# Design and behaviour of the Large Hadron Collider external beam dumps
capable of receiving 539 MJ/dump

J. Maestre  C. Torregrosa  K. Kershaw  C. Bracco  T. Coiffet  M. Ferrari  R.
Franqueira Ximenes  S. Gilardoni  D. Grenier  A. Lechner  V. Maire  J. M.
Martin Ruiz  E. Matheson  N. Solieri  A. Perillo-Marcone  T. Polzin  V.
Rizzoglio  D. Senajova  C. Sharp  M. Timmins  M. Calviani11footnotetext:
Corresponding author.

###### Abstract

Two 6 t beam dumps, made of a graphite core encapsulated in a stainless steel
vessel, are used to absorb the energy of the two Large Hadron Collider (LHC)
intense proton beams during operation of the accelerator. Operational issues
started to appear in 2015 during LHC Run 2 (2014-2018) as a consequence of the
progressive increase of the LHC beam kinetic energy, necessitating technical
interventions in the highly radioactive areas around the dumps. Nitrogen gas
leaks appeared after highly energetic beam impacts and instrumentation
measurements indicated an initially unforeseen movement of the dumps. A
computer modelling analysis campaign was launched to understand the origin of
these issues, including both Monte Carlo simulations to model the proton beam
interaction as well as advanced thermo-mechanical analyses. The main findings
were that the amount of instantaneous energy deposited in the dump vessel
leads to a strong dynamic response of the whole dump and high accelerations
(above 200 g). Based on these findings, an upgraded design, including a new
support system and beam windows, was implemented to ensure the dumps’
compatibility with the more intense beams foreseen during LHC Run 3
(2022-2025) of 539 MJ per beam. In this paper an integral overview of the
operational behaviour of the dumps and the upgraded configurations are
discussed.

##  1 Introduction

The two external dumps of the Large Hadron Collider (LHC), also known as
Target Dump External (TDE), are essential devices for LHC operation [21].
Their function is to absorb the energy of the two intense counter-rotating
beams that circulate inside the LHC vacuum chambers under all foreseeable
circumstances, including abnormal operation conditions of the machine. When
required, a series of magnets located at Point-6 of the LHC (referred to
hereinafter as kickers) deviates each beam trajectory from the LHC ring
towards a dedicated extraction line (one per beam) and spreads it out by
generating a spiral-like sweep. Each of these two $\sim 700$ m long extraction
lines ends in a cavern that contains an LHC dump block, where the beam is
finally intercepted [27].

The original design of the dump block dates from the late 1990s [58, 57]. It
was made up of a series of graphite elements (the core) inside a cylindrical
$8520$ mm long $722$ mm diameter duplex stainless steel vessel (318LN, AISI
1.4462, EN 10088-2, also known by its commercial name URANUS® 45, see Fig. 1).
Different graphite grades, with different densities, were selected to
progressively absorb the primary proton beam. The dump vessel was closed at
its downstream end by a Titanium window and over-pressurized with nitrogen
($\mathrm{{N_{2}}}$) at $1.2$ bar as a protective atmosphere against graphite
oxidation. At its upstream end, the dump block was connected to the LHC
extraction line (operated under Ultra-High-Vacuum, UHV) via a connecting line;
a UHV beam window was fitted between the UHV extraction line and the nitrogen-
filled connecting line.

Figure 1: Schematic section of the original LHC dump block showing the
graphite core configuration

The impact of the beam in the LHC dump block generates a particle shower and
subsequent deposition of energy in the core and adjacent elements. This
phenomenon lasts only $\approx 89$ $\mu$s (nominal dilution time), which
exposes the dump blocks to high thermo-mechanical loads. Since the start of
operation of the LHC in 2009 (Run 1) [30], the beam energy (in each ring of
the LHC) has been progressively increased up to $320$ MJ at the end of Run 2
(2018) [51]. Over the course of the coming years, profiting from the upgrades
of the LHC Injectors Upgrade (LIU) Project, the beam kinetic energy is
expected to reach up to 539 MJ during Run 3 (2022 onwards) in order to
maximize the physics reach of the accelerator and its experiments [31, 46,
47]. These upgrades push the LHC dump blocks to their limits and even beyond
their original design [59].

According to the authors’ knowledge, the only similar beam intercepting device
that can be compared with the LHC dump block is the Fermilab Tevatron collider
external dump [32, 29]. Albeit designed for a lower beam kinetic energy of
$3.2$ MJ, the device incorporates design features that are also present in the
LHC beam dump, such as the requirement of being an external dump (i.e. outside
of the beam ultra-high-vacuum), the choice of graphite as absorbing material
and the requirement of keeping it in an inert atmosphere to avoid graphite
oxidation at high temperature. Nevertheless, the energy absorbed by this
device was two orders of magnitude below that of the dump block in the LHC.

Another device featuring a similar beam kinetic energy ($400$ MJ) was the dump
for the proposed Superconducting Super Collider (SSC) in the United States
[13]. In the case of the SSC, the design used graphite pellets as the
absorber, contained in a water-cooled steel vessel and enclosed in an inert
gas atmosphere. A titanium window was envisaged to separate the SSC beam
vacuum from the dump core. It is interesting to note that the design
considered the graphite as the main absorber material to radially contain the
intranuclear cascade shower and to prevent excessive energy deposition on the
steel container. However, the SSC project was cancelled during its
construction and this device was never studied in detail nor built.

Certainly, the LHC dump block is a unique device of its kind and there is no
previous similar operational experience to learn from. In 2015, after several
years of operation without problems (from 2009), some leakage of nitrogen was
observed coinciding with the intensity ramp-up of the LHC. Rapid interventions
were carried out in the dump caverns to investigate the reasons for the leaks.
Initial inspections revealed loose fasteners on the chain clamping rings used
to attach the connecting lines to the dump blocks in both caverns. After
removal of the chain clamping rings it was found that the metallic Helicoflex®
gaskets that relied on the chain clamping rings to compress them had been
damaged [37, 39]. Further interventions were carried out covering the
replacement of the damaged elements and modification of the nitrogen supply
system to maintain the over-pressure even in the event of increased leaks.
This ensured the dump block could operate until LHC Long Shutdown 2 which
started at the end of 2018.

Interventions were made to install passive interferometers to monitor the
behaviour of the dump blocks during operation.Fig. 2a shows the evolution of
the dumped beam intensities into the dump block from 2015 to 2019;
interventions in the dump caverns were possible during short winter stops,
named YETS and EYETS in the figure (Year-End-Technical Stop and Extended Year-
End-Technical Stop, respectively). Fig. 2b shows the displacements recorded by
the interferometers over several days in May 2018, together with the intensity
of the dumped beam during that period.

Figure 2: a) Evolution of dumped beam intensity during Run 2, plotting in dots
the total proton intensity per dumped pulse (ppp) and in a continuous line the
cumulative number of protons (p) on target/dump (POT). b) Interferometer
measurements during a series of dumped beams in May-2018, showing the
permanent displacement of the dump block after a series of high intensity dump
close to each other in time. The inserted image on the left shows the tri-
axial interferometer installed on the dump.

Readings from the instrumentation revealed that the impact of the LHC beam
resulted in strong vibrations. In addition, it was observed that the dump
blocks had moved longitudinally by several millimeters and also rotated about
their longitudinal axes by a few degrees over the course of repeated beam
dumps (see Fig. 2b). All these findings, together with the requirements
associated with the future LHC exploitation (Run 3), indicated the need for
upgrades to be implemented during CERN’s Long Shutdown 2 (LS2) in 2019-2021 to
make the dump blocks ready for more intense beams [39]. In order to support
these upgrades, complex computer modelling analysis campaigns were launched to
improve understanding of the beam dump behaviour.

Initial findings of the analysis campaigns indicated that the dump block was
subjected to extremely high forces and accelerations - and that it would
therefore not be possible to prevent damage to the gaskets in the beam line
connections by trying to mechanically restrain the dump block. In the original
LHC dump configuration, the vibrations of the dump block were transmitted to
the connecting line and consequently to the UHV system of the extraction line
upstream. Considering the more energetic beam foreseen during Run 3, the risk
of damaging the gasket of the vacuum window in the extraction line became a
major concern, as it could lead to leaks in the LHC vacuum system. For this
reason it was decided to investigate the feasibility of mechanically
uncoupling the dump block from the extraction line upstream of the dump.
Design work was started to develop the necessary hardware upgrades to achieve
this uncoupling. The design work was necessarily an iterative process in
parallel with the ongoing analysis campaigns; the proposed changes were
repeatedly fed into the computer analysis models until the final designs were
arrived at.

In this paper, these activities are described and discussed. The original
configuration of the dump and summary of the upgrades are reviewed in Section
2. In sections 3, 4 and 5, a comprehensive numerical analysis of the dump
behaviour is presented; FLUKA Monte Carlo was used to model the proton beam
interaction with the dump and its output was then fed into thermo-mechanical
simulations. Finally, a description and analysis of the upgraded systems,
addressing the above mentioned issues, is provided in Sections 6 and 7.

##  2 Original configuration and summary of upgrades during LS2

As discussed, each of the two LHC dump blocks is located in a purpose-built
cavern forming part of the underground LHC complex. The layout of the cavern
before the upgrade work reported here is shown in Fig. 2a. Each dump block is
surrounded by a thick iron shielding in order to reduce prompt dose in the
surrounding area as well as to partially shield the core residual dose rate
during human interventions. During operation, air is continuously flushed
underneath the dump core in order to cool it and to circulate the air enclosed
between the shielding and dump block.

In the original configuration, the dump block was physically connected, via a
10 m long connecting line, to the beam extraction line arriving from the LHC
ring. An Ultra-High Vacuum (UHV) beam window separated the vacuum in the
extraction line from the nitrogen in the connecting line and the dump. The
sealing between the incoming extraction line, connecting line, the dump block
and its downstream beam window was assured by spring-loaded metallic
Helicoflex® gaskets between the adjacent flanges of the chambers. These
flanges were squeezed against each other by chain clamping rings. These
connections were found to be the source of the encountered nitrogen leaks.

It is important to note that, in its installed position, the dump block was
simply resting on two steel supports, with only frictional forces to resist
any kind of movement. This freedom is thought to explain the permanent
displacements recorded by the instrumentation. It was realised that the
observed displacements would have led to pulling and pushing forces on the
gaskets and connections with the extraction line. The risk of damaging these
connections was a major concern because it could lead to leaks in the LHC
vacuum system.

Figure 3: Integration of the LHC dump block in one of the two beam dump
caverns a) before and b) after LS2, showing the main modifications

The main changes to the dump block system implemented during Long Shutdown 2
(2019-2021) in order to safely withstand the kinetic energy increase during
LHC Run 3, and that are explained in more detail in the next sections, are
summarised below (see Fig. 3b):

  * •

Uncoupling of the dump block from the LHC vacuum line to avoid generation of
high reaction forces between dump, connecting line and extraction line and
consequently to avoid transmission of vibrations to the upstream components.

  * •

Design of a new upstream window for the dump block and upgrade of the
downstream one.

  * •

Design of a new dump block support system able to cope with the dump block
vibrations and prevent long-term physical displacement of the dump.

  * •

Installation of a new instrumentation system suite to monitor the dump block
behaviour.

##  3 Beam Characteristics and energy deposition in the dump

###  3.1 LHC beam characteristics

Table 1 summarizes the proton beam parameters in past and future Runs of the
LHC, as well as for the High Luminosity (HL-LHC) upgrade. While the maximum
proton energy achieved so far was 6.5 TeV, it will be raised to 6.8 TeV in Run
3. The maximum bunch intensity, which can be handled by different LHC
accelerator systems during Run 3, is 1.8$\times$1011 protons [31]. With such
bunch intensities, the maximum stored beam energy will increase by almost 70%
compared to Run 2. The LHC beams are produced with two main bunch production
schemes, referred to as the standard scheme and the Batch Compression, Merging
and Splitting (BCMS) scheme [43]. The latter one, which allows for smaller
transverse beam emittances, has been extensively used in Run 2 and is also the
baseline scheme for Run 3 [31]. The normalized transverse emittance at top
energy is expected to range from 1.8 $\mu$m rad to 2.5 $\mu$m rad depending on
the emittance growth at flat bottom and in the energy ramp [31]. If not
indicated otherwise, all the studies presented in this paper correspond to a
bunch intensity of 1.8$\times$1011 protons and a transverse emittance of 1.7
$\mu$m rad. The latter value is slightly more conservative than the expected
emittance values mentioned before. The beam energy was assumed to be 7 TeV in
most studies because the actual Run 3 proton energy (6.8 TeV) had not been
finally determined when the simulations were carried out.

Table 1:  Proton beam parameters in the LHC and the HL-LHC era: beam energy $E_{prot}$, bunch spacing $\Delta t_{b}$, number of bunches per beam $N_{b}$, bunch intensity $I_{b}$, stored beam energy $E_{beam}$, and normalized transverse emittance $\varepsilon_{n}$. The values refer to the beginning of collisions in the experiments. For past runs, peak performance values are reported. In particular, standard 50 ns beam parameters from 2012 are shown for Run 1 [33], while BCMS beam parameters achieved in 2017/2018 are given for Run 2 [51]. For Run 3, the table lists expected BCMS beam parameters [31]; the specified bunch intensity of 1.8$\times$1011 protons might only be reached in the second operational year of Run 3. The last column gives nominal HL-LHC beam parameters for standard 25 ns beams. BCMS beams are considered as an alternative for the HL-LHC era, but are not listed in the table. | Run 1 | Run 2 | Run 3 | HL-LHC
---|---|---|---|---
| (2009-2013) | (2015-2018) | (2022-2025) | (2028-)
$E_{prot}$ (TeV) | 4 | 6.5 | 6.8 | 7
$\Delta t_{b}$ (ns) | 50 | 25 | 25 | 25
$N_{b}$ | 1380 | 2556 | 2748 | 2760
$I_{b}$ ($p$) | 1.7$\times$1011 | 1.2$\times$1011 | 1.8$\times$1011 | 2.2$\times$1011
$E_{beam}$ (MJ) | 150 | 320 | 539 | 680
$\varepsilon_{n}$ ($\mu$m rad) |  $\approx$2.5 |  $\approx$2 | 1.8-2.5 | 2.5

###  3.2 Energy deposition processes, scope and assumptions

The beam dump issues encountered in Run 2 operation were mainly related to the
rapid release of energy inside the dump structure. The energy dissipated by
high energy proton beams in matter is governed by a variety of physical
processes. The copious production of secondary hadrons in inelastic nuclear
collisions leads to the build-up of hadronic cascades. The hadronic cascade
development is mainly sustained by strongly forward directed pions, protons,
neutrons and kaons, and ceases once the secondary particle energy falls below
the pion production threshold. Together with the hadronic cascades,
electromagnetic cascades are initiated, mainly by photon pairs produced in the
decay of neutral pions. The electromagnetic cascades play an important role in
dissipating the energy in the dump structure. In this section, we present
energy deposition estimates for Run 3 beam parameters. All studies were
carried out with the FLUKA Monte Carlo code [6, 12, 1]. The calculations were
based on the assumption that the beam extraction and dilution is correctly
executed, i.e. possible failures of the extraction system and their effect on
the beam dump are not discussed.

###  3.3 Energy absorption and leakage

The dump absorber blocks, vessel and windows absorb about 78% of the beam
energy, while the remaining energy fraction escapes in the form of secondary
particles (19%) or is consumed in nuclear collisions (3%). The particles
leaking from the dump deposit their energy in the surrounding shielding, air,
cavern walls and surrounding bedrock, with the exception of neutrinos, which
have a very low interaction cross section and can travel much longer
distances. Of all other secondary particles, muons have the largest range in
the surrounding bedrock, which can amount to up to a few kilometers. Table 2
summarizes the energy deposition in the dump structure and the surrounding
environment for Run 3 peak performance parameters.

Table 2:  Energy deposition in the dump and the surrounding environment for projected peak performance parameters in Run 3 (stored beam energy of 539 MJ). The absolute energy deposition values correspond to an emergency beam abort early in a fill. The remaining beam energy is carried away by neutrinos or is spent in nuclear interactions. | Fraction of | Energy deposition
---|---|---
| beam energy | (MJ)
Dump: |  |
Graphite | 73.6 % | 397
Shell | 4.2 % | 23
Windows, flanges etc. | 0.04 % | 0.2
Total | 77.9 % | 420
Environment: |  |
Shielding | 17.4 % | 94
Air | 0.015 % | 0.08
Cavern | 0.12 % | 0.6
Molasse, rock, etc. | 0.04 % | 0.2
Total | 17.6 % | 95

The numbers in Table 2 correspond to an emergency abort after the beam energy
ramping phase, when the stored beam energy in the collider is maximum (539 MJ
for a bunch intensity of 1.8$\times$1011 protons and a particle energy of 6.8
TeV). In regular physics fills, the dumped intensity will be less due to the
burn-off of protons in the experiments and due to proton losses in the LHC
collimation system. Premature beam aborts are nonetheless unavoidable and the
dump must be able to cope with such scenarios. The energy absorbed by the dump
in such a case is expected to be about 420 MJ in Run 3, while it was around
250 MJ in Run 2. Most of the energy is deposited in the massive graphite
absorber blocks, which contain the developing particle showers. However, the
load on the vessel is still significant due to lateral leakage of particles,
in particular around the low-density graphite segment. The total load on the
stainless steel vessel is estimated to be 23 MJ in Run 3, whereas it was about
13 MJ in Run 2.

Most of the energy escaping from the dump is dissipated in the shielding,
which consists of concrete-filled dipole yokes from the decommissioned
Intersecting Storage Ring (ISR). The energy absorbed by the shielding is
expected to be around 100 MJ in Run 3.

###  3.4 Transverse beam dilution and energy distribution

The horizontal and vertical $\beta$-functions at the location of the beam dump
are about 5 km and 3.7 km, respectively. For a transverse beam emittance of
1.8 $\mu$m (2.5 $\mu$m), this yields a beam spot size of
$\sigma_{x}\times\sigma_{y}$ = 1.1 mm $\times$ 1.0 mm (1.3 mm $\times$ 1.1 mm)
at a beam energy of 6.8 TeV (without contribution of the dispersion). Even the
most robust absorber materials could not sustain the impact of the full beam
on a single spot without being damaged. The beam is therefore swept across the
dump front face by means of four horizontally and six vertically deflecting
kicker magnets [11]. The kicker magnets create phase-shifted sinusoidal
fields, which distribute the bunches along a $\sim$1.2 m long “e”-shaped trace
on the dump face. The dilution kickers are located in the LHC tunnel, more
than 700 m upstream of the dump cavern. This long distance is needed to
achieve the required lateral separation of the bunches when they impact on the
beam windows and eventually on the dump core at the end of the transfer line.
The beam extraction and dilution is executed seamlessly within one beam
revolution, which lasts about 89 $\mu$s.

Figure 4:

Transverse energy deposition density in the low-density graphite segment of
the LHC dump core (at a depth of about 270 cm). The results correspond to beam
energy of 7 TeV and a bunch intensity of 1.8$\times$1011 protons.

Fig. 4 shows the transverse energy density distribution at a depth of about
270 cm inside the dump core. This corresponds approximately to the location
where the shower-induced temperature reaches a maximum. The simulations were
carried out for a beam energy of 7 TeV. Slightly lower values can therefore be
expected for the actual Run 3 proton energy of 6.8 TeV. For simplicity, the
figure neglects any heat diffusion during the sweep. The energy density map
illustrates the sweep pattern, which will be adopted in Run 3. The pattern has
been slightly modified with respect to Run 2 in order to reduce the voltage in
dilution kicker magnets. The energy density and hence the temperature
distribution in the core depends on the overlap of the transverse shower tails
of the swept proton bunches. The maximum energy density occurs after about 15
$\mu$s, when the vertical field is zero and the sweep velocity is minimum.
While individual bunches cannot be discerned in the figure, one can still
identify gaps in the bunch filling pattern arising from the beam production in
the injectors. These particle-free gaps are needed to accommodate the rise
time of the SPS and LHC injection kicker magnets. In the figure, we considered
the BCMS beam production scheme, assuming that each LHC injection train from
the Super Proton Synchrotron is composed of 240 bunches. The injection trains
are arranged in five batches of 48 bunches. The LHC filling scheme might be
subject to evolution in Run 3, but the effect on the maximum energy density in
the dump core is expected to be small if beam parameters like the bunch
intensity and the number of bunches remain similar. FLUKA simulations indicate
that the peak energy density might change at most by a few percent if a
different filling scheme is used.

###  3.5 Longitudinal energy density distribution

Fig. 5 shows the longitudinal peak energy density profile in the different
graphite segments, assuming the same bunch intensity (1.8$\times$1011 protons)
and filling scheme as before. The beam energy was again considered to be 7
TeV. The shower maximum is reached in the central segment, which is composed
of low density Sigraflex® sheets (1.2 g/cm3).

Figure 5:

Longitudinal peak energy density profile in the dump core. The results
correspond to beam energy of 7 TeV and a bunch intensity of 1.8$\times$1011
protons.

The lower material density prevents excessive peak temperatures, whereas the
higher-density graphite blocks (1.7 g/cm3) allow for a reduced length of the
dump while ensuring the required beam absorption. In particular, the higher
material density at the upstream end gives rise to a steeper shower build-up,
while the higher-density blocks at the downstream end ensure a better
attenuation of the longitudinal shower tails. The presence of the upstream
higher-density segment has only a small effect on the maximum energy density
in the central low-density segment because of the beam dilution. In total, the
core represents about 15 inelastic nuclear interaction lengths. This means
that the fraction of surviving 7 TeV beam protons is almost negligible
(3$\cdot$10-5%) and the energy leakage reported in Section 3.3 is largely
dominated by secondary particles.

The simulations indicate that the maximum energy density expected in the core
with Run 3 bunch intensities is about 2.5 kJ/g, which corresponds to a
temperature of about 1400 ∘C. The two curves shown in Fig. 5 correspond to
different transverse beam emittances. The two values reflect optimistic and
pessimistic emittance values expected in the beginning of stable collisions in
Run 3 physics fills. The actual value will depend on the emittance growth rate
at flat bottom and during the energy ramp. Although the spot size
($\sigma_{x}\times\sigma_{y}$) of individual bunches differs by almost 40% for
the two considered values, the effect on the peak energy density in the dump
core is small ($<$3%). This can be explained by the shower development and the
beam sweep. First, the particle showers lead to a transverse dilution of the
energy carried by individual bunches. Therefore, the transverse bunch profile
is only partially preserved by the transverse energy density profile deep
inside the dump. Second, the showers induced by neighbouring bunches in the
beam sweep strongly overlap, as illustrated in the previous section. Hence,
the peak energy density induced by individual bunches becomes less important.
The results demonstrate that the maximum energy density and temperature in the
dump is mainly determined by the bunch intensity.

Although the emittance is of little relevance for the temperature rise in the
graphite core, it still affects the peak temperature in the upstream dump
window since the energy deposited by individual bunches is more focused. We
therefore consider the smaller beam emittance (1.7 $\mu$m rad) when studying
the material response under beam impact in the following sections.

##  4 Thermo-mechanical approach of the analyses

The impact of the proton beam on the dump block and the ensuing secondary
showers results in an energy deposition that produces an almost instantaneous
temperature rise. The beam impact duration is only $\mathrm{\sim 89~{}\mu}$s,
hence the initial thermo-mechanical response is highly dynamic. Two different
dynamic phenomena may be distinguished and are assessed: firstly the
generation of stress waves as a consequence of the material expansion
associated with such a fast temperature rise. These waves evolve at the same
time as the diluted beam impacts the dump. Subsequently, and after the initial
stress wave propagation through the dump block, a general vibration status is
developed over a period of a few seconds because of the excitation of several
of its natural frequencies. Afterwards, despite being over a longer time
scale, the heat transfer phase plays an important role. It redistributes the
energy in the dump over time; the energy is finally extracted by radiation and
convection to the environment in the dump cavern. This heat transfer phase is
a relatively slow process (several hours) and it produces a quasi-static
expansion/contraction cycle of the dump block that is also very relevant for
the system operation. The analysis and understanding of the full thermo-
mechanical behaviour of the dump block during the dynamic and quasi-static
responses (referred to as "fast"and "slow" movement, respectively) was
essential to address the operational problems described and to design the
corresponding upgrades so that the dump could deal with the more energetic Run
3 beam scenarios.

In this section we provide a comprehensive overview of the approach taken for
the different analyses performed for the dump block system as a whole. The
same basic approach was followed for the beam windows and dump support system
- however with some differences. These differences are explained in sections
dedicated to the beam windows and the dump support system.

###  4.1 Finite Element Analysis methods

In order to assess the response of the dump blocks after a beam dump event,
several Finite Element Analyses (FEA) were carried out. As introduced
previously, two different behaviours of the dump blocks can be distinguished:
a short intense fast movement in response to the sudden temperature increase
that lasts few seconds; and a slow or quasi-static movement during a period of
several hours due to the slow thermal energy diffusion.

Because of the different nature of the aforementioned phenomena and their time
frames, different kinds of solvers and software were used to analyse the
respective thermo-mechanical behaviour. Implicit thermo-mechanical solver
(ANSYS® multi-physics software) was used to analyse the quasi-static movement
of the dump block. This technique is able to accurately deal with transient
long term simulations thanks to the implicit temporal integration scheme that
allows unconditional stable (and adaptive) large time steps. Nevertheless, in
fast and short dynamic events, explicit mechanical solvers become
advantageous. These are able to cope efficiently with strong non-linear
dynamic phenomena with a reduced computational cost. Explicit LS-DYNA®
software was employed for the analysis of the fast mechanical response of the
dump block, weakly coupled with a thermal implicit solver [34, 52].

A full FEA model of the dump block system (comprising core, vessel, windows
and support system) was developed to study its global response (see Fig. 6) to
a dump event. The dump air cooling system described in Section 2 is implicitly
considered as a convective boundary condition. The air-vessel heat transfer
coefficient (HTC) was computed via Computational Fluid Dynamic (CFD)
simulations and provides a three-dimensional map (as reference, an average HTC
of $9$ W/mK on the vessel was computed for an average surface temperature of
$75$ ∘C). Radiation heat transfer towards the surrounding (shielding) is also
included, assuming a reference external temperature of $22$ ∘C.

Figure 6:  a) Generic Finite Element Analysis model of the full dump block.
The model is adapted according to the kind of simulation (ranging between
$1-2$ millions Degrees of Freedom, DoF) and the mesh is refined around the
beam impact area. Although the vessel and windows are relatively thin
structures, solid three-dimensional special elements are employed (fully
integrated with shear locking reduction algorithm [10]) to capture the energy
gradient through the thickness and correctly represent the three dimensional
stress status. b) Detail view of the steel locking ring that retains the
Sigraflex® sector. c) Sub-modeling approach of the upstream windows where the
beam is imported as a heat generation load and vessel connection is implicitly
considered as a boundary condition.

The dump block core is made of several graphite grades assembled into the
outer vessel following different procedures. The six isostatic Sigrafine®
blocks are shrink-fitted into the vessel (with a nominal interference of $750$
$\mu$m), whilst the low density sector (made of Sigraflex® sheets) is loose-
fitted and sits inside the vessel with the only contact forces due to gravity.
The Sigraflex® sheets are held in place by two HLM Sigrafine® plates which are
retained longitudinally by two steel locking rings (see Fig. 6b). These
details and the pre-stress generated by the shrink-fitting are important in
the dynamics of the dump block and are therefore included in the model.
Frictional contact is considered between the core and the vessel and a thermal
contact conductance (TCC) is computed analytically based on the contact
pressure [36]. Welds and bolted connections are assumed as bonded contacts.
The assembly methods are recreated in the model in order to realistically
represent the initial pre-stressed status of the components.

To analyse in detail the different sub-systems, in particular the beam windows
(critical components exposed to direct beam impacts) and the dump block
support system, sub-modelling approaches were used. This technique allows to
focus the numerical model only on the sub-system and provides a higher level
of resolution and accuracy than the full model. The interaction between the
systems is directly included in the full model and transferred to the sub-
system by imposing displacements as boundary conditions on the common
interfaces [42]. Fig. 6a illustrates this approach for the upstream beam
window.

###  4.2 Beam load as input of FEA models

Although the beam load is common to all the FEAs related to beam intercepting
devices, its application depends on the kind of simulation and purpose.
Results from FLUKA Monte Carlo are imported as a distributed heat generation
source by an ad-hoc Python plugin (see Fig. 7). To dynamically recreate the
beam dilution pattern (required for the analysis of the waves’ propagation,
for example), the proton beam is re-constructed at the level of the bunches’
distribution (See Section 3.2). This tool uses as input the three-dimensional
energy density deposition map of a single bunch, together with the filling
scheme containing the position and time of each bunch along the dilution path,
and it generates (as output) a series of time-dependent heat generation curves
for each element of the finite element analysis model, including the time-
dependent bunch information. Alternatively when the dynamic bunch structure of
the beam is not relevant from the mechanical response point of view (this is
the case after the waves’ propagation), a step-wise heat source, in which the
beam load is integrated over time may be conveniently applied and it
substantially reduces the computational cost.

Figure 7: Illustration of the beam load application on the FEA model based on
the bunch energy density (generated by FLUKA Mpnte Carlo code) and filling
scheme. FLUKA Monte Carlo results are imported using an ad-hoc Python plugin.
The FEA mesh is adapted to reduce importation errors (with a global error less
than $0.1\%$).

###  4.3 Fatigue assessment method

The dump block is subjected to a series of complex vibrations generating
multi-axial stresses after each beam dump event. Based on previous Run 2
experience, it was conservatively estimated (and taken as the nominal
requirement) that the dump block system should withstand $400$ high energy
dumps/year at full intensity over the next $4$ years of Run 3 operation.
Fatigue analysis was carried out on the vessel, beam windows (which maintain
the enclosed protective environment of the core) and the support system, in
order to ensure reliable operation of the dump as a whole.

A wide variety of multi-axial fatigue criteria can be found in the literature,
each one proposed for different purposes and/or conditions [5]. In the
framework of this study, several fatigue criteria based on the stresses: Sines
[50], Crossland [14], Dang Van [54] and critical plane: Fatemi-Socie [22] are
assessed. An ad-hoc computer aided fatigue analysis approach (FEA-Python code)
was specifically developed. The code post-processes the stress and strain
history of the FEA and generates a fatigue life map of the full model.
Depending on the stress conditions, two different algorithms were implemented.
For cases where the overall principal stress shows a variable pattern,
cumulative linear damage based on Palmgren-Miner’s rule [40] and Rainflow
counting method [2] was used, giving the amount of equivalent damage as
output. In cases of a quasi-constant stress amplitude, the code looks for the
most harmful cycle from the time history and returns the number of cycles up
to failure and equivalent amplitude fatigue stress.

##  5 Results and discussion of the dump block response to beam impact

###  5.1 Quasi-static behaviour ("slow" response)

Fig. 8a shows the simulated temperature distribution in the dump block at
different time steps following a beam dump event. During the beam impact, the
temperature increase is maximized around the beam impact region with a maximum
temperature of $\mathrm{T_{max}=1416}$ ∘C in the Sigraflex® sector for nominal
Run 3 parameters. The initial high temperature gradient in the core together
with the relatively high thermal conductivity of the graphite, and especially
the Sigraflex® ($70$ W/Km and $238$ W/Km at room temperature for the
Sigrafine® and Sigraflex®, respectively), allows a rapid diffusion of the
thermal energy towards the stainless steel vessel. This leads to a temperature
rise in the vessel up to a maximum of $\mathrm{T_{max}=194}$ ∘C after roughly
13 minutes; this is followed by a progressive cooling down over several hours
in which the energy is extracted by convection and radiation to the
surroundings (see Fig. 8b).

Figure 8: a) Temperature distribution in the dump block (longitudinal section)
at different time steps after dumping the beam illustrating the temperature
evolution during a cycle of 12 hrs (assuming no beam dump events in between).
b) Temperature evolution of the vessel and core along with extracted energy to
the surroundings with respect to the total energy deposited in the dump block.

Even after roughly $12$ hours, $13.4\%$ of the deposited thermal energy in the
dump block remains inside the core. The low Biot number (dimensionless index
that relates the internal conduction with the superficial convection) [7],
$Bi=0.04$, explains the quasi uniform radial temperature distribution observed
in the core during the cooling down phase. Note that a Biot number far from
unity indicates that the system is not thermally well balanced. A sensitivity
analysis carried out on several thermal parameters confirmed that the heat
transfer conductivity between air and vessel is the key parameter that limits
the average power that can be deposited in the dump core in the long term.
Although the cooling time could be potentially reduced by improving the
cooling system, it is acceptable for Run 3 (where nominally two beam dumps are
assumed per day) in the current configuration. However, the limited cooling
capacity of the current dumps will be a bottle neck in the future, especially
in the High-Luminosity LHC era.

The quasi-static mechanical evolution of the dump block is illustrated in Fig.
9. The dump expands longitudinally by up to 4 mm over around 40 mins and then
contracts, following a cycle similar to the temperature evolution of the
vessel. At the same time, it experiences a slight bending deformation due to
the non-axisymmetric boundary conditions and core material distribution (as
shown in Fig. 9a). The reason for this behaviour is to be found in the
temperature change of the vessel during the slow heat transfer from the core
and subsequent cooling. The high Young’s modulus and thermal expansion
coefficient of the steel of the vessel (195 GPa, $12.5\cdot 10^{-6}$ 1/K,
respectively) compared with the ones of the graphite core (10 GPa, $2.7\cdot
10^{-6}$ 1/K) results in the dump block deformation being mostly determined by
the vessel. Measurements of the displacement at the upstream end of the dump
block during Run 2 operation confirm this expansion. It is important to note
that both simulations and measurements follow similar trends (see Fig. 9b),
although with different magnitudes. This difference is mainly associated with
the different beam energy deposition (nominal Run 3 scenario is considered in
the calculations) but also with the intrinsic non-linear behaviour of the
mechanical system and the attachment to the connecting line (present during
the Run 2 measurements), which opposed the dump block displacements.

Figure 9: Illustration of the quasi-static mechanical evolution of the dump
block following a beam dump event: a) deformation at the time of maximum
expansion; and b) the evolution of the longitudinal displacements at different
points (upstream flange, $4.2$ m with respect to this flange and downstream
flange) over a cycle of 12 hrs (Run 3 nominal intensity, $4.95\cdot 10^{14}$
protons at $7$ TeV, is assumed for the simulation). For comparison purposes
the displacement measured during Run 2 is included (dated on 9th July 2018
with an effective dumped intensity of $2.05\cdot 10^{14}$ protons at $6.5$
TeV). Positive values indicate a displacement in the beam direction.

###  5.2 Dynamic behaviour ("fast" response)

Fig. 10 illustrates the dynamics of the dump block displacement a few
milliseconds after beam impact. In response to this fast event, after the
transmission of mechanical deformation through the whole dump block via wave
propagation and subsequent rarefaction, several natural frequencies are
excited in the assembly. Unlike the quasi-static behaviour, dominated by the
heat diffusion phenomenon, the fast movement is a direct consequence of the
sudden energy deposition in the stainless-steel vessel, in which inertia and
mass play an important role.

From simulations, it is evident that the longitudinal mode is the main
contributor to the dump dynamics. As a consequence of this mode, both windows
of the dump block: the original downstream and also the new upstream one
(foreseen in the new Run 3 configuration introduced in Section 2) are shaken
by the dump movement with acceleration peaks of $\approx 1900$ m/s2 and $1000$
m/s2, respectively (see top of Fig. 10a and b). This phenomenon has important
implications for the design of the new upstream window, as will be described
in Section 6. In addition, there are two other relevant modes: the bending and
radial modes (see bottom of Fig. 10a and c). The radial mode is clearly
perceptible in the Sigraflex® sector, whilst the phenomenon is partly
attenuated in the shrink-fitted graphite blocks sector. This radial mode is of
particular concern for the support system as the radial expansion induces high
forces ($\approx 2\times$ dump weight) in support components (more details of
the support system are given in Section 7).

Figure 10: Illustration of the dynamic response of the dump block: a) shows
the three main exited natural modes: longitudinal (top); radial and bending
(bottom). b) and c) show the longitudinal and horizontal displacement
evolution at several locations along the dump block (upstream flange, $4.2$ m
with respect to this flange and downstream flange), respectively. For
comparison purposes, graph b) includes longitudinal displacement measured
during Run 2 operation (measurements from 16th August 2018 with an intensity
of $1.04\cdot 10^{14}$ protons at $6.5$ TeV), showing the longitudinal mode in
agreement with the simulation but with a lower amplitude.

In addition to the previously described numerical analysis, experimental modal
analysis was carried out on one of the spare dump blocks being upgraded. This
activity had several aims including pre-characterization of the dump before
Run 3 operation, extraction of the damping ratios (required for the fatigue
analysis) and cross-checking of the numerical simulations. Classical impact
techniques were used such as those reported in Ref. [4, 53, 49, 28].

Table 3 summarises the results of the modal analysis, including both numerical
and experimental results for comparison. It is worth noticing the good
agreement between them. The longitudinal mode was already detected during the
Run 2 operation, thanks to the installed interferometers, at a frequency of
$196$ Hz, (see Fig. 10b), which nicely coincides with both the numerical and
modal analysis results. Radial/breathing mode is also detected at 2.3 kHz and
it confirms the numerical predictions.

Table 3: Experimental [48] and numerical modal analyses of the dump. Two
numerical analyses are reported assuming a linear modal analysis and a non-
linear dynamic analysis in the time domain. The damping ratio is referred to
the critical damping [48, 4]

Simulations Experimental measurements Linear modal analysis Natural freq. [Hz]
Dynamic analysis Natural freq. [Hz] Natural freq. [Hz] Mode shape Damping
ratio [%] 32.0 - 27 Global bending 0.2 36.9 35.4 37 Global bending 0.2 95.3 -
102 Global bending 4.2 125.1 - 134 Global bending 1.7 172.3 - 183 Global
bending 1.4 174.4 199.4 197 Longitudinal movement 1.8 186.4 - 205 Global
bending 0.3 - 2353 2360 Radial movement 0.2

These vibrations are presumed to be the main source of the detected issues
during Run 2 operation, and are presumed to explain the loosening of the
fasteners, damage of the Helicoflex® gaskets (at the connection between dump
and connecting line) and the resulting nitrogen leaks. In the original dump
support system configuration, the dump block sat on two simple metallic
supports which were contoured to match the outer surface of the dump vessel
(see Fig. 6). There were no elements in the original dump support system to
prevent longitudinal or rotational displacements of the dump block apart from
frictional forces between the outer vessel and the supports. It therefore
appears that the vibrations together with the slow expansion and contraction
movements of several mm were responsible for the migration of the dump and
permanent displacements found in operation. It is thought that the only thing
that finally limited these movements was the connection line linking the dump
to the beam tube coming from the LHC.

###  5.3 Dump vessel fatigue analysis results

In view of the highly dynamic conditions to which the vessel is subjected,
fatigue analyses were carried out on the vessel following the approach
described in Section 4.3 and focusing on Run 3 parameters. Table 4 summarizes
the results. It can be observed that all the stress-based fatigue criteria are
in agreement in terms of number of cycles up to the fatigue strength ($>5\cdot
10^{6}$ cycles), except the modified Dang Van criterion that predicts 1
million cycles. The Dang Van criterion employs the Von-Mises equivalent stress
(whereas the other criteria use the deviatoric) and it penalises more strongly
the hydrostatic component. The Fatemi-Socie criterion, based on the critical
shear plane, provides a number of cycles one order of magnitude higher. Note
that the damping phenomenon attenuates the vibrations of the dump block over
time such that only the first $120$ cycles after the beam dump (assuming
$0.2\%$ damping ratio as measured in the modal analysis) are relevant from the
fatigue point of view. Considering, $1600$ beam dumps as the baseline design
requirement over the Run 3 dump block lifetime (see Section 4.3), no fatigue
issues are expected (calculated minimum number of beam dump events up to
fatigue failure $\approx 8900$).

Table 4: Fatigue assessment of the vessel for different criteria assuming the
worst condition in the load history.

Criterion cycles up to fatigue failure Max. Equivalent stress/strain Crossland
$5.20\cdot 10^{6}$ Eq. Stress $=165$ MPa Sines $5.22\cdot 10^{6}$ Eq. Stress
$=166$ MPa Modified Dang Van $1.11\cdot 10^{6}$ Eq. Stress $=260$ MPa Fatemi-
Socie $>1.7\cdot 10^{7}$ Shear strain $=0.13$ $\%$ Normal Stress $=170$ MPa

###  5.4 Dump vessel instrumentation

A new instrumentation system was designed and installed during the LS2 upgrade
for several purposes: to monitor the thermo-mechanical performance of the dump
block, to cross-check numerical simulations and to detect possible anomalies
during Run 3 operation. The vessel was therefore equipped with temperature
sensors (PT100), strain gauges, displacement sensors (Linear Variable
Differential Transformers (LVDT)), velocity sensors (Laser Doppler Vibrometers
(LDV)), and acceleration sensors, as well as imaging and acoustic measurement
equipment. Details of the instrumentation are provided in Table 5.

Table 5: Instrumentation for the dump vessel, including information on the
sensor characteristics and acquisition frequencies.

Measurement Sensor Number Frequency Range Accuracy Temperature PT100 16 10 Hz
20 - 250 °C $\pm\,1$°C Strain Strain Gauges 16 1 kHz $\pm$ 2000
$\mu\text{m/m}$ 5-10 $\mu\text{m/m}$ Displacement LVDT 3 10 Hz $\pm$ 20 mm
$\pm$ 0.1 mm Velocity LDV 1 10 kHz 0 - 24 m/s 0.01 m/s Acceleration Optical
accelerometers 3 240 kHz 0 - 2000 g $\pm$ 10 % Images HD D-SLR 1 1 photo/hr
1465 x 1010 mm (FOV) N/A Sound Optical Microphone 1 96 kHz N/A N/A

All sensors are commercially available, with the exception of the optical
accelerometers which have been developed in house at CERN. These are
interferometer-based inertial accelerometers with a flexible membrane, that
measure acceleration in a single axis. The working principle of this type of
accelerometer is to have a plate that linearly deflects with acceleration,
while the deformation of all other parts of the device is minimised. The exact
accuracy of the system is still under study however the sensors have been
calibrated and validated at CERN. The PT100 sensors are from Omega Engineering
Ltd, the LDV is provided by OptoMet GmBh, the HD cameras and Nikkor 200-500
lens from Nikon, and the LVDTs from Measurement Specialties (Europe) Ltd.
Apart from the camera images which are acquired by a computer (PC), all data
will be acquired by a real-time National Instruments (NI) PXI system upon each
trigger that indicates a beam dump has taken place. The saved data will
consist of a buffer 2 seconds before and 8 seconds after trigger reception. In
addition to the the acquisition times referenced in Table 5, a 1 Hz reading
from each sensor will be saved to the CERN database NXCALS [56] for live
viewing. The general software architecture is shown in Figure 11. All
acquisition and conditioning electronics, including the high definition
cameras, are shielded inside bunkers located in the extraction tunnels, 80 m
upstream of the dumps.

Figure 11:  General architecture of the instrumentation acquisition. Data are
acquired via an NI-PXI system and a Hybrid Multiband (HMB) system then saved
in CERN database NXCALS and CERNBox server.

##  6 Design considerations on the TDE dump block windows

###  6.1 Introduction to window design

The main function of the dump block beam windows is to provide robust
enclosures at the extremities of the stainless steel dump block vessel and
contain the internal nitrogen atmosphere while withstanding the beam-induced
thermo-mechanical and dynamic loads.

The disconnection of the dump vessel from the upstream vacuum line, carried
out during Long Shutdown 2 in order to mitigate the problems induced by
vibrations and expansion / retraction cycles, required the addition of a new
independent window at the upstream end of the dump block made of Ti-Grade 5
alloy to separate the air of the cavern from the $\mathrm{{N_{2}}}$
atmosphere. Its design is described in this Section.

In addition, a study of the dump block downstream window performance,
consisting originally of a 10 mm plate made from Ti-Grade 2 (unalloyed
titanium), indicated that in some Run 3 beam dilution failure scenarios the
maximum temperature and stresses reached were 203 ∘C and 209 MPa respectively,
possibly leading to yielding in this material. For this reason, it was also
decided to upgrade the design of this window during Long Shutdown 2 by
changing it to Ti-Grade 5, with a consequent improvement of the mechanical
properties. Due to the poor performance of the original metallic seals and
chain clamping rings, it was also decided to change the design of the
connection method. This change was implemented by welding a new extension to
the dump block with a bolted flange interface, so that the new window could be
bolted and sealed via a copper gasket, to the downstream end of the dump
vessel.

###  6.2 Design of the new upstream and downstream beam windows

Fig. 12 shows front and sectional views of the new dump upstream window.

Figure 12:  Geometry of the new dump upstream window .

The window has a varying thickness; for the central area, the selected
thickness is 10 mm. This is the thickness that is directly impacted by the
proton beam. Close to the external radius, the thickness is increased up to
nearly 40 mm. This zone of increased thickness – placed at a distance from the
beam path of at least $20$ mm – is added to allow the connection of the
$\mathrm{{N_{2}}}$ presurization system and to allow bolted attachment of dump
monitoring instruments. Furthermore, this increased thickness is vital to
provide additional stiffness to the window, to avoid the resonant frequencies
of the dump longitudinal vibration, and to minimize the induced dynamic
stresses. Finally, a very large transition radius is used between the
different thicknesses to minimize dynamic stresses.

Fig. 13 shows the area at the downstream end of the dump block and
specifically the new configuration of the welded extension and window. The
selected thickness of the window is 10 mm, as for the upstream one. However,
this window does not have a varying thickness in the same way as the upstream
one. This is due to the broader beam footprint in the window, induced by the
particle showering inside the core.

Figure 13:  Geometry of the upgraded dump downstream window. This new window
is bolted, with a CF flange, to an extension which is welded to the vessel.

Titanium alloy Grade 5 (also known as Ti-6Al-4V) was selected as material for
both the upstream and downstream dump windows. This alloy combines low density
(necessary to minimize the beam deposited energy) with exceptionally high
yield strength even at high temperatures. The geometry of the windows was
machined at CERN by computer numerical control turning and milling machines
out of a multi-directional forged disk of 690 mm diameter by 50 mm thickness.
Mechanical tests of representative material were carried out according to EN
ISO 6892, showing a yield and ultimate strength of 935 and 986 MPa
respectively, with associated longitudinal and transversal strain to rupture
of 14% and 39%.

The new dump windows must withstand three different types of loads, which take
place in different time regimes and are induced by various dynamic sources:

  1. (i)

Thermal stresses directly induced by the energy deposition of the beam during
each beam dump event. This energy deposition takes place in $\mathrm{\sim
89~{}\mu s}$, consistent with the sweeping path arising from the beam dilution
system. The window must withstand not only the nominal operation path, but any
foreseeable impacting path arising from the dilution kickers failure
scenarios.

  2. (ii)

Mechanical loads induced by the $\mathrm{{N_{2}}}$ atmosphere at 0.2 bars of
over-pressure inside the dump block vessel, as well as the loads induced by
the internal vacuum required before the nitrogen filling procedure.

  3. (iii)

Dynamic vibration loads arising from the dump block longitudinal vibrations
induced by the energy deposition of the beam shower in the vessel (estimated
at roughly $\approx 200$ Hz, as explained in Section 5.2). This dynamic load,
transmitted by the vessel to the outer circumference of the window, induces
additional vibration loads on the window (see Fig. 10). It takes place over a
time scale of few hundred milliseconds considering the damping ratio
measurements for the longitudinal mode reported in table 3. As will be shown
in the results section, the oscillatory stresses on the windows due to this
vibration load are the highest ones amongst the three types of loads listed.
For this reason, a fatigue analysis using this load was also included in the
scope of this work.

###  6.3 Beam induced load analysis and results

The interaction of the proton beam with the window’s material leads to a fast
deposition of energy, subsequent temperature rise and dynamic thermo-
mechanical stresses. These loads have been analysed using FLUKA Monte Carlo
and LS-DYNA® codes, following the computational approach described in Section
4.1.

Fig. 14 shows the contour plots for the temperature and the associated Von
Mises equivalent stress obtained by this coupled analysis for the upstream
dump window. The temperature plot on the left corresponds to the time stamp at
89 $\mathrm{\mu}$s, once the beam pulse has completed the whole sweep. The
maximum temperature reached during the beam-upstream window interaction under
nominal conditions is 64 ∘C. The stress plot on the right corresponds to the
time stamp at 17 $\mathrm{\mu}$s, when the maximum stresses of the beam-
induced load is reached ($43$ MPa). This plot also shows very clearly the
tails of stress waves that are generated by the beam impact following the
sweep pattern. Therefore, in addition to the inertia effects, this analysis
takes into account the potential constructive interference of such stress wave
fronts.

Figure 14: a) Temperature profile in the dump upstream window at the end of
the beam sweep. b) Von Mises dynamic stresses at upstream windows at the time
stamp of 17 $\mathrm{\mu}$s.

Similarly, Fig. 15a shows the results for the dump downstream window. The
significantly larger area impacted by temperature rise along the beam sweep in
comparison to the dump’s upstream window is evident. This is due to the
developed particle shower generated along the 8 meters long dump core. The
maximum temperature reached in a nominal beam dilution is estimated at 155 ∘C.
The stress plot shown in figure 15b corresponds to the time stamp at 32
$\mathrm{\mu}$s, when the maximum stresses of the beam-induced load are
reached (corresponding to $141$ MPa).

Figure 15: a) Temperature profile in the dump downstream window at the end of
the beam sweep. b) Von Mises dynamic stresses at downstream windows at the
time stamp of 32 $\mathrm{\mu s}$

The described analysis demonstrates that the windows are fully compliant with
the stresses directly induced by the beam-matter interaction in the windows,
since yield strength of Ti-Grade 5 at 150 ∘C is at least 650 MPa [38]. This
analysis has also been carried out for the most likely beam dilution failure
cases, demonstrating compliance also in such cases.

###  6.4 Vibration load analysis and results

Fig. 16a shows the expected maximum Von Mises stress reached in the centre of
the upstream window as a consequence of the dump block longitudinal
vibrations, simulated as described in Section 4.1. The image shows that the
maximum Von Mises stresses are in the order of 110 MPa. This maximum is
reached 2.8 ms after the beam impact. The second critical region is the
connection radius with the thicker part of the window, where the stresses are
also of the same order of magnitude. Fig. 16a-bottom shows the associated
displacement of the centre of the window as a function of time. The centre of
the window moves up to 4.8 mm in the upstream direction as a consequence of
this load.

Figure 16: Contour plots showing the Von Mises stresses in the (a) upstream
and (b) downstream window due to the deformation induced by the longitudinal
vibrations of the dump, whilst the graphs underneath show the maximum
displacements at the center of the upstream and downstream windows,
respectively

Similarly, Fig. 16b shows the calculated maximum Von Mises stress reached in
the dump downstream window. Maximum Von Mises stresses are of the order of 226
MPa. This maximum is reached 14.5 ms after the beam impact. The centre of the
window moves up to 5.4 mm in the upstream direction as a consequence of this
load. Maximum stresses and displacements under this load are considerably
higher in the dump’s downstream window in comparison to the upstream one (even
if the displacement load is similar) due to the specific geometry of the
dump’s downstream window.

It is worth noting that the stresses associated with this dynamic load, that
were not considered in original design studies of the dump [21], are indeed
the dominating ones, for both the upstream and downstream dump windows. In the
case of the upstream window, the 110 MPa reached results in a 6.3 safety
factor against yielding. For the downstream window, the 226 MPa reached
results in a 2.3 safety factor against yielding for the beam dilution failure
scenarios in which the highest temperatures are reached (244 ∘C).

###  6.5 Dump windows fatigue analysis and results

Following the approach described in Section 4.1 a multi-axial fatigue
assessment was performed for the windows. The assessment was made using the
loads of the vessel-induced vibrations, since they are the highest. It results
in maximum fatigue equivalent stresses of 140 MPa and 230 MPa for the upstream
and downstream windows, respectively. These are well below the fatigue
endurance limit in torsion for $2\cdot 10^{6}$ cycles of Ti-Grade 5 at 300 ∘C,
estimated at 314 MPa. Hence, we conclude that fatigue is not an issue for the
windows for the current parameters of Run 3.

###  6.6 Sealing solution for the upstream window

As mentioned in Section 2 and 5.2, the metallic Helicoflex® gaskets used to
seal the dump block and connecting line in the original dump design were
damaged by the vibration of the dump blocks leading to nitrogen leaks. It was
therefore decided to replace them with elastomeric O-rings for the upstream
windows for improved sealing capability under vibration conditions. A second
O-ring was used for the connection of the nitrogen supply to each upstream
window.

Based on FLUKA simulations, the O-rings of the upstream windows are expected
to absorb a mixed radiation dose of around 0.12 MGy over the Run 3 equipment
lifetime. At comparable doses, modifications of O-ring mechanical properties
can be induced, possibly leading to seal failure [8, 15, 45]. EPDM (ethylene
propylene diene monomer) rubber is known to be radiation resistant up to the
MGy dose range [8]. For the upstream windows, O-rings made of EPDM Shieldseal®
663 produced by James Walker were selected. This is a special grade EPDM-based
material designed to be radiation tolerant and declared by the producer as
resistant up to a gamma dose of 1.6 MGy [55]. Additionally, this material was
irradiated in a mixed neutron and gamma radiation field in a previous study
[60], reporting moderate damage at 0.7 MGy and only severe damage at 1.5 MGy
[23], which are well above the 0.12 MGy expected during Run 3.

##  7 Engineering design of the upgraded dump support system

For the Long Shutdown 2 upgrades, it was decided to physically separate the
dump blocks from the extraction lines. This change required the development of
a new support system for the dump block. Since the dump block’s vibrations are
intrinsic to its thermo-mechanical behaviour, the aims of the new support
system were to allow the dump to vibrate freely, expand and retract without
migrating and without transmitting its vibrations or movements to other beam
line components. The description of the support system and design analysis are
explained in this Section.

###  7.1 Support system description

A new support system, compatible with the highly radioactive environment, was
designed to meet the aims listed above. The system is based on two steel wire
rope loops that suspend the dump block inside a frame (see Fig. 17). This
design provides freedom to accommodate vibrations and at the same time avoids
any accumulative movement of the dump over repeated expansion and retraction
cycles as the dump is brought back to its original position by gravity. The
wire ropes are supported at each end by a steel S460ML (1.8838): EN
10025-4-2004 cradle structure that fits around the dump block. The cradles are
separated by longitudinal side members (rectangular section tubes in steel EN
10025 S235JR(1.0038) ). Each cradle has a foot that sits on the shielding (the
original supports act as guides to position the new support frames). The new
support design was designed to fit in the restricted space inside the
shielding blocks around the dump block and to be compatible with the remote
handling equipment (overhead travelling crane and spreader beam) used for the
dump block installation and removal.

Figure 17: a) 3D view of the new dump support frame with cradles at each end.
The inset photo shows both upgraded dump blocks assembled in their support
systems prior to installation. b) Cradle details: the two wire rope loops that
support the dump block can be seen inside the cradle structure fitted at each
end of the support frame.

###  7.2 Dump suspension - steel wire rope selection and assembly

The steel wire rope is a key element in the new support system. A $21$ mm
diameter galvanized high strength steel wire rope with a configuration
8xK26WS-IWRC, manufactured by DIEPA, was selected for this application
(commercial ref: DIEPA H40®). The two rope assemblies used to support the dump
block include swaged end-fittings which interface the ropes to the support
frame via spherical bearings. This arrangement is used to accommodate the
relative movements between the dump and the support frame. Since the selected
rope is not rotation-resistant (ordinary cross-lay configuration), the design
incorporates anti-rotation levers at each end of the rope assemblies to
prevent unravelling of the wire rope. Details of the cradle can be seen in
Fig. 17b.

###  7.3 Thermo-mechanical assessment of the support system frame

The design of the new support system was developed through an iterative
process in parallel with the analysis described above to meet the structural,
operational and integration requirements. The new support system does not only
have to withstand the dump weight but also its dynamic loads. The dump block
and support frame are coupled by the wire ropes and the vibrations from the
dump block, although attenuated by ropes, are transmitted through them. In
addition, a substantial amount of energy ($4.2$ MJ) is also deposited in the
support frame due to the particle shower generated at the beam impact. This
is, in fact, the most important load on the frame.

Fig. 18 illustrates the mechanical response of the support frame. The frame
expands longitudinally due to the sudden temperature increase (energy
deposition in the side members). As a result, this leads to a global bending
deformation of the side tubes and strong dynamic movement of the dump
supporting cradles. The design was optimized to keep stresses ($<200$ MPa)
under the yield stress of the material ($235$ MPa), reducing at the same time
the weight and the inertia effects. According to fatigue analyses, no issues
are expected during the support lifetime, and it should be able to withstand
more than $35000$ beam dump events.

Figure 18: a) Illustration of the mechanical response of the support system
frame (viewed from above) after a beam dump event, including b) a detail of
the upstream cradle response.

###  7.4 Mechanical assessment of the dump supporting rope

Detailed FEAs were carried out on the supporting ropes, which included the
rope-dump interactions (see Fig. 19). Fig. 19b shows the axial force in the
rope assembly against time, reaching a maximum of roughly $30$ kN. In this
application the rope works mainly in tension-tension mode (TT mode) as opposed
to a bending mode that is found in lifting equipment where ropes move over
pulleys and drums [44, 26]. The rope exhibits oscillations around the static
weight of the dump ($17$ kN), and the main frequency matches that of the
radial mode of the dump block (see Table 3, modal analysis measurements).
These oscillations tend to attenuate with time due to damping. Considering the
rope strength (minimum breaking force of $430$ kN), there is a large quasi-
dynamic safety factor ($\approx 13$).

Figure 19: Axial force evolution of the rope after a beam dump event, where
the average dashed line corresponds to the weight of the dump block. The rope
elongates and contracts at the radial natural frequency of the dump block as
shown in the frequency analysis.

As for the other components of the dump block system, the steel wire rope
fatigue resistance was assessed. According to literature [26], fatigue
properties of steel wire ropes are mainly driven by the kind of steel and the
configuration and structure of the wire rope. Müller [41] demonstrates that
lubrication has an important effect on rope endurance (e.g. non-lubricated
wire ropes have an endurance of about $\approx 75\%$ with respect to
lubricated ones in TT-fatigue [41]), hence the importance of grease to
service-life. Following the fatigue analyses procedure described in Section
4.3, a damage of $3\cdot 10^{-5}\%$ per beam dump event (where $100\%$ means
failure) was estimated (see Fig. 20), giving a total expected damage after $4$
years of Run 3 operation of $0.05\%$.

Figure 20: Fatigue damage decomposition of the rope for each beam dump event
depending on the mean value and amplitude of the vibrations. Fatigue
properties based on literature data [16, 26]

A series of tension-tension fatigue tests were carried out to confirm the
fatigue performance of the rope assemblies including their end fittings. The
tests were performed under constant amplitude, in the range of $[4-30]$ kN, at
$2$ Hz on both a fully de-greased (worst case to cover lubricant degradation
by radiation) and a greased rope. Samples of degreased rope successfully
completed more than $2.24$ million cycles. Inspection showed some minor
fretting marks and a subsequent quasi-static tensile test on the de-greased
sample resulted in an effective breaking force of $413.7$ kN. As shown in Fig.
20, only the cycles at high amplitude ($>2$ kN) are considered to produce
significant damage, this is, $\approx 140$ cycles/beam dump. Therefore, no
fatigue issues are expected (safety factor $>10$) during the service life.

###  7.5 Preparation of the dump support ropes for the operating environment

The support system and the ropes are exposed to a radioactive environment and
relatively high temperatures. Based on FLUKA-FEA simulations mentioned in
Section 3 and Section 4, the rope is expected to absorb a radiation dose of
around $15$ MGy over the equipment lifetime during Run 3 and to operate at
temperatures slightly above $100^{\circ}$C. This level of radiation is
extremely challenging for polymers and in particular polymeric lubricants[9,
25], which should therefore ideally be avoided or selected from highly
radiation resistant products. Commercial steel wire ropes normally include
plastic inserts, whose radiation resistance is unknown and that could be
severely damaged at the expected dose levels. To prevent this, the selected
rope does not include any plastic inserts. However, as is standard practice
during production, the rope is assembled to include a commercial lubricant
(Elaskon® SK-DL) in order to prevent corrosion and reduce wear. With a drop
point around $70$ ∘C, this product is expected to melt and partially drop out
from the ropes during operation due to the temperatures and vibrations to
which it will be exposed (see Fig. 21a). Moreover, according to the authors’
knowledge, the radiation resistance of Elaskon® SK-DL has never been
experimentally assessed. Considering the available information on its
composition and the radiation tolerance of similar products previously tested,
it is expected to degrade due to radiation damage before the end of the
equipment lifetime. As mentioned above, the fatigue tests on samples of the
steel wire rope assemblies were therefore carried out after deep cleaning to
remove all lubricant in order to simulate a worst-case scenario of a complete
loss of lubricating properties (see Section 7.4).

As fatigue safety factors of un-lubricated wire ropes could be increased by
using a temperature and radiation resistant lubricant it was decided to
investigate suitable alternatives. Several solutions were investigated such as
deep cleaning followed by re-greasing with a radiation-tolerant grease, but
this cleaning process resulted in a reduced thickness of the galvanised layer
on the steel wires. Therefore, a lubrication solution was selected that
combines a heat treatment to remove excess Elaskon ® SK-DL without impacting
the galvanised layer, and coating the ropes with a grease having a much higher
expected radiation resistance (Fig. 21b). Lubrilog® LX AGFA 2 was selected for
this application based on its resistance to temperatures up to $350^{\circ}$C,
the high radiation resistance declared by the producer [35], and its
Polyphenyl ether-based composition; previous studies [9, 3, 24] demonstrated
superior resistance of Polyphenyl ether-based lubricants to radiation.
Experimental studies to further assess the radiation tolerance of LX AGFA 2
are ongoing in collaboration with the producer.

Figure 21: a) Wire rope with original lubricant (Elaskon® SK-DL) showing signs
of dropping after exposure to the temperatures expected in mid-Run 3; and b)
Beam dump support steel wire rope with a double lubrication: a limited
quantity of Elaskon® SK-DL between strands and individual wires along with
Lubrilog® LX AGFA 2 on the outer surface.

##  8 Conclusions and outlook

The investigations, analysis and design work carried out to resolve
operational problems have led to an improved understanding of the behaviour of
the LHC beam dumps in response to the energy deposited by the dumped proton
beams. A particularly interesting finding was that the almost instantaneous
heating of the dump outer vessel due to the secondary particle shower leads to
high frequency and high intensity vibration of the LHC dump block system.
Another key finding was that the stresses in the beam windows due to the beam
impact on the window itself are dwarfed by the stresses induced by the strong
vibrations transmitted from the dump outer vessel to the window.

Although the main focus of the work reported here was to prepare the LHC Beam
dumps for the next operational run (Run 3) of the LHC, a secondary goal was to
acquire knowledge, develop analysis techniques and gain design, manufacture
and operational experience that can be applied to future upgrades of the LHC.
In addition to the upgrades of the dumps, supporting systems and beam windows,
a new extensive instrumentation system has been installed in order to measure
temperatures, strains, vibrations and displacements of the dump during
operation. Even though the new instrumentation system is not the main focus of
this paper, future publications are planned to report the operational
behaviour of the LHC dump blocks and validation of the present analyses, which
should be a major input for the design of new dumps to cope with High
Luminosity LHC (HL-LHC) energy levels (around 680 MJ/dump).

The process and results presented in this paper are also fully relevant to any
future high energy and high intensity hadron or lepton machine, for example
FCC [17, 18, 19], ILC or CLIC [20], and in general for the design of beam
intercepting devices and absorbing systems.

## Acknowledgments

The authors wish to acknowledge the support of CERN’s main design office,
workshop and mechanical measurement laboratory in the execution of these
hardware upgrades and the vital operational support provided by CERN’s
Radiation Protection, Transport, Robotics, Survey and Coordination teams among
others. Special thanks are given to the ACC-CONS (Accelerator Consolidation)
Project and CERN Management for their support and trust in the execution of
the Long Shutdown 2 upgrades and ensuing activities. The support of the
Project Reviewers who provided their time and valuable insights is kindly
acknowledged.

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