positioned with very high accuracy (±20 μm) close the beam in order to
absorb energetic particles. Each collimator has 5 axes of motion.
The Position Readout and Survey (PRS) system in the low level control
system is responsible for verifying in real time the actual position of the jaws,
in order to ensure the level of machine safety required by LHC [6].
The PRS is based on radiation resistant LVDT (Linear Variable Differential
Transformer); the choice of the absolute position sensor felt on the LVDT
because of their ruggedness, intrinsic accuracy and infinity resolution.[6]
The LVDT is basically a transformer with one primary winding and two
secondary windings; a movable ferromagnetic core is responsible for the
relative magnetic coupling between the primary and the two secondary [8].
Because of the radioactive environment the conditioning electronics is located
in safe zones up to 800 m away from the sensors. Under these conditions,
standard conditioning techniques cannot guarantee the accuracy requested of
20 µm for this application because of cable impedance, noise immunity,
crosstalk between signals of different sensors passing within the same
multiwires cable and temperature variations. A fully digital approach based on
a sine-fit algorithm has been chosen to fulfill the project requirements [6].
In addition the LVDTs used as displacement sensors for the LHC collimators
jaws, work in an environment characterized by a high presence of magnetic
fields generated by many high current cables (up to 5 kA) hosted in cable trays
no so far from collimators. These cables supply the resistive magnets of the
same sector where the collimators are installed. The magnetic field produced
8
9
by the cables perturbs the nominal LVDT behaviour; it can generates position
errors (i.e. drift) of some hundreds µm. This problem is much more important
in the LHC transfer lines than the LHC arcs where the resistive magnets are
pulsed, i.e. they are supplied with current cycle. Experimental data have shown
that the LVDTs position reading error follows the magnets current.
Moreover the conditioning electronic is installed in crowded electronic rack
where, for instance, the stepping motor drivers to move the collimator are
installed too. It can experience temperature excursions of several degrees due
to the overheating of the electronics components. On the other side, the
LVDTs installed on the collimators can experience thermal excursion as result
of the near stepping motors overheating or the impact of the beam on the
collimator jaws. These thermal excursions can reduce the performance of the
positioning reading system.
Summary
This thesis work deals with the analysis the two abovementioned problems of
characterizing the LVDT magnetic interference, and the metrological
characterization of the PRS.
In the first four chapters, we illustrate the state of art on: the Large Hadron
Collider (LHC), the Collimator System, the Linear Variable Differential
Transformer (LVDT) and the Position Survey System (PRS).
In chapter 5 we analyze the magnetic interferences on the LVDT. The goal is
to describe the interaction between the LVDT reading and an external
stationary magnetic field providing a figure of the LVDT sensibility to
external magnetic fields of different directions.
As first step of this work, a test bench that generates the external magnetic
field, acquires contemporaneously the LVDT secondary voltages and
measures the magnetic flux density that interferes with the LVDT has been
developed.
Resistive magnets have been used to generate a dipolar magnetic field before
longitudinal (i.e. direct along the axis of the LVDT) and after transversal. In
addition, in order to reproduce the same effects experienced in the LHC
tunnel, not uniform magnetic fields have been taken into account. These have
been generated by a current wire close to the LVDT and placed in different
orientations (orthogonal, parallel to the LVDT axis).
10
11
The magnetic interference has been characterized evaluating the LVDT
position error as function of external magnetic field intensity, the LVDT
excitation voltage and the LVDT core position. Where the relation between
the position error and the external magnetic field was linear, a sensibility
coefficient has been evaluated.
In chapter 6 we analyze the thermal effects. A complete metrological
characterization of the PRS system has been carried. LVDTs have been
connected via a 500 m long cable to the system to reproduce the working
condition in the tunnel. The system reading accuracy as well as the stability
over long time (24 h) has been evaluated and compared with a reading
solution based on standard multimeters. Thermal cycles have been applied to
the LVDT conditioning electronic used in order to study the thermal stability
of the solution adopted. The same cycles have been applied only on the
LVDTs to evaluate the thermal sensitivity of the sensors.
Chapter 1
LHC - Large Hadron Collider
1.1 CERN and LHC Project
CERN is the European Organization for Nuclear Research, the world’s largest
particle physics centre. It sits astride the Franco-Swiss border near Geneva.
CERN is a laboratory where scientists unite to study the building blocks of
matter and the forces that hold them together.
Founded in 1954, the laboratory was one of Europe’s first joint ventures and
includes now 20 Member States. The motivation for this project, in the wake
of the World War, was to prove that European countries could cooperate, in a
field as sensitive such as nuclear physics, in order to advance fundamental
science.
Starting from the early stage of the Proton Synchrotron (PS) accelerator,
subsequent projects enhanced the scientific complex with more machines. The
SPS (Super Proton Synchrotron) machine provided the energy to discover the
weak force particles W+,W−,Z0 resulting in the 1984 Nobel prize attributed to
Carlo Rubbia and Simon Van de Meer. On the way to higher energies the LEP
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(Large Electron Positron collider) was built, providing high precision values
for the aforementioned particles already during start up.
The Large Hadron Collider, currently under construction at CERN, is an
example of circular accelerator and it will be the world biggest and the
powerful accelerator. The LHC will be installed in a 27 km long underground
tunnel (Figure 1.1), that has been housing the Large Electron-Positron collider
(LEP) until 2000. The project has been approved in 1994 and it will be
commissioned in 2008.
Figure 1.1 Overview of the Geneva area with a drawn of the two circular accelerators:
Super Proton Synchrotron (SPS 7 Km) and the larger Large Hadron Collider (LHC 27 Km).
The main scientific goal of the LHC is to provide experimental evidences for
the Higgs boson and to investigate the first 1 TeV
2
range of energy, in which
13
existing theories strongly indicate that new particles will begin to emerge.
Scientists have found, indeed, that everything in the Universe is made up from
a small number of basic building blocks called elementary particles, governed
by a few fundamental forces. Some of these particles are stable and form the
normal matter; the others live for fractions of a second and then decay to the
stable ones. All of them coexisted for a few instants after the Big Bang. Since
then, only the enormous concentration of energy that can be reached in an
accelerator at CERN can bring them back to life. Therefore, studying particle
collisions is like "looking back in time", recreating the environment present at
the origin of our Universe. The answer may lie within the Standard Model, in
an idea called the Higgs mechanism. According to this, the whole of space is
filled with a "Higgs field", and by interacting with this field, particles acquire
their masses. Particles which interact strongly with the Higgs field are heavy,
whilst those which interact weakly are light. The Higgs field has at least one
new particle associated with it, the Higgs boson. If such particle exists, the
LHC will be able to make it detectable.
Two counter-rotating proton beams will collide at a nominal centre-of-mass
energy of 14 TeV and a nominal luminosity of 1034 cm−
2
s−
1
in order to study
the interaction of the basic constituent of matter at the TeV energy level. The
collision will allow also experiments with lead nuclei that will reach collision
energies up to 1150 TeV and luminosities up to 1027 cm−
2
s−
1
[1].
14
Figure 1.2 A part of the LHC tunnel.
Figure 1.3 shows the chain of the CERN accelerators. Bunches of about 1011
particles (spaced by delays of 25 to 75 ns) are prepared in the Booster and PS,
and are accelerated up to the injection energy of the SPS (26 GeV ). The beam
will then be injected from the SPS into the LHC at the insertion points IP2 and
IP8 (Fig. 1.4) at the energy of 450 GeV .
The two counter rotating proton beams will be accelerated by the Radio
Frequency cavities (RF) placed at the insertion point four (IP4) in order to
achieve the nominal energy of 7 TeV and then steered to collide in the centre
of the four experimental detectors LHCb(LHC beauty), ATLAS (A Toroidal
LHC ApparatuS), ALICE (A Large Ion Collider Experiment) and
CMS(Compact Muon Solenoid) placed in the interaction points IP8, IP1, IP2
and IP5, respectively as depicted in Fig. 1.4.
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In addition to the experimental points, there is install two cleaning area of the
beams concerning orbit: betatron cleaning (IP3) and momentum cleaning
(IP7). Beam dump is located at IP6.
The LHCb (standing for "Large Hadron Collider beauty" where "beauty"
refers to the bottom quark) experiment is a specialist b-physics experiment,
particularly aimed at measuring the parameters of CP violation in the
interactions of b-hadrons (heavy particles containing a bottom quark).
The experiment ATLAS is designed to observe phenomena that involve highly
massive particles which were not observable using earlier lower-energy
accelerators and might shed light on new theories of particle physics beyond
the Standard Model.
ALICE is optimized to study heavy ion collisions. Pb-Pb nuclei collisions will
be studied at a centre of mass energy of 5.5 TeV per nucleon. The resulting
temperature and energy density are expected to be large enough to generate a
quark-gluon plasma, a state of matter wherein quarks and gluons are
deconfined..
Finally the goal of CMS experiment are: to explore physics at the TeV scale,
to discover the Higgs boson, to look for evidence of physics beyond the
standard model, such as supersymmetry, or extra dimensions ,to study aspects
of heavy ion collisions[2].
Physicists hope to answer the following questions using LHC:
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• Is the popular Higgs mechanism for generating elementary particle
masses in the Standard Model realized in nature? If so, how many
Higgs bosons are there, and what are their masses?
• Will the more precise measurements of the masses of the quarks
continue to be mutually consistent within the Standard Model?
• Do particles have super symmetric ("SUSY") partners?
• Why are there apparent violations of the symmetry between matter and
antimatter? Are there extra dimensions indicated by theoretical
gravitons, as predicted by various models inspired by string theory, and
can we "see" them?
• What is the nature of dark matter and dark energy
• Why is gravity so many orders of magnitude weaker than the other
three fundamental forces?
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Figure 1.3: The CERN accelerators structure from the beam production trough
different acceleration steps up to the largest accelerator the LHC.
18
Figure 1.4: Layout of the Large Hadron Collider project with all the interaction points, the
radio frequency insertions and the beam cleaning area.
1.2 Particle Circular Accelerators
Accelerators can be divided in two types: linear accelerators and circular
accelerators. In a linear accelerator, charged particles travel along a straight
trajectory and go through a number of accelerating structures. In a circular
accelerator, also referred to as accelerator ring, the beam is circulated many
times in the closed orbit along which a number of accelerating stations are
present. Bending magnets and focusing elements are distributed over the
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accelerator arcs to keep the particles, during and after acceleration, on the
same orbit and within the accelerator acceptance. This offers at least two
advantages: the particle beams can be accumulated and stored in the
accelerator ring and it only requires a few accelerating stations, through which
particles go at every turn. It has two main disadvantages: it calls for a large
number of trajectory-bending elements distributed over the ring and the level
of radiation emitted by the rotating particles can be very high, especially for
light particles such as electrons.
The LHC will use a crossed beams collision (Figure 1.5). In the vacuum tube
of the accelerator the protons will be accelerated in groups named bunches;
there will be two bunches: one will circulate clockwise, the other will rotate in
the opposite direction describing two different circumferences. When the
energy levels will be reached, the bunches will be deviated by a magnetic field
in a prestablished point: the two bunches will intersect and the particles will
collide. Special machine will take and analyze the fragments produced by the
collision.
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Figure 1.5: Crossed Beam Collision.
In general particle accelerators are machines that accelerate charged particles
to high kinetic energies by applying electro magnetic fields. The influence of
electro-magnetic fields can be divided into two effects: longitudinal
acceleration, due to electric fields along the direction of motion of the particle,
and transverse bending of the trajectory due to transverse electric and
magnetic fields.
A particle of charge q and momentum moving through an electromagnetic
field is submitted to the Coulomb and Lorentz’s forces given by:
()BvEq
td
pd
F
r
r
r
r
r
×+==
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Where F
r
the electromagnetic force is exerted by the electric field ~E and the
magnetic field B on a particle of velocity v
r
.
The electric field E
r
changes the particle trajectory and velocity so the
momentum and the energy can be modified. This force can be used to
accelerate and decelerate particles. A constant magnetic field ~B normal to the
particle velocity produces variations of the particle trajectory without
changing the module of the particle’s momentum. Modern circular
accelerators, such as the LHC, make use both principles. The particle beams
are constrained by strong magnetic fields to circulate on a closed orbit. In this
condition the particle beams can be accumulated, stored in the ring and
accelerated. The acceleration is provided by a small number of cavities that
accelerate the beams at each revolution by applying an electric field in the
direction of the motion.
Three fundamental elements are necessary to realize this principle design:
• Particle beams have to be accelerated. Radio Frequency cavities (RF)
are installed in the arc in order to increase the particle energy on every
turn.
• Particles must be guided on the reference “circular” orbit; for this
reason 1232 dipole field magnets will be installed in the arcs to bend the
beam on the reference trajectory.
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• Particle beams must maintain during their revolution a proper intensity
and size. They must be focused; for this reason 360 quadrupole magnets
are used to focus particles onto the reference orbit.
.The bending dipole field intensity is imposed by the curvature of the orbit and
by the particles energy. At the equilibrium, the Lorentz and the centrifugal
forces of the particle beam are equal in intensity and opposite in sign. In the
LHC, particle beams will be highly relativistic, practically circulating at the
speed of light c.
The equilibrium condition results in the following expression:
pcq
E
qpc
Ev
B ==
2
Where E is the energy of particle of charge q and c is the speed of light. The
equilibrium condition requires a magnetic field that changes with and respect
to the particle energy and velocity for a designed circular orbit of bending
radius ρ.
For the LHC the orbit radius is constrained by the existing LEP tunnel, which
will be used for housing the accelerator, and the energy will range from a 450
GeV injection level up to the nominal beam energy of 7 TeV . To reach the
energy of 7 TeV on a circular trajectory with a curvature radius of 2803 m, a
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nominal bending dipole field B of 8.33 T at collision for protons beam is
calculated.
Similar reasoning can be used to determine the quadrupole gradient necessary
to achieve the nominal working point. The LHC quadrupoles magnets are
designed for a gradient of 223 T/m and a peak field of about 7 T. These high
intensity magnetic fields can only be achieved with superconducting magnets.
A complex machine like the LHC must also rely on a series of corrector
magnets, which are used to stabilize the beam during its long running time, so
The LHC will contain a total of 8.400 magnets, including the 1232 (15 m
long) dipoles, 360 (3.25 m long) quadrupoles and the various families of
corrector magnets (dipoles, quadrupoles, sextupoles, octupoles and
decapoles). These magnets will be installed with 8-fold symmetry in arc
sectors composed mostly of regular cells (23 per sector), dispersion suppressor
and matching sections and straight sections before the experiments. A regular
cell has six dipole magnets and two quadrupole magnets (see Fig. 1.5).
Dipole magnets are used to deflect the beam whereas quadrupole magnets act
as lenses to focus the beam. Different from an optical lens, a magnetic lens
focuses in one transverse direction and defocuses in the other transverse
direction.
Sextupole, nested octupole and decapole magnets are placed at the ends of the
main dipole magnets to correct field errors. Other octupole and combined
sextupole and dipoles corrector magnets are installed close to the main
quadrupole magnets to control orbit and average beam parameters.
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