CHAPTER 21
THE LHC AS A LEAD ION COLLIDER
21.1 INTRODUCTION
Heavy ion collisions were included in the conceptual design of the LHC from an early stage and collisions
between beams of fully stripped lead ( 208 Pb82+ ) ions are scheduled for one year after the start-up of the collider
with protons. With the nominal magnetic field of 8.33 T in the dipole magnets, these ions will have a beam
energy of 2.76 TeV/nucleon, yielding a total centre-of-mass energy of 1.15 PeV and a nominal luminosity of
1.0 × 1027 cm−2 s−1 . Collisions between ion beams will be provided principally at IP2 for the specialised ALICE detector. However the CMS and ATLAS detectors also plan to study ion collisions with similar luminosity.
While the major hardware systems of the LHC ring appear compatible with heavy ion operation, the beam
dynamics and performance limits with ion beams are quite different from those of protons in a number of respects. The LHC also enters new territory where, for example, the copious nuclear electromagnetic interactions
in peripheral collisions of the ions can directly limit luminosity and beam lifetime. While these phenomena are
present in RHIC, for example, they are not straightforward to observe and do not limit performance. Yet they
become critical in the LHC because of the combination of its unprecedented energy and magnet technology.
At the time of writing, it is premature to make firm predictions about some of the factors that may limit the
performance of the LHC with ions. In particular, there are substantial uncertainties concerning some vacuum
issues and the ion beam parameters during ramping. Some effects limiting the luminosity appear more serious
now than in earlier discussions although means to alleviate them are under study.
Starting with the first acceleration of ions in the CERN Proton Synchrotron (CPS) in 1976, CERN has
built up a wealth of experience in creating and accelerating ion beams. Recent years have seen the successful
exploitation of lead and indium ion beams for fixed target experiments at the SPS. The creation, acceleration and
injection of ion beams for the LHC, including the new LEIR accumulator ring, are founded in this experience.
The ion injectors are covered in Part 4 of Volume III of this report. The present chapter will describe ion beams
in the LHC main ring itself.
21.2 PARAMETERS OF THE LHC WITH LEAD IONS
Some aspects of ion beams are similar to the proton beams. For example, the nominal emittance of the
ions has been chosen so that the ion beams have the same geometric size as the nominal proton beams (at
beam energies corresponding to the same magnetic field in the dipole magnets). Then at least the most basic
considerations of beam size and aperture will be the same as for protons, implying that this is a safe operational
value. Despite this, the physics of ion beams is qualitatively and quantitatively different from that of protons
and the values of some parameters are necessarily very different.
There are two reference sets of parameters for lead ion beams:
Nominal Ion Scheme: A peak luminosity of around 10 27 cm−2 s−1 has been the overall performance goal for
lead ions for some time [1, 2, 3, 4]. Yet there are several phenomena specific to heavy ions that may
turn out to be serious impediments to reaching this level of luminosity. The most important ones will be
discussed in Sec. 21.4 and Sec. 21.5 below. The main parameters of the beams at injection and collision
energies are given in Tab. 21.1.
Early Ion Scheme: The first period of operation of the LHC as a lead-lead collider, running-in and early
physics, will be carried out with identical single bunch parameters but ten times fewer bunches and a
larger value of β ∗ . These relaxed parameters will provide more margin against some of the performance
limits discussed in Sec. 21.5 and Sec. 21.4, namely those that depend on the total beam current. The
reduced luminosity will nevertheless give access to important physics. Parameters at collision energy are
given in Tab. 21.2.
The reasons for the values given will be discussed in the following sections.
Table 21.1: LHC beam parameters bearing upon the peak luminosity in the nominal ion scheme.
Injection
Collision
Beam parameters
Lead ion energy
[GeV]
36900
574000
Lead ion energy/nucleon
[GeV]
177.4
2759.
Relativistic “gamma” factor
190.5
2963.5
Number of ions per bunch
7. × 107
Number of bunches
592
Transverse normalised emittance
[µm]
1.4 a
1.5
Peak RF voltage (400 MHz system)
[MV]
8
16
Synchrotron frequency
[Hz]
63.7
23.0
RF bucket half-height
1.04 × 10−3
3.56 × 10−4
Longitudinal emittance (4σ)
[eV s/charge]
0.7
2.5 b
RF bucket filling factor
0.472
0.316
RMS bunch lengthc
[cm]
9.97
7.94
Circulating beam current
[mA]
6.12
Stored energy per beam
[MJ]
0.245
3.81
∗
Twiss function βx = βy = β at IP2
[m]
10.0
0.5
RMS beam size at IP2
µm
280.6
15.9
Geometric luminosity reduction factor F d
1
Peak luminosity at IP2
[cm−2 sec−1 ]
1. × 1027
a
The emittance at injection energy refers to the emittance delivered to the LHC by the SPS without any increase due to injection
errors and optical mismatch.
b
The baseline operation assumes that the longitudinal emittance is deliberately blown up during, or before, the ramp in order to
reduce the intra-beam scattering growth rates.
c
Dimensions are given for Gaussian distributions. The real beam will not have a Gaussian distribution but more realistic distributions
do not allow analytic estimates for the IBS growth rates.
d
The geometric luminosity reduction factor Equation 3.3 depends on the total crossing angle at the IP. The crossing angle for lead
ions is discussed in Sec. 21.3.2
Table 21.2: LHC beam parameters bearing upon the peak luminosity in the early ion scheme. Only those
parameters that differ from those in the nominal ion scheme, given in Tab. 21.1 are given.
Injection
Collision
Beam parameters
Number of bunches
Circulating beam current
Stored energy per beam
Twiss function βx = βy = β ∗ at IP2
RMS beam size at IP2 e
Peak luminosity at IP2
[mA]
[MJ]
[m]
[µm]
[cm−2 sec−1 ]
62
0.641
0.0248
10.0
280.6
-
0.386
1.0
22.5
5.4 × 1025
Table 21.3: LHC beam parameters bearing upon the beam or luminosity lifetime in the nominal ion scheme.
Interaction data
Total cross section
[mb]
a
Beam current lifetime (due to beam-beam)
[h]
Intra Beam Scattering
RMS beam size in arc
[mm]
RMS energy spread δE/E0
[10−4 ]
RMS bunch length
[cm]
Longitudinal emittance growth time
[hour]
Horizontal emittance growth timeb
[hour]
Synchrotron Radiation
Power loss per ion
[W]
Power loss per metre in main bends
[Wm −1 ]
Synchrotron radiation power per ring
[W]
Energy loss per ion per turn
[eV]
Critical photon energy
[eV]
Longitudinal emittance damping time
[hour]
Transverse emittance damping time
[hour]
c
Variation of longitudinal damping partition number
Initial beam and luminosity lifetimes
Beam current lifetime (due to residual gas scattering) d
[hour]
Beam current lifetime (beam-beam, residual gas)
[hour]
Luminosity lifetimee
[hour]
Injection
Collision
-
514000
11.2
1.19
3.9
9.97
3
6.5
0.3
1.10
7.94
7.7
13
3.5 × 10−14
8 × 10−8
1.4 × 10 −3
19.2
7.3 × 10 −4
23749
47498
230
2.0 × 10−9
0.005
83.9
1.12 × 10 6
2.77
6.3
12.6
230
?
-
?
< 11.2
< 5.6
a
Each “lifetime” in this table is the instantaneous time-constant for the decay of a quantity when the beam current and emittances
have their nominal values; it is not a direct indication of the length of a fill. It is assumed that two experiments receive the nominal
luminosity.
b
An IBS growth time for the vertical emittance is not quoted since the direct effect of IBS in this plane is very small.
c
This is the derivative dJ /dδ where δ = −1/αc ∆fRF /fRF is the fractional momentum difference of the closed orbit with respect
to the one for which the closed orbit passes through the centres of the magnet apertures.
d
Currently under review.
e
Including the effects of beam-beam, radiation damping and IBS; no accounting for residual gas.
Table 21.4: LHC beam parameters bearing upon the beam or luminosity lifetime in the early ion scheme. Only
those parameters which differ from those in the nominal ion scheme, given in Tab. 21.3 are given.
Injection
Collision
-
21.8
8.5 × 10−9
1.5 × 10 −4
5.0 × 10−4
8.8
-
< 21.8
< 11.2
Interaction data
Beam current lifetime (due to
beam-beam) a
[h]
Synchrotron Radiation
Power loss per metre in main bends
[Wm −1 ]
Synchrotron radiation power per ring
[W]
Initial beam and luminosity lifetimes
Beam current lifetime (beam-beam, residual gas)
[hour]
Luminosity lifetime (as in Tab. 21.3)
[hour]
a
Assuming that two experiments receive the nominal luminosity.
βy
Dx
2.5
4000.
2.0
3500.
5000.
4500.
1.0
2500.
2000.
0.5
2000.
-0.5
0.0
2700.
3000.
3300.
3600.
-1.0
3900.
2.2
1.8
2500.
500.
2.5
Dx
3500.
3000.
0.0
βy
2.0
1.5
1000.
βx
4000.
3000.
1500.
LHCB2 Ion Collision
1.5
1.2
1.0
0.8
1500.
0.5
1000.
0.2
500.
0.0
0.0
2700.
Dx (m)
4500.
βx
3.0
βx (m), βy (m)
LHCB1 Ion Collision
Dx (m)
βx (m), βy (m)
5000.
3000.
3300.
s (m)
3600.
-0.2
3900.
s (m)
Figure 21.1: Collision optics in IR2 for lead ions with β ∗ = 0.5 m, showing Beam 1 (left) and Beam 2 (right).
As usual, the azimuthal coordinate s is given relative to IP1.
21.3 ORBITS AND OPTICAL CONFIGURATIONS FOR HEAVY IONS
21.3.1 Optical functions
As in Chap. 4, the optical configuration described in this section is the LHC Version 6.4, including the
repositioning of the Q3 triplet magnets, which is part of Version 6.5.
The optics in IR2, for head-on collisions of ion beams in the ALICE detector, will be quite different from that
used for protons (see Chap. 4) in which β ∗ = 10 m and beams are collided with an offset. For ions, collisions
will be head-on with β ∗ values down to β ∗ = 0.5 m. Moreover, since this value is somewhat smaller than
the limit of β ∗ = 0.55 m for high-luminosity p-p collisions at IP1 or IP5, the peak values of β x and βy in the
insertion quadrupoles will be higher in the ion collision optics. The lower value of β ∗ is possible with ions
because the separation bumps are smaller (see the following section), leaving more aperture for the peaks in the
β-functions.
For ion collisions in either IP1 or IP5 the optics can be the same as for protons (see Chap. 4) or may be
adjusted to β ∗ = 0.5 m as in IP2. Otherwise, the pre-collision optics can be maintained in any IP in which
the beams do not collide. Thanks to the modularity and independence of the optics in the various interaction
regions, it is in principle straightforward to adapt the optics of the LHC to any set of collision points. However it
should be remembered that switching between the various possible configurations may require some operational
time in order to establish the appropriate corrections. In particular, each configuration will contribute differently
to the horizontal and vertical dispersions around the ring.
21.3.2 Beam Separation near the Interaction Points
Compared with the nominal proton beams, the relatively low intensities and larger bunch spacing of the
lead ion beams lead to weak beam-beam effects which do not, in themselves, impose any minimum separation
around the interaction points. If these were the only considerations, it might be possible to eliminate the crossing angle entirely. However this would create additional head-on beam-beam encounters, reducing the beam
lifetime. Moreover the ALICE detector has a spectrometer magnet compensated by its own orbit separation
bump around IP2 Sec. 4.2.3. The total separation will be the superposition of this bump and the “external”
crossing angle and parallel separation bumps. At the interaction point, the full crossing angle is given by
[θc /µrad] ' 140fALICE − 340fIP2bump
(21.1)
0.01
0.005
0.005
ycm
ycm
0.01
0
sm
-0.005
0
sm
-0.005
3100
3200
3300
3400
3500
fIP2bump= 17%, fALICE= 100%, Θc= 82.2 Μrad
3600
3100
3200
3300
3400
fIP2bump= -65%, fALICE= -100%, Θc=
3500
81. Μrad
3600
0.01
ycm
0.005
0
sm
-0.005
3100
3200
3300
3400
3500
fIP2bump= 42%, fALICE= 100%, Θc= -2.8 Μrad
3600
Figure 21.2: Separation of lead ion beams around IP2 for positive and negative polarities of the ALICE compensation bump in an ion collision optics with β ∗ = 0.5 m. The vertical closed-orbit distortion of Beam 1 is
represented by the solid line and that of Beam 2 by the dashed line. In the first two cases, the amplitude of the
external bump is chosen to provide a crossing angle of about 80 µrad at IP2. As usual, the azimuthal coordinate s is given relative to IP1. In the first case, the ALICE bump and the external separation bump generate
contributions to the crossing angle of equal sign at the IP; in the second they are opposite, leading to larger
separations outside the ALICE bump. In the third case, the bumps are chosen to cancel at the IP, resulting in
zero crossing angle.
where fALICE and fIP2bump are amplitude factors for the bumps (normalised so that θ c = −200 µrad for
fALICE = fIP2bump = 100%. The collisions at additional encounters would also interfere with the trigger
for ALICE. It is desirable to use the minimum separation needed to avoid these problems because, with the full
separation used for protons, the criteria for minimum aperture Sec. 4.3 are violated. Further discussion of the
separation scheme in IR2 can be found in Sec. 4.2.3.
Since the ion collision optics in IR2 has higher maximum values of β x and βy in the insertion quadrupoles,
the need to observe the minimum physical aperture criteria is another strong reason for reducing the separation
bump amplitudes in the collision optics.
Pending final optimisation, some illustrative configurations of the separation bumps around IP2 are shown
in Fig. 21.2. The first two arrangements are chosen to provide a similar crossing angle at IP2 but differ in
the relative polarities of the external separation bump and the ALICE compensation bump. In the second
configuration, where the two bumps cancel each other to a large extent close to the IP, a greater separation, of
about 7σy at the first beam-beam encounter (which lies outside the ALICE bump in the nominal ion scheme)
is achieved; this could be considered a very safe configuration for the nominal ion scheme where unwanted
collisions should be avoided for reasons of beam lifetime and experimental background and triggering. The
first configuration gives a minimum separation of about 2.6σ y which is marginal.
In the third configuration, the two bumps have been combined in such a way as to achieve an almost zero
crossing angle. This arrangement is of particular interest for ion collisions. According to Equation 3.3, reducing
the crossing angle to the minimum possible provides some gain in luminosity. Reducing the bump amplitudes
also tends to reduce the vertical dispersion around the ring. In this configuration, the separation at the first
parasitic encounter is 2.5σy on both sides. It is probably close to the optimum for the early ion scheme but may
be marginal for the nominal ion scheme, in which case the crossing angle could be increased to 20 µrad to give
a minimum separation of 3σy at the closest encounter.
The only obvious advantage of a scheme of the first type is the reduction of parasitic vertical dispersion
created by the smaller overall amplitude of the bump.
The mechanical acceptance of IR2 in each of these separation configurations is shown in Fig. 21.3. Each of
them meets the requirements specified in Chap. 4. It should be noted that a bump amplitude similar to that used
in the nominal collision scheme for protons would not meet the requirements with β ∗ = 0.5 m.
In principle, the overall polarity of each case shown in Fig. 21.2 could also be reversed. However the polarities shown are those most easily accessible by continuous variation from the injection conditions described
in Chap. 4.
For collisions of ion beams in IP1 or IP5, the optics may be the same as for protons but the crossing-angles
can be reduced, possibly to zero in the early ion scheme.
During injection and ramping, the requirements for the separation of ion beams at the IPs appear even less
demanding. The final choice of separations in these conditions is still to be made but is likely to be determined
mostly by operational considerations. If, for example, there are well-established corrections of the injection
and ramp for protons then it may be most straightforward to simply adopt the same scheme for ions, differing
only in the final steps to the collision configuration. The examples given in this section were intended to show
that the separation schemes have sufficient flexibility to accommodate the requirements of heavy ion operation.
21.3.3 Longitudinal dynamics
Nominal longitudinal parameters for lead ions at injection and collision energies are given in Tab. 21.1. The
relatively small injected longitudinal emittance of l = 0.7 eV s/charge is necessary for efficient injection as
long as the 200 MHz capture system (discussed in the Introduction to Chap. 6) is not installed. All parameters
given in this chapter assume these conditions. Because of mismatch and nonlinearities there will likely be some
filamentation to a slightly larger value after injection. In these conditions the bunches occupy about half the
RF bucket area. The relatively short growth times for the longitudinal emittance with nominal intensity (see
Fig. 21.6) imply that, if the bunches have to be kept for some time at injection for any reason, their longitudinal
emittance will increase further. At some point, ions may start to spill out of the RF bucket but, since beamloading is very small with the currents in the ion beams, a reserve of 50 % or the total RF voltage is available to
counter this. Controlled blow up to l = 2.5 eV s/charge is in any case necessary during the ramp to collision
energy to reduce the growth of the transverse emittances from intra-beam scattering.
21.4 EFFECTS OF NUCLEAR INTERACTIONS ON THE LHC AND ITS BEAMS
When ultra-relativistic lead ions collide at LHC energies numerous processes of fragmentation and particle
production can occur. Some of these have direct consequences as performance limits for the collider.
Besides the hadronic nuclear interactions due to direct nuclear overlap,
208 Pb82+
nuclear
+ 208 Pb82+ −→ X
(21.2)
for which the cross section is
σH ' 8 barn
(21.3)
there is an important class of longer-range, or peripheral, collisions dominated by electromagnetic interactions.
In collisions of light ions, the cross sections for these processes are small (some are zero in the case of protons)
compared with σH . For heavy ions (with Z >
∼ 30), and Pb in particular, the cross sections for these electromagnetic interactions are much larger than σ H . While simple elastic (Rutherford) scattering and free e + e− pair
production are of little consequence, other processes change the charge state or mass of one of the colliding
ions, creating a secondary beam emerging from the collision point. For a change, ∆Q, in the charge, Q, and
20
20
LHCB1case1.tfs_n1(s)
layout schem
spec=7
6.5
n1
15
n1
15
10
10
5
0
2800
LHCB2case1.tfs_n1(s)
layout schem
spec=7
6.5
5
3000
3200
3400
3600
0
2800
3800
3000
3200
3400
3600
s
20
20
LHCB1case2.tfs_n1(s)
layout schem
spec=7
6.5
LHCB2case2.tfs_n1(s)
layout schem
spec=7
6.5
n1
15
n1
15
10
10
5
0
2800
5
3000
3200
3400
3600
0
2800
3800
3000
3200
3400
3600
s
20
3800
s
20
LHCB1case3.tfs_n1(s)
layout schem
spec=7
6.5
LHCB2case3.tfs_n1(s)
layout schem
spec=7
6.5
n1
15
n1
15
10
10
5
0
2800
3800
s
5
3000
3200
3400
3600
3800
s
0
2800
3000
3200
3400
3600
3800
s
Figure 21.3: Mechanical acceptance in IR2, expressed in terms of the primary aperture quantity n 1 , as defined
in Chap. 4 at 2.75 TeV/nucleon and β ∗ = 0.5 m (ion collision optics with parallel separation switched on),
showing Beam 1 (left) and Beam 2 (right) for each of the three separation configurations shown in Fig. 21.2.
As usual, the azimuthal coordinate s is given relative to IP1.
∆A in the number of nucleons, A, the magnetic rigidity of the secondary beam corresponds to an effective
fractional momentum deviation given approximately 1 by
δ(∆Q, ∆A) '
1 + ∆A/A
− 1.
1 + ∆Q/Q
(21.4)
This parametrisation in terms of δ(∆Q, ∆A) will be used in the following sections and also in the discussion
of collimation for ions where similar processes occur in collimator materials.
Recent reviews of the nuclear physics and the calculations of cross sections can be found in [7, 8, 9].
All contributions to the total cross section for ion collisions will of course contribute to the total loss rate and
resulting beam lifetime. However certain processes have consequences beyond this.
Electron capture from pair production (ECPP)
In this process, an e+ e− pair is produced but the electron is captured by one of the nuclei
208 Pb82+
γ
+ 208 Pb82+ −→ 208 Pb82+ + 208 Pb81+ + e+
(21.5)
The seriousness of this effect hinges on the knowledge of the cross section and many papers have been devoted to its calculation and measurement; some recent references are [10, 11]. Most authors are now in close
agreement (the differences with some earlier calculations being understood). The present estimates are based
on values from the theoretical calculations in [11] including the sum over final ion-electron bound states as
detailed in [12] giving
σECPP ' 281 barn.
(21.6)
Note that the variation of these cross sections with energy is rather weak, of the form σ ECPP ' A log γ + B so
reducing the beam energy would have little impact on the rate of production of these ions.
According to (Eq. 21.4), the effective momentum deviation of the secondary beam emerging from the collision point is δ(−1, 0) ' 0.012, a value well outside the momentum acceptance of the ring. The secondary beam
strikes the beam screen inside one of the cryo-magnets of the downstream dispersion suppressor as illustrated
in Fig. 21.4. This occurs on each side of every IP where ions collide.
Earlier estimates of the consequences of this effect [13, 14, 15, 12, 16] were based on simplified models
using the linear optical functions. However the strong chromatic effects of the insertion quadrupoles modify
the size of the secondary beam considerably: the beam size “beats” with respect to the size of the main beam.
In more recent studies with new software for localisation of beam losses [17], the ions are tracked in the
full optics model to the entrance of the magnet. Inside the magnet, a detailed 3D tracking algorithm has been
implemented to localise the impact points of particles on the beam screen. A typical result is shown in Fig. 21.5.
Unfortunately, in this case, the secondary beam is somewhat smaller than the main beam at the impact point in
the dipole magnet MB.B10R2.B1, resulting in a more concentrated deposition of ion beam energy in the beam
screen. The longitudinal RMS spot size is 0.5 m whereas an estimate based on linear optics gives 0.7 m.
The energy deposition will take place over a length corresponding to this distribution, convoluted with the
shower length. Pending the results of further study including a proper model of the ion fragmentation, this
is estimated to be about 1 m [15], resulting in an effective ( 2σ ) length l eff ' 1.4 m for the energy density
distribution.
Heating of the beam screen may induce a quench of the superconducting magnet. The quench limit for lead
ions at 2.75 TeV/nucleon can be inferred [18] from that of protons at the same energy, 2.75 TeV, by dividing by
the mass number
fq (Pb) '
1
1.7 × 107 p/m/s
' 8 × 104 Pb/m/s.
A
(21.7)
This assumes that the momentum per nucleon of all final state components—for example, emitted neutrons—in the laboratory
frame remains close to its value in the initial state. It is easy to see that the approximation is good for the electron capture process
considered in Sec. 21.4. Detailed calculations [5, 6] show that this holds, in an average sense, to a fairly good approximation in the
electromagnetic dissociation processes considered in Sec. 21.4.
400
sm
300
200
100
0
0.02
xm
0
-0.01
0
-0.02
-0.03
-0.02
ym
Figure 21.4: Beam screen, seen cut away from above and 5σ envelopes of the main Beam 1 ( 208 Pb82+ ) and
secondary beam ( 208 Pb81+ , shown with a darker surface) created from it by the ECPP process. The coordinate
system is the usual beam dynamics system for Beam 1 in which s is the azimuthal coordinate along the
reference orbit x = y = 0 except that, in this plot, s is given relative to IP2. Both beams travel from left to
right in this image. Moving away from the interaction point, the two beams develop very different orbits in
both planes because of the dispersive effects of the bending magnets. They also develop very different sizes
because of the chromatic effects of the quadrupoles. Close to its point of impact in the dispersion suppressor,
the 208 Pb81+ beam has a much larger beam size in the vertical plane but is narrower in the horizontal plane,
increasing the longitudinal density of the ion flux on the beam screen. The image also illustrates that it is not
easy to find a place where the two beams are sufficiently separated for the 208 Pb81+ beam to be effectively
stopped or collimated.
Assuming the nominal luminosity, L = 10 27 cm−2 s−1 , the flux of lead ions from the ECPP process is then
f (Pb) =
LσECPP
= 2 × 105 Pb/m/s >
∼ 2fq (Pb),
leff
(21.8)
i.e., at the nominal luminosity the heating due to this flux of ions on the beam screen is about twice the quench
limit. While the quench limit figure certainly contains some reserve, this is currently understood as the most
serious limit on luminosity with lead ions.
Measures to reduce this effect are under study. These may work either by intercepting a fraction of the
208 Pb81+ ions before they strike the beam screen or by spreading out the spot size when they do. One way to
spread out the secondary beam spot might be to adjust the chromatic effects of the insertion optics. However
this is not easy since no sextupolar correction is available in the relevant region. Other possibilities may include
special collimators or stripping foils in places where the main and secondary ion beams are sufficiently separated by dispersion in the horizontal or vertical plane. The feasibility of such schemes in a given IR is closely
linked to the separation schemes used, not only in that IR but in all the others and requires further detailed
study.
Calculations of ion fragmentation and the resulting heat deposition in the environment of the beam screen
and cold mass are planned.
x m
x/m
-0.02
-0.01
0.01
0
0.01
0.02
0.8
0.6
0.4
0.2
0.01
9.5
y/m
10
10.5
11
11.5
12
0
3700
y m
-0.01
s/m
3705
s m
3710
Figure 21.5: Image of the 208 Pb81+ beam spot on the beam screen, just above the median plane of the ring, seen
from the outside. The wire-frame image represents the beam screen inside the dipole magnet MB.B10R2.B1
to the right of IP2. The embedded histogram of the longitudinal density of ion flux on the screen (in which the
longitudinal coordinate is the distance from the entrance face of the magnet) shows that the beam spot has an
RMS length of 0.5 m. The coordinate system is the usual beam dynamics system for Beam 1 in which s is the
azimuth along the reference orbit x = y = 0. As usual, the azimuthal coordinate s is given relative to IP1.
It has been shown [9, 12] that the rate of Lorentz stripping of the 208 Pb81+ ions back to the fully stripped
state in the magnetic fields of the LHC is utterly negligible.
Although the present estimate of the effects of ECPP gives serious cause for concern, it must be emphasised
that there are uncertainties and safety margins still in hand, together with reasonable hope for effective cures.
Therefore the nominal luminosity of 1.0 × 10 27 cm−2 s−1 has been maintained as a design goal pending the
results of further studies.
Electromagnetic dissociation (EMD)
Electromagnetic dissociation processes can be thought of as proceeding in two stages. First, one of the lead
ions makes a transition to an excited nuclear state that then decays with the emission of a neutron, leaving a
lighter isotope of lead. The dominant process of this sort in lead-ion collisions at the LHC is
208 Pb82+
γ
+ 208 Pb82+ −→ 208 Pb82+ +
208 Pb82+ ∗
↓
207 Pb82+
(21.9)
+ n.
According to calculations using the RELDIS program [5, 6], at the LHC lead beam energy, the cross section for
this process is 104 barn out of a total cross section for all electromagnetic dissociation processes of σ EMD '
226 barn.
Similar basic processes are important both in the heat deposition and secondary scattering processes that
occur whenever ions strike the beam-screen or collimators (see the discussion of the ECPP process above and
Sec. 21.7).
According to (Eq. 21.4), the process described in (Eq. 21.9) results in a negative effective momentum deviation δ(0, −1) ' −0.0048. This places the resulting 207 Pb82+ ion in the band of momenta that should be
intercepted by the collimation system (the RELDIS results also show that these ions have a spread in momentum
around this value that will tend to increase the longitudinal spread of any heat loss.)
The next most important electromagnetic dissociation process is the production of a secondary beam of
206 Pb82+ with δ(0, −2) ' −0.0097 with about 20% of the intensity of the 207 Pb82+ beam. This is outside
TIBSh
TIBSh
14
14
12
12
Txh
10
10
8
8
6
6
Tlh
4
Txh
Tlh
4
2
2
¶leV.s
0.25
0.5
0.75
1
1.25
1.5
¶leV.s
1
2
3
4
Figure 21.6: Emittance growth times from intra-beam scattering as a function of longitudinal emittance for
at injection (left plot) and collision (right plot) energies. The transverse emittances and beam intensities are taken to have their nominal values and the total circumferential voltage from the 400 MHz RF system
are VRF = 8 MV and VRF = 16 MV respectively. Solid and dashed lines correspond to the growth times for
horizontal and longitudinal emittances.
208 Pb82+
the momentum acceptance of the ring and will result in a beam spot longer than that shown in Fig. 21.5, at
a location further downstream but on the inside wall of the beam screen. This secondary beam is unlikely to
quench a magnet.
The rates of transmutation of the lead ions to isotopes of lighter elements are very small compared with the
processes in which the lead ion emits one or two neutrons.
Detailed studies to localise the losses of these ions and evaluate their effects are under way and will be
pursued with high priority.
21.5 LUMINOSITY AND BEAM LIFETIME
21.5.1 Intra-beam Scattering
Multiple Coulomb scattering within an ion bunch, known as intra-beam scattering (IBS), is a diffusive process that modifies all three beam emittances. Already significant for protons in the LHC (see Chap. 5), it is
even stronger for lead ion beams of nominal intensity and determines the acceptable longitudinal emittance,
particularly at injection from the SPS.
The values of the IBS growth times given in Tab. 21.1 refer to the initial bunch parameters and nominal
intensity. As the emittances increase, the growth rates will diminish. Fig. 21.6 shows how they depend on
longitudinal emittance.
The calculations of emittance growth times from IBS were done with the theory of [19] as implemented in
the program MAD [20].
21.5.2 Synchrotron Radiation from Lead Ions
The LHC is not only the first proton storage ring in which synchrotron radiation plays a noticeable role
(mainly as a heat load on the cryogenic system, see Sec. 5.6) but also the first heavy ion storage ring in which
synchrotron radiation has significant effects on beam dynamics. Surprisingly, perhaps, some of these effects
are stronger for lead ions than for protons.
Quantities such as the energy loss per turn from synchrotron radiation and the radiation damping time for
ions are obtained from the familiar formulas for electrons by replacing the classical electron radius and the mass
by those of the ions2 . The principal characteristics of the incoherent synchrotron radiation of fully stripped ions
of atomic number Z and mass number A can be related to those of protons (assuming the same field in the
2
The nuclear radius being much smaller than relevant wavelengths, the nucleus radiates coherently, like a single charge Ze
bending magnets) by
Z6
Uion
' 4 ' 162,
Up
A
ucion
Z3
'
' 0.061,
ucp
A3
(21.10)
Nion
Z3
'
' 2651,
Np
A
τion
A4
' 5 ' 0.5
τp
Z
(21.11)
where U is the energy lost per ion per turn by synchrotron radiation, u c is the critical energy of the synchrotron
radiation photons, N is the number of photons emitted per turn and τ is a synchrotron radiation damping time;
the numerical values are given for the case of 208 Pb82+ . The critical energy of the radiation from lead ions at
collision energy falls in the visible spectrum. Precise values of these quantities are given in Tab. 21.3.
It is notable that radiation damping for heavy ions like lead is about twice as fast as for protons and that the
emittance damping times are comparable with the growth times from intra-beam scattering 3 . Since emittance
growth due to the quantum fluctuations of the synchrotron radiation is negligible, shrinking transverse emittances are a real possibility below some intensity level. In addition there appears to be some scope for varying
damping partition numbers with momentum (see Tab. 21.3) to switch some damping from the longitudinal to
the horizontal plane; this comes at the price of a displaced central orbit. It should be remembered that, even
when radiation damping overcomes intra-beam scattering, noise in the RF system will ultimately determine the
minimum longitudinal emittance; the level at which this occurs remains to be quantified.
21.5.3 Beam loss from collisions
The total cross section for removal of an ion from the beam is
σT = σH + σEMD + σECPP ' 514 barn
(21.12)
As discussed in Sec. 21.4, nuclear electromagnetic processes dominate the beam loss rate, leading to a nonexponential decay during a fill. The initial beam (intensity) lifetime due to beam-beam interactions in the
nominal ion scheme with beams colliding at n exp interaction points:
τN L
22.4 hour
kb Nb
=
=
nexp LσT
nexp
1027 cm−2 s−1
L
(21.13)
If this intensity loss were the sole mechanism involved
in
√
the evolution of the luminosity, the initial luminosity
half-life (sometimes quoted) would be τ L/2 =
2 − 1 τN L .
Given that the intensity decays and the emittance evolves under the influence of radiation damping, IBS and
other effects, the formula for luminosity
L=
kb Nb2 f0
kb Nb2 f0
γ
=
4πβ ∗ n
4πσ ∗2
(21.14)
suggests that the rapid initial decay of the intensity could be offset by varying β ∗ ∝ Nb2 /n in the course of a
fill. This so-called “β ∗ -tuning” would be very valuable during collision to maximise integrated luminosity—
especially if there turns out to be some scope for increasing the initial value of N b , whose value is limited at
injection into the SPS (see Vol. III of this report). A higher initial value of β ∗ would also push up the margin for
the ECPP quench limit—should this prove necessary—providing further grounds for interest in this capability.
However β ∗ -tuning is not expected to be a straightforward operational procedure in the LHC as the beams
will have a tendency to move apart by distances comparable with the beam size at the IP.
Note that the luminosity lifetimes quoted in (Eq. 21.13), Tab. 21.3 and Tab. 21.4 are those that apply at the
beginning of a fill with the full intensity and nominal transverse emittance. Fills with lower initial luminosity
will have much longer lifetime and the lifetime will increase in inverse proportion to luminosity as the fill goes
on.
3
Radiation damping of light ions can be up to 16 times slower (deuterons) than protons; equality occurs for Z ' 20.
Table 21.5: 208 Pb+ ion/matter interactions in comparison with proton/matter interactions. Values are for particle
impact on graphite.
p
injection
0.12 %/m
p
collision
0.0088 %/m
208 Pb+
208 Pb+
injection
9.57 %/m
collision
0.73 %/m
73.5 µrad/m1/2
4.72 µrad/m1/2
73.5 µrad/m1/2
4.72 µrad/m1/2
-
-
20 cm
312 cm
Electron stripping length
-
-
0.028 cm
0.018 cm
ECPP interaction length
-
-
24.5 cm
0.63 cm
38.1 cm
38.1 cm
2.5 cm
2.2 cm
-
-
33.0
19.0 cm
Physics process
Ionisation energy loss
dE
E dx
Multiple scattering
projected RMS angle
Electron capture length
Nuclear interaction length
(incl. fragmentation)
Electromagnetic dissociation
length
The evolution of the luminosity during a fill can be predicted and optimised straightforwardly by solving
the coupled differential equations for the beam currents and emittances, taking into account the luminosity
losses, emittance blow-up due to intra-beam scattering countered by radiation damping, β ∗ -tuning and any
other known loss mechanisms. Pending a full revision of these calculations, previous versions can be found in
[21, 4].
21.6 VACUUM
The study of vacuum phenomena specifically related to heavy ions is in an early stage. Unexpectedly high
levels of desorption of gas molecules by lost ions have recently been measured at lower energies [22, 23, 24,
25, 26] and have a potential impact on LHC vacuum conditions, particularly in view of the loss mechanisms
described in Sec. 21.4. Experiments and further study are planned.
For these reasons, estimates of the beam-gas lifetime from nuclear scattering and the emittance growth rates
from multiple Coulomb scattering are not given in Tab. 21.1.
Otherwise, thanks to the reduced intensity and larger bunch spacing and the much lower synchrotron radiation
power, there should be no electron cloud build-up as for protons. Desorption induced by residual gas molecules
ionised by the beam is expected to be very small.
21.7 COLLIMATION ISSUES FOR ION OPERATION
The purpose, specifications and design of the LHC collimation system are described in detail in Chapter 18
of this report; this section focuses on those system issues specific to operation with ions. Although the stored
energy of the nominal ion beam is only 1 % of that of the nominal proton beam (3.81 MJ for ions compared with
362 MJ for protons), some attention has to be paid to the ion collimation because of the different characteristics
of the beam-matter interactions. An overview of the main interaction mechanism of high energy ions in the
collimator material is given in Tab. 21.5. A discussion of the various processes can be found in [10]. The values
for nuclear interaction length and electromagnetic dissociation length are computed with the methods described
in [5, 27]
The nominal ion beam hitting a material surface (i.e., a collimator) produces a local heat deposition at the
surface comparable with the heat deposition caused by the nominal proton beam. This is due to the much higher
Graphite Protons 7 TeV/c/2 1012p
Max. Energy Deposition (GeV/cm3)
10
13
Graphite Protons 450
10
GeV/c/3.2 1013 p
12
Graphite Pb+ 2.76TeV/c/amu/1.4 108 Pb+
10
11
0
20
40
60
80
100
120
140
160
Length z [cm]
Figure 21.7: FLUKA results for energy deposition of protons and
of an erroneous trigger of a dump kicker module.
208 Pb82+
ions in the collimator jaws in case
ionisation energy loss of ions compared to protons. Once the ions have fragmented the resulting hadronic
shower behaves similarly for both particle species and the heat deposition is in proportion to the beam energies.
Fig. 21.7 shows this behaviour as a result of a FLUKA simulation for the case of an erratic firing of a dump
kicker module [28]. From this simulation it can be concluded that the heat deposition of the ions on the
collimators nowhere exceeds those of the protons.
Another concern is the local cleaning inefficiency of the collimation system η c as defined in Equation 18.3.
Because the stored beam energy of the ions is lower, η c can be relaxed from the proton value of 2 × 10 −5 m−1
to 2 × 10−3 m−1 for ions. However, as explained below it is presently not clear if even this relaxed value can
be achieved. The design philosophy of the collimation system is based on a two-stage system. In the first
stage, short primary collimators intercept halo particles and off-momentum particles and increase their betatron
amplitude by means of multiple scattering. In the second stage these particles are absorbed by long secondary
collimators. In comparison with single stage systems, this scheme has the advantages that the fraction of errant
particles escaping from the collimators to be subsequently lost elsewhere in the accelerator is very substantially
reduced and that the heat load on the collimators is distributed over a larger volume. However, in the present
system, which has been so far only optimised for proton operation, it is implicitly assumed that the main action
of the primary collimators on an intercepted particle is scattering, while energy loss has a comparably small
effect on the particle trajectories. This assumption is no longer valid for heavy ions, because:
1. The relative energy loss due to ionisation is two orders of magnitude larger.
2. Peripheral collisions with collimator nuclei lead to nucleon losses by hadronic fragmentation and electromagnetic dissociation. From a beam dynamics point of view these effects are analogous to a change of
longitudinal particle momentum according to (Eq. 21.4), while the related changes of trajectory angle are
usually small.
3. The average increase of trajectory angle due to multiple scattering is the same as for protons.
Thus, the collimation system tends to put ions on trajectories characterised by large momentum errors but
of moderate betatron amplitude increase. The secondary collimators, however, are designed to cut into the
betatron amplitude. In consequence the cleaning inefficiency is substantially greater for ions than for protons.
0
10
208
Pb
Pb
205
Pb
204
Pb
203
Tl
205
Tl
204
Tl
198
Hg
appearance probability
207
−1
10
−2
10
−3
10
0
2
4
6
penetration depth (cm)
8
10
Figure 21.8: The probability to convert a 208 Pb nucleus into a neighbouring nucleus as a function of penetration
depth. The calculation is performed for ion impact on graphite at LHC collision energy.
A study is underway to quantify ηc for the case of ion beams and to compute the expected particle losses
in the superconducting magnets for the scenarios considered in Chapter 18. An important ingredient for this
study is a quantitative estimate of the fragment distribution generated in the collimators. For this purpose the
cross sections for dissociation and fragmentation of 208 Pb ions and their products have been computed with
appropriate Monte-Carlo programs [5, 27]. The probability of appearance has been derived from the cross
section tables generated by these programs with a simple transport code. Results are shown in Fig. 21.8 for
some of the most probable fragments. Apparently the probability of losing a single neutron from the nucleus
is particularly high. This is due to the large cross section of electromagnetic dissociation for this process. The
change of magnetic rigidity for this dissociation process corresponds to δ(0, −1) ' −0.0048, which is of the
same magnitude as the LHC momentum aperture (approximately 0.6% for a pencil beam). The transverse
momentum transferred in this process is small (<30 MeV/c [6]) and in consequence the 207 Pb fragment has a
high probability of exiting from the primary collimator without being intercepted by the secondary collimator.
To determine the loss pattern and related heat loads for this kind of process, more detailed tracking studies need
to be performed.
21.8 OPERATION AND BEAM INSTRUMENTATION
From an operational point of view, the most striking difference between running the LHC with lead ions and
with protons is the much smaller beam current and stored energy. While this has obvious advantages—notably
the almost total absence of conventional collective and beam-beam effects—there are disadvantages related to
the dynamic range of the beam instrumentation (for the specifications, see Chap. 13).
21.8.1 Beam Position Monitors
In order to provide accurate readings, the arc beam position monitors in the LHC require a minimum charge
per bunch ' 2.0 × 109 e, equivalent to some Nb ' 2 × 107 Pb ions/bunch. Since the lowest range of beam
currents will occur in operation with lead ions, this mode of operation determines the specification of their
resolution.
However there is little more than a factor of 3 between the minimum bunch current for which the orbit can
be measured and the single-bunch intensity for full nominal performance, implying a very narrow gap between
“commissioning” and “design” conditions.
21.8.2 Beam Current Monitors
The LHC has two systems (see Chap. 13) for measuring the beam current:
• The ”BCTDC” measures total DC current in each beam and has a typical resolution of 10 µA on total
current
• The ”FBCT” measures individual bunch currents. Although there are presently uncertainties in extrapolating the performance of the system tested in a laboratory to operational conditions in the LHC tunnel, the
resolution hoped for is about 5% of the proton pilot bunch (9 µA). The examples given here are a factor 2
more conservative and assume 1 µA.
21.8.3 Motivation for Early Ion Scheme
With the full complement of 592 ion bunches of the minimum single-bunch current necessary to measure
orbits, commissioning would have to be done dangerously near the ECPP quench limit. These and other
reasons related to relaxing the performance requirements on the injector chain, are the motivation for the early
ion scheme mode of operation (see also Vol. III of this report) of the injectors, leading to about 10 times fewer
bunches in the LHC. This scheme is envisaged for use in an initial period of running with lead ions.
With this many bunches, Nb and β ∗ (and hence the beam lifetime) could have their nominal values but
the ECPP quench limit would be far away, the bunches would be visible on the BPMs, the injector scheme
would be simplified and some interesting heavy ion physics would be accessible with the reduced luminosity.
To simplify further the value of β ∗ is raised to 1 m to increase the beam lifetime and generally simplify the
operational conditions.
The initial performance parameters in the nominal ion scheme and early ion scheme are summarised in
Tab. 21.1 and Tab. 21.2.
Fig. 21.9 gives a global view of the luminosity as a function of single-bunch current in both the early ion
scheme and nominal ion scheme, with indications of the thresholds of visibility of the beams on the instruments.
The largest single bunch current in the lead ion beam for which the beam would be invisible on the BPMs is
about Ib ' 3.6 µA, corresponding to a stored energy of 1.3 MJ in the nominal ion scheme. This is much smaller
than the beam energy in proton beams and is very likely to be safe to keep in collision even without the ability
to measure the closed orbit.
It also provides a useful luminosity so one may well wish to continue colliding beams of this intensity. In
particular, it is easy to imagine situations where lead ion injection is not available and beams are kept in the
LHC for longer than they might otherwise be, allowing the experiments to take data. Such situations are most
likely to arise in early operation.
The expected resolution of the BCTDC (see Chap. 13), around 10 µA total beam current, is adequate for all
situations likely to arise with Pb ion beams. It reaches I b ' 0.02 µA for all Pb bunches evenly filled in the
nominal ion scheme or about Ib ' 0.2 µA in the early ion scheme. These values correspond to luminosity
around 1022 cm−2 s−1 , well below what would be useful for physics.
With the assumed resolution of the FBCT fast single-bunch monitor, around 1 µA in a single bunch, a beam
at the threshold of visibility may still yield a luminosity of 10 24 –1025 cm−2 s−1 . Although modest, these luminosities may be of interest in early running. Resolution at this level will also be useful for checking the
injection. It will be possible to verify the absence of unwanted “ghost” bunches only if they have sufficiently
high current. However such bunches—should they exist—are not expected to have very adverse effects in ion
operation.
It will be difficult to make useful lifetime measurements for individual ion bunches. The situation is somewhat better for lifetime measurements of a multi-bunch beam as a whole.
2
1
cm -2s -1
L / cm
s
1027
1.
ECPP Quench limit
1026
1.
l
na
i
m
No
1025
1.
1024
1.
1022
V
n
eo
bl
i
s
i
C
TD
C
B
V
eo
bl
isi
n
C
TD
BC
Nominal single bunch current
1.
Visibility threshold on arc BPM
1023
1.
Visibility threshold on FBCT
rly
a
E
I
0.01
0.05
0.1
0.5
1
5
10
Ibb / A
Figure 21.9: Variation of luminosity with single bunch current, I b , for both the nominal ion scheme and early
ion scheme (note that the values of β ∗ are different in the two cases). Thresholds of visibility on the FBCT
and the arc BPMs are shown as vertical lines. Another vertical line indicates the nominal single bunch current.
The threshold of visibility on the BCTDC is indicated as points since it occurs at different values of the single
bunch current in the two filling schemes. Dipole quenching due to the ECPP effect (Sec. 21.4) is expected to
26
−2 −1
limit the luminosity at some level >
∼ 0.5 × 10 cm s .
In summary, Fig. 21.9 shows the unusually constrained range of operating parameters for lead ion beams.
Commissioning and initial adjustment of the beams will have to be done with beam currents within a factor of
3 of the nominal maximum.
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