, the peak luminosity for flat optics can be
written as a function of r∗
and β∗eq. as defined in (2) and (3), of the normalised crossing
angle αX , and of the r.m.s. bunchlength σz:
Lflat[r∗, β∗eq.
]= L0
(β∗eq.)× F (r∗) with F (r∗) ≡ 1√
1 +1
r∗
(αXσz2β∗eq.
)2 , (6)where L0(β∗) denotes the peak luminosity obtained for
head-on collisions and a round collisionoptics matched to a certain
β∗. It is worth mentioning that the normalised crossing angle is
bydefinition normalised by the beam divergence in the plane of
largest β∗, i.e.
αX ≡ ΘX/√�/β∗X , (7)
3
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with � denoting the r.m.s. transverse beam emittance, assumed to
be round, and ΘX the physicalcrossing angle at the IP. This detail
is of great importance in the sense that when working at
constantnormalised crossing angle αX , the physical crossing angle
is then reduced by the factor r∗
1/4 forflat optics compared to a round optics with the same
equivalent β∗:
αX[r∗, β∗eq.
]≡ cst⇒ ΘX ∝ 1/β∗
1/2
eq. /r∗1/4 . (8)
A naive inspection of Eq. (6) would conclude that flattening a
given round optics at constant β∗eq.,and constant normalised
crossing angle αX , could asymptotically lead to the full recovery
of thehead-on luminosity L0 at infinitely large β∗ aspect
ratio:
limr∗→∞
Lflat[r∗, β∗eq.
]= L0
(β∗eq.). (9)
In practice, the β∗ aspect ratio is obviously limited by the
available triplet aperture. But still, a β∗
aspect ratio of up to r∗ ∼ 3 − 4 seems to correctly match the
mechanical aperture of the existingLHC triplets, assuming of course
the crossing plane re-orientation previously discussed (see
Sec-tion 1.2). On the other hand, the normalised crossing angle can
in general not be preserved, i.e.should itself be increased with r∗
to work at constant dynamic aperture when flattening a givenround
optics at constant β∗eq.. The physical reason behind this fact is
two-fold. The first one, whichis LHC specific, comes from the
self-compensation of the tune shift and, in general, of the
b4n+2-like detuning terms (n = 0, 1, . . .) induced by the
long-range beam-beam (BBLR) interactions inthe two high-luminosity
insertions IR1 and IR5, assuming the same round optics in both IR’s
andan alternated HV or VH crossing scheme. For flat optics, this
compensation is only partial and van-ishes quite rapidly with r∗.
Secondly, even at constant physical crossing angle ΘX , and a
fortioriat constant normalised crossing angle leading to the
scaling ΘX ∝ 1/r∗
1/4 [see Eq. (8)], the non-linear perturbations induced by the
long-range beam-beam interactions is substantially enhanced.For
instance, the BBLR-induced octupole-like tune spread increases like
∼ r∗2 when flattening around optics at constant normalised crossing
angle and constant β∗eq. (see Section 2.5). A simplerule of thumb
is that for LHC flat optics with a typical β∗ aspect ratio of 4,
the physical crossingangle ΘX should be more or less kept constant
in comparison with the round optics of the sameequivalent β∗. This
in turns means that the normalised crossing angle should be
increased by thefactor r∗1/4 , i.e. that the factor 1/r∗ occurring
in the denominator of the luminosity loss factor for-mula [Eq. (6)]
should actually be replaced by ∼ 1/
√r∗. Therefore, without any dedicated action,
the peak luminosity offered by flat optics should still be
increased with respect to that accessibleby round optics but,
qualitatively, not at a level which could really justify the
additional level ofrisk and complexity, e.g. induced by the net
increase of the peak β-function in one of the twotransverse
planes.In this context, two possible BBLR mitigation strategies
have been developed in the past few yearsin order to further
motivate a possible operation of the LHC with flat collision
optics. The firstone consists in using long-range beam-beam
compensation DC current wires, as proposed twodecades ago during
the design phase of the LHC assuming round collision optics [6],
with dedi-cated hardware recently developed and being tested in the
LHC in order to assess this techniqueexperimentally [7]. Combined
with flat optics, this alternative approach offers the only
existingback-up machine configuration which is able to preserve the
HL-LHC performance in case ofstrong limitation in the crab-cavity
system [8, 9], the so-called HL-LHC Plan B. This configura-tion
will not be further discussed in the rest of the paper, although it
represents one of the main
4
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1 2 3 4 5 6Telescopic Index
2
3
4
5MO tune spread relative increase
Figure 2: Relative increase of the total tune spread induced at
constant strength by the latticeoctupoles (MO) in both transverse
planes, as a function of the telescopic index of ATS optics,
forround (black) and flat (red) optics. In the case of flat optics,
the telescope is assumed to be onlydeployed in the plane of
smallest β∗ (i.e. parallel separation plane, vertical in IR1 and
horizontalin IR5), while β∗ is supposed to be maintained to its
pre-squeezed value in the crossing plane.
justifications for developing and testing flat optics in the
LHC, starting from dedicated machinedevelopment sessions (see
Section 4). The second mitigation strategy consists in using the
exist-ing lattice octupoles with negative polarity. Indeed, (i)
more than 25 % of them are substantiallyboosted in terms of tune
spread induced at constant strength, more precisely half of Landau
oc-tupoles located in the four arcs where the telescopic techniques
of the ATS is deployed (see Fig.2), and (ii) the latter are
correctly phased (at ∼ k π) with respect to the long-range
beam-beamencounters in IR1 and IR5 [10, 11]. A dedicated machine
configuration was set up recently tovalidate this technique with
beam, and gave extremely encouraging results for round
telescopicoptics of high telescopic indexes [12]. Furthermore, as
will be shown later (see Section 2.5), firstsimulation results seem
to demonstrate that the technique works as well for flat telescopic
optics,indicating that a normalised crossing angle as small as 10σ
could still be acceptable for a β∗ aspectratio up to 4, and
assuming the present LHC beam intensity (1.10− 1.25× 1011
proton/bunch with16 BBLR encounters per IP side). This normalised
beam-beam separation becomes quite close totypical values
recommended for round optics in the LHC, ranging in between 9.4σ
[13] and 8.6σ,at least for a beam emittance not smaller than
2−2.5µm to keep the head-on beam tune shift undercontrol, as
obtained in more aggressive and/or sophisticated scenarios, in
particular with workingpoint optimization [14].All this brings us
to a possible quantitative comparison between round and flat optics
in termsof peak luminosity reach in Run III, or, let us say, in
terms of virtual luminosity to employ theHL-LHC terminology.
Working at a quasi-constant normalised aperture (see Section 2.3)
of 9.0“collimation” σ in the inner triplet1, which is a value
agreed by the collimation and machine pro-tection teams for the
2018 LHC Run [15], two natural optics candidates show up:
• Round Optics with β∗ = 27.0 cm and a full crossing angle of
320µrad (8.7σ). This set ofparameters will serve as reference to
compare with flat optics, even if already pushed with
1The so-called collimation σ refers to a reference emittance of
γ� = 3.5µm.
5
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Beam Energy [TeV] 6.5Bunch length r.m.s. [cm] 7.5Normalised
emittance [µrad] 2.5Number of collisions in IP1/5 2592 2592 2592
2748Protons /bunch [1011] 1.25 1.25 1.25 1.80 (2.20)Optics Round
Flatβ∗X/β
∗|| [cm] 27.0/27.0 60.0/15.0 50.0/15.0 50.0/15.0
Full crossing angle [µrad] 320 245 270 270Virtual Luminosity
[1034 cm−2s−1] 2.36 2.73 2.83 6.2 (9.3)Lumi levelling period at
2×1034 [h] 2.2 4.0 4.4 18.4 (27.8)Pile-up events (PU) at 2×1034
62.5 62.5 62.5 59.2Peak PU density in stable beam [mm−1] 0.74 0.58
0.61 0.57
Table 1: Estimated performance reach for typical LHC beam
parameters, and LHC-compatibleround and flat collision optics, in
various cases including higher bunch population as foreseen inRun
III. A beam energy of 6.5 TeV is still assumed. The hour-glass
effect (a few %) is taken intoaccount in all cases. The levelling
time is estimated in the (ideal) configuration of no
emittancevariations in stable beam, with the burn-off limit
(corresponding to the inelastic hadron cross sec-tion of 81 mb)
reached immediately after collapsing the parallel separation bumps
and preserved instable beam (which is still an optimistic
assumption, presently by up to 20 % for Beam 1 accordingto the
present 2018 experience, but does not impact on the comparison in
relative between roundand flat collision optics).
respect to the ones recommended for the 2018 proton run (β∗ = 30
cm and ΘX = 320µrad,with crossing angle anti-levelling followed by
β∗-levelling down to 25 cm, but only after acouple of hours in
stable beam, i.e. when the beam intensity is reduced [16]).
• Flat Optics with β∗X = 60 cm or β∗X = 50 cm, β∗|| = 15 cm,
i.e. r∗ = 4 or r∗ ∼ 3.33,and a full crossing angle of 245µrad or
270µrad, respectively (10.0σ in both cases, seeSection 2.5).
In the case of round optics, the inner triplet aperture
bottleneck is essentially located in the cross-ing plane. In the
case of flat optics, it is in the parallel separation plane (except
in one case, seeSection 2.3), i.e. the plane of smallest β∗.
Therefore in both cases, the plane of tightest aperturecorresponds
to the vertical plane in IR1 and horizontal plane in IR5. The
virtual luminosity esti-mated in these two optics scenarios is
reported in Tab. 1, assuming BCMS beams in most of thecases, i.e.
2604 bunches2 (2592 collisions per turn at IP1 and IP5), with 1.25×
1011 protons/bunchwithin γ� = 2.5µm as for the 2018 LHC Run [16].
The case of flat optics is also consideredassuming an intermediate
(or full) LIU beams with 2760 bunches (2748 collisions at IP1/5)
at1.8 (2.20)× 1011 protons/bunch, as possibly available as of the
second year (or in the very end) ofRun III [17]. In all cases,
luminosity techniques shall be put in place in order to avoid
exceeding
2BCMS beams with 2604 bunches assume a not yet proven MKI rise
time of 750 ns, to be compared with 2556bunches for the present
2018 LHC filling scheme.
6
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the cooling capacity of the inner triplet (L
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its limit of β∗Pre = 40 cm (limited by the available sextupole
strength for the LHC case [1]), andusing the telescope to further
squeeze β∗ down to 15 cm in the parallel separation plane,
whileun-squeezing it up to 50 cm or 60 cm in the crossing plane.
Such approach might be beneficialto mitigate specific hardware
limitations (e.g. magnet strength) at too large telescopic index,
butwhich is a priori not expected to happen for the telescopic
range under discussion (see Section 3.1).The other approach is to
limit the pre-squeezed β∗ in the two transverse planes to a value
which islarger or equal to its value in collision, which means
rTeleX ≥ 1 and rTele|| ≥ 1 according to the l.h.s.of the relations
(10). In this case, the aim is to maximize the β-beating waves
induced in the arcs(within certain hardware-related limits, e.g.
related to the mechanical acceptance of the arcs or tothe strength
available in the matching quadrupoles), in order to create the most
favorable conditionsfor the octupolar long-range beam-beam
compensation techniques introduced in Section 1.2. Thissecond
approach will be chosen in the following. Then, a net preference
emerges for the optionof starting from a round pre-squeezed optics
before the telescopic squeeze, leading de facto to atelescopic
configuration with rTele|| � rTeleX >∼ 1 according to the r.h.s.
of the relations (10), a choicedriven by the possibility to use the
same pre-squeeze sequences for IR1 and IR5, but also to startthe
β∗-levelling process with round optics only, i.e. when the beam
intensity is still high (see also asimilar discussion in Section
1.2). Accordingly, the two flat collision optics candidates
introducedin Section 1.2 (see also Tab. 1) are shown in Fig. 3 and
have been constructed as follows.
• The flat optics (60/15-15/60) is built starting from a round
pre-squeezed optics matched toβ∗Pre = 60 cm, i.e. corresponds to
the telescopic indexes r
Telex×y = 1.0×4.0 for IR1 and
rTelex×y = 4.0×1.0 for IR5.
• The flat optics (50/15-15/50) is built starting from a round
pre-squeezed optics matched toβ∗Pre = 75 cm, i.e. corresponds to
the telescopic indexes r
Telex×y = 1.5×5.0 for IR1 and
rTelex×y = 5.0×1.5 for IR5.
2.2 Crossing bumps and gymnasticsAs we will see in Section 2.5,
assuming the present LHC bunch population of ∼ 1.2 × 1011
pro-tons/bunch, a normalised crossing angle of 10σ seems still
acceptable for flat optics with a β∗
aspect ratio of up to r∗ = 4, therefore including the two flat
optics configurations (15/60) and(15/50). As explained earlier, the
crossing planes shall however be rotated in IR1 and IR5 withrespect
to their nominal configuration with round optics. To this aim, two
options are in principlepossible, namely:
• Operate the machine with the crossing bumps already rotated
since injection.
• Perform this rotation later in the cycle, e.g. at the end of
the ramp (or during the ramp itself),when the optics is still round
and aperture margins are sufficient.
Due to the aperture constraints at 450 GeV, the first option
would require to further increase β∗
and/or to already flatten the optics at injection (for rounding
it again in the ramp in order to bein a position to start the
β∗-levelling process with round optics in stable beam, see previous
dis-cussions). For simplicity, but also aiming at commissioning a
multi-purpose combined ramp andsqueeze, which is compatible with
both round and flat collision optics, the second option is
pre-ferred, in particular keeping the nominal crossing plane
orientation at injection (VH in IR1 and
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0.0 10.0 20.0 30.0s (m) [*10**( 3)]
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Zoom in IR1 Zoom in IR5 Zoom in IR1 Zoom in IR5
Figure 3: Flat optics (60/15-15/60) and (50/15-15/50) shown for
Beam 1 around the LHC Ring(top), and zoomed in IR1 and IR5
(bottom). The pre-squeezed β∗ is matched to β∗Pre =60 cm in
thefirst case, and to 75 cm in the second case. The difference
between the two cases is hardly visible,hidden behind the very
small β∗ in the parallel separation plane (β∗||=15 cm in both
cases).
IR5). Accordingly, for the flat optics machine development
session which took place in 2017 (seeSection 4), the injection
optics and the ramp were kept nominal, and the crossing plane
rotationwas achieved by a dedicated beam process inserted at the
end of the ramp at β∗ = 1 m, where theaperture margins are still
sufficient enough to be compatible with an either horizontal or
verticalcrossing angle in IR1 and IR5, i.e. regardless of the
orientation of the triplet beam-screen.Two subtleties shall however
be kept in mind. First, the crossing bump rotation should be
clock-wise or anti-clockwise in both IR1 and IR5, in order to
preserve a relative angle of 90◦ betweenthe crossing planes of
these two insertions during the whole process. Therefore, since the
crossingangle shall always be taken positive for Beam 1 when the
beams cross horizontally at either IP1or IP5 (otherwise the two
beams would cross a second time inside D1 as well), the polarity of
thevertical crossing angle in IR1 before the crossing bump rotation
defines univocally the one of IR5after the rotation, namely: [90◦,
0◦] −→ [0◦,−90◦] or [−90◦, 0◦] −→ [0◦, 90◦] for the two pos-sible
crossing plane orientations in [IR1, IR5], at injection and after
this gymnastic taking placeat higher energy. Concerning
specifically IR5, the crossing plane after the gymnastic
thereforecoincides with the plane of another special orbit bump
which is deployed later on in the vertical
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ir5b1:’ beta* = 0.15/0.50 (204.1 T/m)’
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(c) Crossing and IP shift bumpscombined with p∗y = +135µrad
(d) Crossing and IP shift bumpscombined with p∗y = −135µrad
Figure 4: Crossing and IP shift bumps shown for Beam 1 in IR5
for the (15/50) flat optics case.
plane, when bringing the two beams in collision (that is when
collapsing the now horizontal par-allel separation bump). This
special bump follows a specific demand from the CMS experimentto
lower down the IP as much as possible in the vertical plane (by
-1.5 mm in 2017, and furtherdecreased down to -1.8 mm in 2018), in
order to better adjust it to the actual center of the
centraltracker (something which may be improved in Run III assuming
some re-alignment campaign inLS2, presently under discussion). The
shape of the IP shift bump is shown in Fig. 4(a) for the (15-50)
optics, while the standard crossing bumps (crossing angle and
parallel separation), i.e. withoutIP shift, are shown in Fig 4(b).
The polarity of the vertical crossing angle can therefore play a
veryimportant role when adding up these two bumps in the vertical
plane, i.e. when the two beams arecolliding. When the crossing
angle is chosen positive for Beam 1, the peak vertical orbit
excursionreached in the inner triplet is preserved [compare Figs.
4(b) and 4(c)], and therefore the tripletmechanical aperture is not
expected to suffer from the IP shift bump. On the other hand, when
thecrossing angle polarity is negative, i.e. has the same sign as
the one given for the present CMSIP shift, the peak vertical orbit
excursion is degraded by more than 2 mm in the inner triplet
[seeFig. 4(d)] (at Q2.R5 for Beam 1 and Q2.L5 for Beam 2), which,
as will be discussed in Section 2.3,will limit the minimum possible
β∗ accessible in this case in the crossing plane. Another concernis
the possible impact of the IP shift bump on the normalised
beam-beam separation in IR5. As
10
-
Optics case β∗X/β∗|| ΘX Crossing Min. IR1 / IR5 Min. IR5
aperture
[cm] [µrad] plane in IR1/5 aperture at EoS [σ] in collision
[σ]Round optics 27/27 320 V/H 8.87 /8.89 8.76Flat optics I 60/15
245 H/V 9.02 /9.02 9.03 - 9.14Flat optics II 50/15 270 H/V 9.00
/9.00 7.84 - 9.11
Table 2: Minimum normalised aperture obtained from Q13.L to
Q13.R over the ATLAS and CMSinsertions at the end of squeeze (EoS),
and calculated for the specific case of IR5 in collisionas well,
that is when the vertical IP shift bump is deployed, and the
parallel separation bump isoff. The aperture normalization is made
assuming a beam energy of 6.5 TeV and an emittance ofγ� = 3.5µm (as
used by the collimation system). For each of the two cases with
flat optics, twonumbers are given for the IR5 aperture in
collision: the first one corresponds to a negative verticalcrossing
angle for Beam 1, and the second to a positive angle. In all cases,
the limitation is locatedin the triplet (with D1 at the same level
in the case of IR1 for round optics with vertical crossing).
will be shown in Section 2.5, the conclusions on this aspect are
exactly opposite, namely: when thecrossing angle is chosen positive
for Beam 1 (resp. negative), i.e. when the impact of the IP shift
isneutral (respectively detrimental) to the mechanical acceptance
of the inner triplet, the normalisedbeam-beam distance at the
long-range beam-beam encounters is actually degraded
(respectivelyimproved) with respect to the ideal situation without
IP shift bump.
2.3 ApertureAssuming the aperture tolerance budget recently
revisited for the LHC in collision (0.5 mm closedorbit, 5 %
β-beating, 10 % spurious dispersion, 2×10−4 momentum errors, see
Tab. 2 of Ref. [19]),the mechanical acceptance of IR1 and IR5 is
reported in Tab. 2 for the three optics configurationsconsidered so
far [(27/27), (15/60) and (15/50)], and expressed in terms of
so-called “collimationsigmas” (namely using a physical emittance
corresponding to γ� = 3.5µm at 6.5 TeV). In eachof these three
configurations, the aperture has been estimated at the end of the
squeeze, with theparallel separation still on, set to its nominal
value of ± 0.55 mm for the round optics case, andto ± 0.30 mm for
the two flat optics configurations. In the specific case of IR5,
the aperturecalculation has been repeated in collision as well,
that is without the parallel separation bump, butafter implementing
the CMS IP shift bump in the vertical plane (see Section 2.2).
Accordingly,for the flat optics configurations, where crossing and
IP shift planes coincide in IR5, the resultsobtained for the two
possible polarities of the crossing angle are carefully
distinguished in the lastcolumn of Tab. 2.A certain number of
important information can be extracted from the above summary
table, whilemore details can be found by scrutinizing the Figures 5
and 6 where the aperture has been plottedover the full insertions
IR1 and/or IR5 (from Q13.L and Q13.R) in the most relevant cases.
Firstof all, without considering the effect of the CMS IP shift
(before last column of Tab. 2), the twoflat optics cases give very
similar, if not strictly identical, results, regardless of the
choice of β∗
in the crossing plane, 60 or 50 cm, and of the corresponding
crossing angle, 245 or 270 µrad,respectively. This result simply
illustrates the fact that the aperture bottleneck is no longer
locatedin the crossing plane, as it is generally the case for round
optics, but in the other plane where
11
-
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip1b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem spec
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip1b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem spec
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip1b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem spec
Round IR1 (27/27) Flat IR1 (60/15) Flat IR1 (50/15)
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip5b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem
n1spec
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip5b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem n1 spec
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip5b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem
n1
spec
Round IR5 (27/27) Flat IR5 (15/60) Flat IR5 (15/50)
Figure 5: Normalised aperture for Beam 1 in IR1 (top) and IR5
(bottom), shown from Q13.Lto Q13.R, for the three optics cases
reported in Tab. 2 at the end of the squeeze at 6.5 TeV (i.e.with
parallel separation bump but without IP shift). The horizontal
green line corresponds to atargeted normalised aperture of 9.0σ.
The aperture bottleneck located in the triplet (and/or D1 inthe
case of IR1 with round optics) is very similar in all cases,
corresponding to the above target.The ATS signature is visible for
the flat optics cases, through slight aperture reductions which
canbe observed in the dispersion suppressor, mainly in IR1 where
the telescopic index is high in thevertical plane. In the matching
section, more significant aperture reductions are also showing up
inthe two flat optics configurations (with D2/Q4/Q5 approaching the
∼ 15σ aperture level in somecases). This situation could however be
greatly improved thanks to a so-called “CT-PPS opticssqueeze” [20]
leading to a net reduction of the beam sizes in the matching
section (and aiming atincreasing the normalised dispersion at the
roman pots for the CT-PPS experiment). A “CT-PPSsqueeze” has indeed
been included in the 40 cm pre-squeezed optics on which the 27 cm
roundtelescopic optics has been based, which explains the very
comfortable aperture of the matchingsection obtained in this case.
This refinement has however not yet been applied to the 60 cm and75
cm pre-squeezed optics which have been presently used to build up
the two flat telescopic opticsunder study (see Section 2.1).
12
-
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip5b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem n1 spec
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip5b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem n1 spec
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip5b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem n1 spec
(15/60) withoutIP shift
(15/60) with IP shift andp∗y = −122.5µrad for Beam 1
(15/60) with IP shift andp∗y = +122.5µrad for Beam 1
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip5b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem
n1
spec
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip5b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem
n1
spec
0.0 200. 400. 600. 800. 1000. 1200. s (m)
ip5b1
0.0
5.
10.
15.
20.
25.
30.
onel
em, n
1, s
pec onelem
n1
spec
(15/50) withoutIP shift
(15/50) with IP shift andp∗y = −135µrad for Beam 1
(15/50) with IP shift andp∗y = +135µrad for Beam 1
Figure 6: Normalised aperture of IR5 (Beam 1) obtained with the
(15/60) and (15/50) flat optics(top and bottom pictures,
respectively): (i) at the end of the squeeze without IP shift
(left), and(ii) in collision, with the CMS IP shift set to -1.8 mm
and assuming the two possible polarities forthe vertical crossing
angle, negative for Beam 1 (middle pictures) or positive (right
pictures). Forthe (15/50) flat optics, with the crossing angle
chosen negative for Beam 1, the normalised tripletaperture drops
down by more than 1σ below the targeted aperture of 9.0σ due to the
big verticalorbit excursion induced in this case.
β∗|| = 15 cm is the same for the two flat optics configurations.
The triplet aperture, reaching 9.0σin these two cases, is then
equivalent to the one obtained with the round optics configuration.
Thisobservation justifies a posteriori the various optics parameter
sets chosen in Tab. 1, in order tocompare the potential performance
reach of round and flat optics. The situation becomes
morecomplicated in IR5 when including the CMS IP shift in the
calculation (last column of Tab. 2).While the impact is quite
modest in the round optics configuration (for which the CMS IP
shiftbump is deployed in the plane perpendicular to the crossing
plane), the triplet aperture suffers morein the two flat optics
cases. More precisely, in the first case (15/60), and for both
possible crossingangle polarities in IR5, a naive inspection of
Tab. 2 could conclude that the situation tends on thecontrary to
even slightly improve with the CMS IP shift. Looking more into the
details, the reasonis that the IR5 aperture bottleneck without IP
shift is in the horizontal plane (located at Q2.L5for Beam 1, and
on the other side for the other beam), which therefore slightly
improves whencollapsing the horizontal parallel separation bump.
But then a second bottleneck starts to show up
13
-
(at Q2.R5 for Beam 1), this time in the vertical plane, when the
IP shift bump is deployed (comparethe three pictures on top of Fig.
6). Then, for the second flat optics case with β∗x/β
∗y = 15/50 cm at
IP5 (see bottom of Fig. 6), a crossing angle chosen negative for
Beam 1 results into a net reductionof the triplet aperture,
bringing it down by more than 1σ below the 9.0σ target. In this
respectthe operability of the CMS insertion with flat optics could
be sensibly limited, preventing to pushβ∗ below 60 cm in the
crossing plane, while 50 cm seems perfectly within reach in the
case of theATLAS insertion. However, dedicated aperture
measurements are first needed before drawing anyfinal conclusions,
and for the following specific reason. Indeed, as it has been
already observedin the past, the beam-screen sagitta due to the
gravity could in the end substantially improve thesituation in IR5
(for the advantageous configuration of a negative IP shift in the
vertical plane). Onthe other hand, this effect may as well degrade
the triplet aperture in IR1 compared to the aboveexpectations,
because the limitation, still in the vertical plane in this case,
does no longer comefrom a signed orbit deviation, but from the beam
sizes themselves, with β∗y taken as small as 15 cmat IP1 in the
vertical plane.
2.4 Chromatic aberrationsAs for any ATS optics, flat telescopic
optics feature remarkable chromatic properties, in terms of(i)
off-momentum β-beating (see Fig. 7), (ii) chromatic variations of
the betatron tunes (see Fig. 8),and (iii) correctability of the
horizontal and vertical spurious dispersions induced by the
crossingangles in IR1 and IR5 (using very modest orbit bumps
deployed in the sectors 81, 12, 45, 56, seeFig. 9).
0.0 7.5 15.0 22.5 30.0s (m) [*10**( 3)]
lhcb1:beta*=[0.60/0.15]-[0.15/0.60]
0.0
70.
140.
210.
280.
350.
420.
490.
560.
630.
700.
Wx,
Wy
Wx Wy
0.0 7.5 15.0 22.5 30.0s (m) [*10**( 3)]
lhcb1:beta*=[0.50/0.15]-[0.15/0.50]
0.0
70.
140.
210.
280.
350.
420.
490.
560.
630.
700.
Wx,
Wy
Wx Wy
(15/60) optics (15/50) optics
Figure 7: Chromatic Montague functions W shown for Beam 1 over
the LHC ring for the (15/60)and (15/50) flat optics configurations.
The machine starts at IP1. A W function reaching 100units can be
interpreted as a pure off-momentum β-beating, a pure off-momentum
α-beating, ora combination of the two, reaching the 10 % level at a
momentum error of 10−3. The horizontaland vertical W functions are
nicely minimized in the collimation insertions IR3 and IR7 (at s ∼7
km and 20 km, respectively). The off-momentum β-beating is
vanishing in the inner triplets ofIR1 and IR5 (and at the IP’s),
which means that the peak W functions observed at those
locationsactually correspond to a peak of the chromatic
α-functions, which is therefore not impacting onthe off-momentum
aperture of the inner triplets.
14
-
-0.0015 0.0 0.0015 deltap
lhcb1:beta*=[0.60/0.15]-[0.15/0.60]
62.300
62.305
62.310
62.315
62.320
62.325
62.330
q1
60.300
60.305
60.310
60.315
60.320
60.325
60.330
q2q1 q2
-0.0015 0.0 0.0015 deltap
lhcb1:beta*=[0.50/0.15]-[0.15/0.50]
62.300
62.305
62.310
62.315
62.320
62.325
62.330
q1
60.300
60.305
60.310
60.315
60.320
60.325
60.330
q2q1 q2
(15/60) optics (15/50) optics
Figure 8: Chromatic variations of the betatron tunes for the
(15/60) and (15/50) flat optics con-figurations. The linear
chromaticity is matched to 2 units. On purpose, the momentum
windowis extended up to δp = ±1.5 × 10−3, i.e. well beyond the
half-height of the RF bucket at flat-topenergy (δp = ±0.40 × 10−3),
in order to highlight the quality of the chromatic correction for
thenon-linear chromaticity terms such as Q′′ and Q′′′.
2.5 Beam-beam effects2.5.1 Generalities
For colliding flat beams or, more specifically, for round
emittance beams colliding with flat optics,the beam-beam effects
present some specificities which are discussed hereafter.
Head-on beam-beam effects
Let us first consider round emittance beams colliding without
crossing angle at one single IP.Assuming the optics to be flat at
the IP, the head-on beam-beam tune shift is not the same in thetwo
transverse planes. More precisely, neglecting the hour-glass effect
and in the approximationof small angles, this quantity is given by
the well-known following expression:
∆Q(ho)X,|| = −
Nb rp2πγ
β∗X,||
σ∗X,||
(σ∗X + σ
∗||
) = − N rp2π (γ�)︸ ︷︷ ︸
def= ξ0
×
√r∗
1 +√r∗
1
1 +√r∗
, (12)
with r∗ denoting the β∗ aspect ratio introduced in Eq. (2), (γ�)
the normalised emittance, Nb thebunch population, and rp = 1.535 ×
10−18 m the classical proton radius. In the presence of acrossing
angle, a rigorous derivation found in [21] shows that the above
expression still holds aftersubstitution of the beam size by the
projected beam size in the crossing plane, that is after the
15
-
0.0 7.5 15.0 22.5 30.0s (m) [*10**( 3)]
lhcb2:beta*=[0.60/0.15]-[0.15/0.60]
-3.
-2.
-1.
0.0
1.
2.
3.
Dx(m
),Dy
(m)
Dx Dy
0.0 7.5 15.0 22.5 30.0s (m) [*10**( 3)]
lhcb2:beta*=[0.50/0.15]-[0.15/0.50]
-3.
-2.
-1.
0.0
1.
2.
3.
Dx(m
),Dy
(m)
Dx Dy
0.0 10.0 20.0 30.0s (m) [*10**( 3)]
lhcb1:beta*=[0.60/0.15]-[0.15/0.60]
-0.0110
-0.0088
-0.0066
-0.0044
-0.0022
0.0
0.0022
0.0044
0.0066
0.0088
0.0110
x (m
), y
(m
) x y
0.0 10.0 20.0 30.0s (m) [*10**( 3)]
lhcb1:beta*=[0.50/0.15]-[0.15/0.50]
-0.0110
-0.0088
-0.0066
-0.0044
-0.0022
0.0
0.0022
0.0044
0.0066
0.0088
0.0110
x (m
), y
(m
) x y
0.0 7.5 15.0 22.5 30.0s (m) [*10**( 3)]
lhcb1:beta*=[0.60/0.15]-[0.15/0.60]
-3.
-2.
-1.
0.0
1.
2.
3.
Dx(m
),Dy
(m)
Dx Dy
0.0 7.5 15.0 22.5 30.0s (m) [*10**( 3)]
lhcb1:beta*=[0.50/0.15]-[0.15/0.50]
-3.
-2.
-1.
0.0
1.
2.
3.
Dx(m
),Dy
(m)
Dx Dy
(15/60) optics (15/50) optics
Figure 9: Spurious dispersion for the (15/60) and (15/50) flat
optics configurations (left and rightpictures, respectively),
induced by the crossing bumps in IR1/5 (see Section 2.2), in IR2
(β∗ =10 m, p∗y = 200µrad, δx
∗ = 1 mm), and in IR8 (β∗ = 3 m, p∗x = −250µrad, δy∗ = 1 mm),and
including as well the contribution from the vertical shifts of IP2
(δy∗ = −2 mm) and IP5(δy∗ = −1.8 mm). Only Beam 1 is shown. The top
and bottom pictures illustrate the situationbefore and after a
correction measure, acting only on the dominant contributions from
IR1 and IR5,and consisting into the generation of dispersive orbit
bumps in the arcs on either side of IP1 and IP5(see middle
pictures). The negative horizontal dispersion in IR3 (Dx ∼ −3 m) is
nominal, whilesome unwanted peaks of vertical (∼ 2 m) and
horizontal (∼ 1 m) spurious dispersion are showingup before
correction in the triplets of IR1 and IR5. After correction, the
spurious dispersion isstrongly reduced, with a residual coming from
the remaining contributions from IR2, IR8, andfrom the IP5 shift.
The non-zero nominal horizontal dispersion of IR6 resulting from
the hightelescopic index is also restored after correction (see the
peak of Dx ∼ −2 m showing up in IR6in the bottom right
picture).
16
-
Optics case β∗X/β∗|| ΘX Loss ∆Qx [10
−3] ∆Qy [10−3] ∆Q
(ho)tot
[cm] [µrad] Factor from MADX from MADX from Eq. (15)Round optics
27/27 320 0.635 -7.72 -7.88 -7.76Flat optics I 60/15 245 0.848 -
9.71 -9.97 -9.81Flat optics II 50/15 270 0.799 -9.08 -9.30
-9.14
Table 3: Total head-on beam-beam tune shift versus optics at
constant beam parameters (IP1 andIP5 only, Nb = 1.25× 1011
protons/bunch, γ� = 2.5µm, E = 6.5 TeV, σz = 7.5 cm).
transformation σ∗X −→ σ∗X/F , where F represents the geometric
loss factor introduced in (6).After the substitution, the beam-beam
tune shift takes the following expression:
∆Q(ho)X,|| = −ξ0 × F ×
F√r∗
F +√r∗
1
F +√r∗
. (13)
Therefore, for one single IP one gets
∆Q(ho)X
∆Q(ho)||
= F ×√r∗ , (14)
which is lower than 1 for round optics (F 1/F 2). Now
considering two IP’s, where the planesof smallest and largest β∗
are alternated from one IP to the other, together with the crossing
anglewhich is deployed in the plane of largest β∗, the (x − y)
symmetry is restored, and the overallbeam-beam tune shift takes the
following expression:
∆Q(ho)tot (r
∗) = −ξ0 × F ×1 + F
√r∗
F +√r∗
, (15)
which somehow generalizes an expression given in [22] in the
case of two IP’s with round op-tics and alternated HV crossing. The
third term on the r.h.s. of the above expression
decreasesmonotonously from 1 to F when increasing r∗. As a result,
at constant geometric loss factorF < 1, flattening an optics at
constant equivalent β∗ [in the sense of Eq. (4)] systematically
de-creases the head-on beam-beam tune shift which, asymptotically,
tends to the following limit:
limr∗→∞
∆Q(ho)tot (r
∗) = −ξ0 × F 2 . (16)
In that respect, (alternated) flat optics go in the direction of
reducing the head-on beam-beam tuneshift (and tune spread) at
constant peak luminosity.As shown in Tab. 3, the formula (15)
matched quite closely the MADX expectations (using Beam 1as the
weak beam, and modeling the head-on beam-beam interaction with 100
slices for Beam 2).The slight (x − y) asymmetries, also observed in
the round optics case, are due to second andhigher-order effects
with the bunch charge, in particular the dynamic β-beating, which
depends on
17
-
the unequal horizontal and vertical betatron phase advances from
IP1 and IP5. In all cases, themain conclusion is that the
configuration proposed with “alternated flat optics” at IP1 and IP5
doesnot substantially impact on the total head-on beam-beam tune
shift, and on its overall topology(see also Fig. 10).
Long-range beam-beam effects
Considering first identical round optics in IR1 and IR5, with
the beams crossing horizontally in oneof the two insertions and
vertically in the other, the b2-like and b2n+4-like (e.g. b6)
components ofthe long-range beam interactions self-compensate in
terms of tune shift and tune spread induced ineach IR separately.
Due to the two-fold symmetry of the machine with respect to IP1 and
IP5, thisattractive feature is also preserved for the so-called
pacman bunches, located at the beginning andat the end of the LHC
trains, and therefore missing the same long-range beam-beam
encounterson a given side of each of the two main IP’s. The
situation is quite different for flat optics, evenassuming an
alternation between the two IR’s in terms of crossing planes and β∗
aspect ratios. Inthis configuration, some compensations still exist
for the tune shift and the tune spread, but areonly partial, and
vanish rapidly with the following scaling laws:
∆Q(LR)2n,2IR−flat = r
∗n/2 ×(r∗
n/2
+(−1)n
r∗n/2
)×∆Q(LR)2n,1IR−round , n = 1, 2, . . . , (17)
where the quantities ∆Q(LR)2n,2IR−flat represent the total tune
shift and tune spread induced by theb2n-like components of the
long-range beam-beam interactions in the two insertions, as a
functionof the same observables, namely ∆Q(LR)2n,1IR−round, but
considering the contribution of one singleinsertion with a round
optics matched to the same equivalent β∗ and with the same
normalizedcrossing angle. In order to obtain the above scaling law,
it is sufficient to observe that: (i) thepeak β-function in a given
plane scales with
√r∗ in one low-β insertion, and with 1/
√r∗ in the
other, after flattening the optics at constant β∗eq. [see Eq.
(4)]; (ii) the b4k+2-like components ofthe BBLR interactions, k =
1, 2, . . ., add up between the two IR’s, while the b4k
componentscompensate each other [9], which explains the factor
(−1)n; (iii) the bl-like component of theBBLR interactions, l = 1,
2, . . ., is inversely proportional to the lth power of the
physical crossingangle [9], the latter decreasing with r∗1/4 when
working at constant normalised crossing angle [seeEq. (8)], which
explains the addtionnal enhancement factor r∗n/2 factorized on the
r.h.s. of Eq. (17).In particular the long-range beam-beam
interactions do impact on the betatron tunes in the caseof flat
optics, and almost exactly at the same level as the head-on
beam-beam tune shift itself, asshown in Fig. 10, for the (15/60)
optics case. For the same reasons, pacman bunches also move inthe
tune diagram, but still along the diagonal, thanks to the (x−y)
symmetry which is preserved bythe alternated flat optics
configurations under discussion (see Fig. 11). These strong
perturbationsinduced on the long-range beam-beam interactions
motivate the already mentioned strategy ofgoing in collision with
round optics at high intensity, or, let us say, with the minimum
possible β∗
aspect ratio corresponding to the maximum prescribed luminosity
(2× 1034 for Run III), and, onlylater on, further reduce β∗ in the
parallel separation plane during the β∗-levelling process.
18
-
0.280 0.285 0.290 0.295 0.300 0.305 0.310Qx
0.290
0.295
0.300
0.305
0.310
0.315
0.320
Qy
Nb=1.25×1011 ppb, =-245 rad
IP1/5 HOIP1 HOIP5 HOIP1/5 HO+LRIP1/5 HO+LR+IMO=-550 A
Figure 10: Various contributions to the beam-beam tune footprint
(shown for particles up to 6σbetatron amplitudes) for the (15/60)
flat optics configuration: starting from the asymmetric impactof
the head-on collisions taken separately at IP1 and IP5, adding them
up, then considering thelong-range beam-beam effects in IR1 and
IR5, which further increase the tune spread on the anti-diagonal
but also shift the working point along the diagonal, and finally
including the contributionfrom the Landau octupoles, powered with
negative polarity and which mitigate the overall spread.
19
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0.280 0.285 0.290 0.295 0.300 0.305 0.310Qx
0.290
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Qy
Nb=1.25×1011 ppb, =-245 rad, IMO=-550 A
IP1/5 HO+LRIP1/5 HO+Right PACMANIP1/5 HO+Left PACMAN
Figure 11: Beam-beam tune footprint for the (15/60) flat optics
configuration and three differentclasses of bunches: (i) the
nominal bunches, at the middle of the trains, seeing the
maximumpossible number of parasitic collisions on either side of
IP1 and IP5, and (ii) the so-called left andright pacman bunches,
at the beginning of the first train and at the end of the last
train before theabort gap, and with long-range beam-beam encounters
only on the left and right side, respectively,of IP1 and IP5. The
contributions from IR2 and IR8 are not included. The octupoles are
switchedon with negative polarity. The long-range beam-beam tune
shift is obviously about halved for thepacman bunches, together
with the spread, which is even over-compensated in this case by
thelattice octupoles.
20
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2.5.2 Crossing angle validation for flat optics
Long-range beam-beam separation and IP shift
As soon as the crossing planes are rotated, flat optics were
initially not expected to add any otheradditional level of
complexity, in particular in terms of normalised beam-beam
separation in theinner triplet. This is effectively the case for
the ATLAS insertion. However, as already announced,the sizable IP
shift bump requested by the CMS experiment (see Section 2.2), and
the crossingbump rotation driven by the preservation of the triplet
aperture, lead to the unfortunate situationwhere both bumps are
deployed in the same (vertical) plane. In this configuration, not
only themagnitude, but also the sign of the crossing angle matters
to preserve the normalised beam-beamseparation, as seen by both
beams in the inner triplet. As shown in Fig. 12, the normalised
distancebetween the two beams can improve by up to 2 σ in the inner
triplet, relative to the case without IPshift, when the crossing
angle is chosen negative for Beam 1 (but with the triplet aperture
reducedby ∼ 1σ in this case, see Section 2.3), and conversely for
the other polarity. The impact onthe beam is already quite clear in
view of the beam-beam footprint (see Fig. 13). While, for
the(15/60) optics configuration, the two crossing angle polarities
remains a priori compatible with theaperture of the inner triplet,
only one of the two is allowed for the (15/50) optics as we have
seenin Section 2.3. On the other hand, the preferred polarity
aperture-wise (positive crossing angle forBeam 1) actually
corresponds to the worst case for the long-range beam-beam effects,
bringingthem at the limit of accept-ability, as we will see
now.
80 60 40 20 0 20 40 60 80Distance from IP5 [m]
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[]
No IP shift, =± 245 rad-1.8 mm IP shift, =+245 rad-1.8 mm IP
shift, =-245 rad
Figure 12: Normalised beam-beam separation in IR5 for Beam 1
(left) and Beam 2 (right), calcu-lated with the (15/60) optics
configuration. In the presence of the vertical CMS IP shift of -1.8
mm,which is in the same plane as the crossing plane in flat optics
operation mode, the beam-beam sep-aration in the inner triplet can
be substantially improved or, on the contrary, strongly
degraded,depending on the crossing angle polarity (see also Section
2.3 for the impact on the triplet aper-ture). The situation in IR1
(with horizontal crossing and no IP shift) is not shown because it
strictlycorresponds to the case of IR5 with zero IP shift.
21
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0.280 0.285 0.290 0.295 0.300 0.305 0.310Qx
0.290
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Qy
Nb=1.25×1011 ppb, IMO=-550 A
No IP shift, =± 245 rad-1.8 mm IP shift, =+245 rad-1.8 mm IP
shift, =-245 rad
Figure 13: Beam-beam tune footprint including the contribution
of the four experimental inser-tions, without or with IP shift in
IR5, and, in the second case, for the two possible crossing
anglepolarities in IR5. The worst case is clearly visible (positive
angle for Beam 1 shown in red, which,at the opposite, corresponds
to the best case in terms of triplet aperture, see Section 2.3).
Theoctupoles are powered with negative polarity, which mitigates
this effect.
22
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Multi-parametric dynamic aperture study
In this paragraph, only the (15/60) flat optics configuration is
considered, corresponding to a worstcase both for the long-range
and the head-on beam-beam effects, compared to the (15/50)
configu-ration with a slightly increased β∗ aspect ratio, and
therefore more pronounced self-compensationof the long-range
beam-beam induced tune spread between IR1 and IR5, and also
slightly reducedhead-on beam-beam tune shift (see Tab. 3). An
approach similar to the one developed in [14] isnow used to
determine the appropriate conditions for approaching or even
reaching the 10σ levelfor the crossing angle in IR1 and IR5
(245µrad). Optimizing various machine parameters (tunes,octupole),
the goal is to satisfy the 5σ dynamic aperture criteria, which is
now routinely used torun the LHC [14, 16].First of all, as shown in
Fig. 14(a), using the nominal collision tunes of (.31/.32) and with
the oc-tupoles still off, a normalised crossing angle of 10σ, even
if chosen negative for Beam 1 (“good”polarity), does not seem to be
manageable for a reference bunch population of 1.25 × 1011
pro-tons/bunch. The dynamic aperture is still unacceptable (< 4
σ) even at a somehow lower intensityof 1.07×1011 protons/bunch,
corresponding to the maximum luminosity of 2×1034 cm−2s−1 actu-ally
sustainable by the inner triplet. However, (i) re-optimizing the
machine tunes [see Fig. 14(b)],in particular to compensate for the
negative BBLR-induced tune shift, and (ii) pushing the oc-tupoles
to their nominal current of 550 A with negative polarity [compare
Figs. 14(b) and 14(c)],help to build up very substantial margins
compared to the 5σ dynamic aperture criteria, whichshould enable
the machine operability with a normalised crossing angle as low as
10σ for theso-called “good” polarity case. Indeed, as showed in
Fig. 14(d), the dynamic aperture is 5.5σwith this crossing angle at
1.25× 1011 protons/bunch (L = 2.73× 1034 cm−2s−1, see Tab. 1),
andis about 6σ at 1.07 × 1011 protons/bunch, which corresponds to
the above-mentioned luminositylimit (and where β∗-levelling is
implicitly assumed in order to mitigate the BBLR effects at
higherbeam current). The working point chosen in Fig. 14(d)
(0.326/0.329) is however challenging (forlinear coupling).
Increasing the tune split (e.g. working at 0.325/0.330) would
reduce the margins,but still preserving the 5σ dynamic aperture
criteria [see the tune scan in Fig. 14(c) performed atthe reference
bunch population of 1.25× 1011 protons/bunch].As expected, the
situation is however more difficult for the other polarity of the
crossing angle inIR5, positive for Beam 1, i.e. opposite to the CMS
IP shift. While this configuration is preferablefor the triplet
aperture (see Section 2.3), it is detrimental to the normalised
beam-beam separationin the triplets of IR5 (see Fig. 12). Comparing
Fig. 15(a) with Fig. 14(c), the available tune space(i.e.
satisfying the 5σ dynamic aperture) is substantially reduced, but
the optimal tunes are moreor less preserved. Even after tune
re-optimization, and with the octupoles pushed to -550 A,
thedynamic aperture is still slightly below 5σ for a bunch
population of 1.07×1011 proton/bunch anda crossing angle of 10σ in
IR1 and IR5, i.e. when operating the machine at the luminosity
limit of2×1034 [see Fig. 15(b)]. A sufficient margin could however
be restored in this configuration as-suming a full crossing angle
of e.g. +260µrad (10.6σ instead of 10.0σ), still fitting well with
thetriplet aperture (since it is the case for the (15/50) optics
with a full crossing angle of +270µrad,see Fig. 6), but of course
slightly reducing the virtual luminosity by 1.5 %.The situation
with no CMS IP shift has also been studied and is illustrated in
Figs. 15(c) and 15(d)(where, in this case, the polarity of the
vertical crossing angle becomes irrelevant in IR5). Underthese
conditions, the 10σ level for the crossing angle seems to be within
reach, but at the limit(compared to the 5σ dynamic aperture
criteria).
23
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3.0
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DA
[]
(c) (d)
Figure 14: Flat optics configuration (15/60) assuming the “good”
polarity for the crossing anglein CMS (IR2 and IR8 contributions
included, with halo collision at IP2, luminosity levelling at2×1032
with parallel separation at IP8, and so-called worst polarity for
the LHCb spectrome-ter): (a) dynamic aperture [σ] scan (and
luminosity contour lines superimposed in red in units of1034
cm−2s−1) vs. half-crossing angle and bunch population with nominal
machine tunes and oc-tupoles switched off; (b) tune scan in same
conditions at a reference bunch population of 1.25×1011and a
reference crossing angle of 245µrad (10.0σ) in IR1 and IR5; (c)
tune scan in the same con-ditions, but with the octupoles set to
-550 A; (d) second dynamic aperture scan with the octupolesON and
the machine tunes re-optimized to (0.326/0.329). This working point
is challenging (forlinear coupling), but on the other hand, leading
to considerable margins in terms of dynamic aper-ture. Increasing
the tune split (e.g. working at 0.325/0.330) would reduce these
margins, but stillpreserving the 5σ dynamic aperture criteria [see
Fig. (c)].
24
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62.300 62.305 62.310 62.315 62.320 62.325 62.330 62.335Qx
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Min DA LHC FlatHV, *X/ *//=60cm/15cm, Nb=1.25×1011ppbIP
shift=-1.8mm, =245 rad, =2.5 m, Q′=15, IMO=-550A
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60.328)IP shift=-1.8mm, =+, =2.5 m, Q′=15, IMO=-550A
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(c) (d)
Figure 15: Flat optics configuration (15/60) assuming the “bad”
polarity for the crossing angle inCMS, with [top pictures (a) and
(b)] and without [bottom pictures (c) and (d)] IP shift (IR2 andIR8
contributions included, with halo collision at IP2, luminosity
levelling at 2×1032 with parallelseparation at IP8, and so-called
worst polarity for the LHCb spectrometer): (a)-(c) tune scans
withthe octupoles set to -550 A at a reference bunch population of
1.25× 1011 and a reference crossingangle of 245µrad (10.0σ) in IR1
and IR5; (b)-(d) dynamic apertures [σ] scan with the octupolesON
and the machine tunes re-optimized to (0.325/0.328). Working with a
full crossing angleslightly relaxed to +260µrad (compared to the
initial target of +245µrad) could help to build upsubstantial
margins, or to relax the aggressive tune split of 0.003 considered
here, at a very modestcost in terms of peak luminosity (1.5 %
reduction).
25
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=-, =2.5 m, Q′=15, IMO=-550A
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Left pacman Right pacman
Figure 16: Flat optics configuration (15/60) with “good”
polarity for the crossing angle in CMS(IR2 and IR8 contributions
included, with halo collision at IP2, luminosity levelling at
2×1032 withparallel separation at IP8, and so-called worst polarity
for the LHCb spectrometer): dynamic aper-ture [σ] scan for the left
and right pacman bunches vs. half-crossing angle and bunch
population,with the octupoles set to -550 A and the machine tunes
re-optimized to (0.326/0.329).
Finally, as shown in Fig. 16, the margins becomes considerable
for the so-called left and rightpacman bunches, despite of their
different tunes (shifted up by about 0.005 along the diagonal,
seeFig. 11), and different tune spread topology.
3 Expected ATS-related limitations in Run III and
mitigationmeasures
As we have already seen with the CMS IP shift, running the
machine with telescopic optics, andin particular with flat optics,
might lead to specific, and sometimes unexpected limitations
comingfrom one or several LHC sub-systems. The aim of this section
is to identify the main ATS-relatedlimitations, with the LHC Run
III put into perspective, when operating the machine at higher
en-ergy (7.0 TeV), with higher beam intensity (LIU beam), and
assuming the deployment of ATSoptics with large telescopic indexes
in one or the two transverse planes. Whenever possible, miti-gation
measures will also be suggested along the discussion. Very often,
the same limitations (andpossible mitigation steps) will stand as
well for round telescopic optics, which, de facto, will alsobe
included into the discussion.
3.1 Magnet systemSurprisingly enough, flat (resp. round)
telescopic optics, with H×V telescopic indexes as high as2 × 5 in
IR1 and 5 × 2 in IR5 (resp. 4 × 4 in IR1 and IR5), are found to be
compatible with thenominal performance of (almost) all LHC magnets
up to 7 TeV, considering as well some non-
26
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conform magnets such as MQTL’s. With such telescopic indexes,
and knowing that the lower limitof the pre-squeezed β∗ is in the
range of 40 (50) cm for the (HL-)LHC [1], nearly all relevantoptics
configurations are a priori within reach, in particular flat optics
with a collision β∗ as smallas 10 cm in the parallel separation
plane. The only exception concerns the Q5 magnet on theleft side of
IP6 (MQY type with a nominal current specified to 3610 A), for
which the ultimatecurrent of 3900 A is actually requested when the
telescopic indexes are pushed to 5 × 2 in IR5 ata beam energy of 7
TeV (worst case). Correspondingly, a dedicated training campaign
has beenrecently requested and successfully conducted on these two
circuits (RQ5.L6b1/2), demonstratingtheir reliable operability
(still without beam) up to a current 3950 A [23]. In summary, the
existingLHC magnet system is a priori not expected to limit the
full deployment of ATS optics in Run III,up to a beam energy of 7.0
TeV3.
3.2 Machine protection systemOne possible hindrance to the full
deployment of ATS optics, and in particular of flat
telescopicoptics, is however related to the LHC beam dump system
(LBDS).
3.2.1 MKD-TCT phase advance
In order to maximize the minimum allowed normalised aperture of
the inner triplet in the contextof beam dump failure scenarios, and
therefore to maximize the β∗ reach, the horizontal phase ad-vances
between the extraction kicker (MKD) in IR6 and the horizontal
tertiary collimators (TCTH)in IR1 and IR5 should ideally be
adjusted to kπ for both beams, with k an integer. While this
ad-ditional constraint does not present any conceptual challenge
for standard optics, the situation ismore delicate for ATS optics,
which already relies on a specific global phasing configuration
ofthe ring, both for the chromatic correction of the inner triplets
in IR1 and IR5, and for a smoothdeployment of the telescopic
squeeze in the sectors adjacent to these two insertions.
Furthermore,preserving these phase advances during the whole
telescopic squeeze, or at least towards its endwhen the demand on
the triplet aperture is the highest, is also not trivial, since the
IR6 optics itselfis varying during this process. A tolerance of±30◦
is however generally accepted [24] with respectto the
above-mentioned ideal configuration. Despite the recent development
of a second generationof ATS optics to better match this
constraint, and to actually implement competitive ATS opticsin the
LHC [25], this target cannot always be met for large telescopic
indexes. While IR1 is anon-issue in this respect, the real
difficulty is to match and preserve this constraint during the
tele-scopic squeeze for the two TCT’s of IR5 (both beams). As shown
in Fig. 17, the recommended±30◦ tolerance can no longer be strictly
preserved for Beam 2 when the horizontal telescopic indexreaches
the value of 3 in IR5, both for round and flat optics, that is with
H×V telescopic indexes of3×3 and 3×1, respectively. More precisely,
in the specific case of the flat telescopic squeeze [seeFig.
17(b)], the situation is still acceptable for Beam 1, but 2.9◦
(respectively 6.8◦) are missing forBeam 2 for the MKD-TCT5 phase
advance, when the horizontal telescopic index reaches 4 (resp.5) in
IR5. Strictly speaking, however, this limitation on the telescopic
index does not prevent at allthe realization of the two flat optics
under consideration, namely the (15/60) and (15/50)
configu-rations, since the pre-squeezed optics can be matched to
any β∗ arbitrarily chosen in between 2 m
3Not considering other possible non-ATS related magnet strength
limitations, as e.g. in the main dipoles, for
someseparation/recombination dipoles in IR4, or some “weak” triplet
orbit corrector magnets MCBX.
27
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(a): Round telescopic squeeze
(b): Flat telescopic squeeze
Figure 17: Beam 1 (solid lines) and Beam 2 (dashed lines)
MKD-TCT5 phase advance, as afunction of the telescopic index
product rTeleX × rTele|| , for a typical round (top) and specific
flat(bottom) telescopic squeeze. In the case of round optics, the
telescopic squeeze is performedkeeping rX ≡ r|| at each step, till
reaching a telescopic index of 4 in both transverse planes. In
thecase of flat optics, for practical reasons related to the LHC MD
program aiming at covering bothLHC and HL-LHC (see Section 4), the
telescopic squeeze was prepared following the sequencerTeleX ×
rTele|| = 1 × 1 → 1 × 5 → 2 × 5. As an example rTeleX × rTele|| ≡
4.0 (resp. 9.0) onthe horizontal scale actually means rTeleX ×
rTele|| ≡ 2.0 × 2.0 [resp. 3.0 × 3.0] for Fig. (a), andrTeleX ×
rTele|| ≡ 1.0× 4.0 [resp. 1.8× 5.0] for Fig. (b).
28
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and 40 cm for the LHC [1], and, if necessary, might even be
(moderately) flattened as well in thehorizontal plane. On the other
hand, the highest possible telescopic indexes are also
recommendedfor the realization of such optics, in order to maximize
the mitigation of the long-range beam-beameffects by the lattice
octupoles, as it was presented in Section 2.5. In view of the
above, the realiza-tion of flat optics with telescopic indexes not
exceeding 4 in the parallel separation plane thereforelooks to be a
reasonable target (assuming further optics optimization and/or
negotiation to gain2-3 degrees in the above tolerance). A
posteriori, the parameter choices made in Section 2.1
forconstructing the (15/60) optics are then found to be fully
appropriate, in terms of pre-squeezed β∗
(60 cm) and corresponding H×V telescopic indexes in IR1 and IR5
(1× 4 and 4× 1, respectively).But retrospectively, these choices
shall be revisited for the (15/50) configuration, i.e. pushing
thepresqueezed β∗ down to 60 cm as well in this case, and relaxing
accordingly the telescopic indexesto rTeleX × rTele|| = 1.2× 4
(instead of 75 cm and 1.4× 5, respectively, proposed in Section
2.1).
3.2.2 TCDQ constraints at flat-top energy: move-ability and
minimum gap
One drawback of the ATS scheme is related to the IR6 optics
modifications which are inducedduring the telescopic squeeze,
leading in particular to some variations of the horizontal
β-functionat the TCDQ (and TCSP). Indeed, since the TCDQ settings
are interlocked by the beam energytracking system (BETS), this
device is presently no longer move-able when the ramp is
finished.Therefore, any change of the IR6 optics subsequent to the
ramp can have a direct impact on thenormalised gap of the TCDQ,
then on the overall collimation hierarchy and, in fine, on the
β∗
reach. The variations of the horizontal β-function at the TCDQ
are shown in Fig. 18 for the twotelescopic squeeze sequences, round
and flat, which have been introduced in the previous sub-section.
These variations are always positive for Beam 1, and conversely for
Beam 2 (within somesmall fluctuations at low telescopic indexes).
The effect is small enough to be manageable fortelescopic indexes
less than ∼ 1.5− 2, where the machine can still be operated at
constant TCDQsettings (in mm) during the telescopic squeeze. For
the present LHC operation mode, for instance,the TCDQ settings are
adjusted at the end of the ramp, and kept constant afterward, in
such a waythat they actually correspond to a normalised gap
prescribed at the smallest possible targeted β∗
(7.3σ both for 2017 and 2018 [15]). This strategy however
requires to open the TCDQ gap morethan necessary for Beam 1 at the
end of the ramp (due to the increase of the β-function at theTCDQ
during the telescopic squeeze), and conversely for Beam 2. The
limitation may thereforecome from Beam 2, when the β-function
reduces by, let us say, 10 % at the TCDQ over thetelescopic
squeeze, therefore imposing a tightening of the TCDQ gap by 5 % ×
7.3 ∼ 0.4σ atthe end of the ramp, i.e. corresponding already to
half of the nominal retraction between the IR7secondary collimators
(TCSG presently at 6.5σ) and the TCDQ itself (presently at 7.3σ).
In thecase of the round optics, the βx variations at the TCDQ are
bounded to 6% for Beam 2 over the fulltelescopic squeeze [β(TCDQ)x
= 530 → 500 m for rTeleX × rTele|| = 1 × 1 → 4 × 4, see Fig.
18(a)].On the other hand, in the case of the flat telescopic
squeeze, the β(TCDQ)x variation limit is met,and even already
slightly exceeded for a telescopic index larger than or equal to 4
in the horizontalplane [β(TCDQ)x = 530→ 475→ 450 m for rTeleX
×rTele|| = 1×1→ 1×4→ 1×5, see Fig. 18(b)].This borderline situation
is clearly not satisfactory and, in any case, does not go in the
direction ofenabling a further tightening of the collimation
hierarchy in order to push the β∗ reach in Run III.Although the
main argument to justify any action will come later, three possible
options could apriori be envisaged to mitigate this second
limitation (after the MKD-TCT phase) impacting on the
29
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(a): Round telescopic squeeze
(b): Flat telescopic squeeze
Figure 18: Horizontal beta function at the TCDQ for Beam 1
(solid lines) and Beam 2 (dashedlines), as a function of the
telescopic index product rTeleX × rTele|| , for a typical round
(top) and spe-cific flat (bottom) telescopic squeeze (see also the
caption of Fig. 17 for a more detailed descriptionof these two
squeeze sequences).
30
-
maximum possible horizontal telescopic index in IR5.
• Option 1 - ATS optics are built such that, as soon as
prescribed left and right betatron phaseadvances are reached in IR1
and IR5 during the pre-squeeze, the continuation of the pre-squeeze
sequence (IPQ functions in IR1 and IR5) and the telescopic squeeze
itself (IPQfunctions in IR8/2/4/6) can be combined, exchanged or
interleaved in a strictly commutativemanner. Said differently,
inserting the telescopic squeeze in the ramp, partially or in
totality,is in principle perfectly feasible (i.e. may be only
limited by the ramp duration). Subse-quently, redefining
accordingly the TCDQ ramp functions would offer in this case a
veryelegant alternative to mitigate or fully solve the problem,
since this approach would allowto minimize or strictly cancel the
IR6 optics changes at flat-top energy. In practice, how-ever, the
maximum allowed presqueezed β∗ is presently 2 m (where the
match-ability of theleft/right phase advances of IR1 and IR5 starts
to be difficult [1]). At the opposite, the endof ramp β∗ is
recommended not to be substantially lower than 1 m, as in the
present LHChypercycle since 2017. More precisely, an end of ramp β∗
of 80 cm is very likely the limit,in order to leave open the
possibility to achieve the crossing plane rotation at the end of
theramp with still sufficient aperture margin in the inner triplet
(see later Fig. 24 in Section 3.3).Under these conditions,
deploying a telescopic index strictly larger than 2.5 in the
ramplooks already challenging. More specifically, demanding a
telescopic index of 4 alreadyreached at the end of the ramp, as
requested in the parallel separation plane for the (15/60)and
(15/50) optics configurations, would impose to deeply rework the
pre-squeeze sequence,that is targeting a maximum pre-squeezed β∗ in
the range of 3.2 m to 4 m, which is maybenot impossible, but was
already tried out without success. Furthermore, even if a
solutioncould be found, another argument making this option not
really appealing lies in the fact thatthe optics would be already
flat at the end of the ramp, and de facto at the beginning of
theβ∗-levelling process. This configuration is not recommended, as
already discussed, since theidea is on the contrary to keep the
optics round as long as possible at high intensity (with theLIU
beam in perspective), in order to preserve as long as possible the
mutual compensationof the BBLR-induced tune spread coming from the
two high-luminosity insertions.
• Option 2 - A second approach would consist in making the
necessary changes to the BETS,in order to allow the displacement of
the TCDQ jaw at flat-top energy, as a function of theactual
telescopic index, the latter being univocally connected to the
normalised strengths ofsome matching quadrupole magnets, in
particular Q5.L6b1, already discussed in Section 3.1,and Q4.L6b2
(see Fig. 19). Concerning possible TCDQ reproducibility issues,
this actioncould be restricted to Beam 2 only, for which the TCDQ
gap variations would be monotonousover the full cycle, decreasing
both during the ramp and during the telescopic squeeze at flat-top
energy.
• Option 3 - A third option would consist in moving the beam
instead of the single-jaw of theTCDQ [26], and in re-working the
BPM@P6 interlock by introducing a movable referenceorbit, together
with the corresponding horizontal orbit bump. The amplitude of this
bumpwould be a function of the telescopic index during the LHC
cycle (e.g. a function of theQ5.L6b1 and Q4.L6b2 measured currents
and of the beam energy). In order to work atstrictly constant
normalised TCDQ setting, and although not strictly needed for Beam
1 (seeabove discussion), this bump would displace the beam away
from the TCDQ jaw by up to
31
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1σ, i.e. ∼ 0.6 mm, in order to cope with the increase of the
horizontal β-function at theTCDQ during the flat telescopic squeeze
[β(TCDQ)x = 530→ 700 m for rx × ry = 1× 1→5× 1, i.e. ∆xCO[σ] =
n(TCDQ) ×∆β/(2β) ∼ 1σ, see Fig. 18(b)]. Conversely for Beam 2,this
bump would move the beam towards the TCDQ jaw by up to 0.6σ
[β(TCDQ)x = 530 →450 m for rx × ry = 1 × 1 → 5 × 1, i.e. ∆xCO[σ] =
n(TCDQ) × ∆β/(2β) ∼ 0.6σ, seeFig. 18(b)].
As previously mentioned, the additional level of complexity
induced by the ATS scheme (i.e. the“IR6 squeeze” and subsequent
variations of the β-functions at the TCDQ) is however at the
limitto fully justify any of the above actions. Another much
stronger argument, not ATS-related butfurther degrading the
situation, lies in the fact that the TCDQ gap is actually severely
constraintfor the LIU beam [27], to be larger than 3.6 mm (in the
best case), and up to 4.6 mm, taking intoaccount possible alignment
errors (0.3 mm), effects from the dispersion (0.4 mm), and 0.9
mmfor the threshold before dump for uncontrolled orbit movements at
the TCDQ (taking the 2018updated value for this critical setting).
This in turns imposes to the horizontal β-function to behigher than
a certain value at the TCDQ, for a given TCDQ gap (normalized
and/or in mm), and agiven beam energy:
β(TCDQ)x ≥ 515 m×(
7.3
n(TCDQ)[σ]
)2×(E [TeV]
7.0
)×(
Min. Gap [mm]3.6
)2. (18)
Considering first a minimum allowed TCDQ gap of 3.6 mm (actually
corresponding to the endof the ramp TCDQ setting for Beam 2 in
2018), and superimposing the above criteria on top ofFig. 18(a),
the present normalised TCDQ settings of 7.3σ could a priori be kept
up to 7 TeV, and forround telescopic optics with an index of up to
∼ 3. On the other hand, as shown in Fig. 18(b), thissetting would
not be valid for Beam 2, assuming flat IR5 optics with H×V
telescopic indexes of4×1, therefore preventing a priori the
operability of the machine with the (15/60) and (15/50)
opticsconfigurations. Also, further tightening the collimation
hierarchy in order to continue to maximizethe β∗ reach, e.g. with
the TCSG/TCDQ settings adjusted to 6σ/6.8σ instead of
6.5σ/7.3σpresently (see the “option 2018b” reported in [16]), the
515 m limit of above would have to bereplaced by ∼ 600 m at 7 TeV
beam energy. As shown in Fig. 18, such requirement would bestrictly
incompatible with the Beam 2 IR6 optics, regardless of the optics
configuration, round orflat, and of the telescopic indexes.
Finally, imposing 4.6 mm for the minimum gap of the TCDQat full
intensity (full LIU beam), and no telescopic index yet, which would
make the situationeven worst for Beam 2, the corresponding
normalised TCDQ gap would have to be relaxed tonearly 7.3 × 4.6/3.6
= 9.3σ instead of 7.3σ, therefore imposing an additional aperture
marginof 2σ in the inner triplet, which actually does no longer
exist at the end of the telescopic squeeze.The TCDQ gap limit is
however a function of the beam intensity, clearly still to be
preciselydetermined, but which, in principle, could be relaxed in
stable beam with the proton burn-off. Inorder to eliminate any
impact of this constraint on the β∗ reach (and assuming
β∗-levelling), oneof the last two options previously mentioned is
therefore highly recommended, i.e. moving theTCDQ or moving the
beam as a function of β∗, and then within certain limits allowed by
theactual beam current. On the other hand, even in this favorable
scenario, the demand of relaxing thepresent (2018) collimation
hierarchy by 2σ, at all stages above the TCDQ (i.e. TCDQ, TCT
andinner triplet), would still hold at the end of the ramp and
beginning of stable beam, i.e. when thebeam intensity would still
be above a certain threshold (still to be determined). A net
preference
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(Round telescopic squeeze)
(Flat telescopic squeeze)
Figure 19: Current [A] requested at 7 TeV in Q5.L6b1 (solid
lines) and Q4.L6b2 (dashed lines),as a function of the telescopic
index product rTeleX × rTele|| , for a typical round (top) and
specificflat (bottom) telescopic squeeze (see also the caption of
Fig. 17 for a more detailed description ofthese two squeeze
sequences).
33
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goes for the second option (moving the beam), which seems
intuitively easier to implement, andmore flexible in order to vary
the effective TCDQ gap in arbitrary direction during the
β∗-levellingprocess, therefore eliminating, a priori, any risk of
reproducibility.
3.3 Octupole polarity and Landau damping managementThe highest
level of complexity is reached in this section, when trying to
combine the demandsof Landau damping (basically requesting the
highest possible tune spread), with the long-rangebeam-beam
