LHCC

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Experimental Methods
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• Before 1950s, cosmic rays were the source of
  high energy particles,
• and cloud chambers and photoemulsions were the
  means to detect
• The quest for heavier particles and more precise
  measurements
• lead to the increasing importance of
  accelerators to produce
• particles and complicated detectors to observe
  them

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• All accelerators employ electrical
• fields to accelerate stable
• charged particles (e, p..)
• Simplest machine d.c. High Voltage
• source (Van der Graaf)
• ? beam energies of 20 MeV
• To do better use a high a.c.
• Voltage and carefully time a bunch
• of particles
• 1) Linear accelerators (Linacs)
• (accelerating elements drift tubes
• in line)
• 2) Cyclic (Cyclotrons,Synchrotrons)
• single radio-frequency voltage source

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Linear Accelerators

• Used mostly to accelerate electrons which are
  accelerated along a sequence of cylindrical
  vacuum cavities
• Inside cavities, an em field is created with a
  frequency 3,000 MHz (radio-frequency) and
  electric component along the beam axis
• Electrons arrive into each cavity at the same
  phase of the electric wave.

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Standing-wave Linacs

• Used to accelerate heavier particles, like p
• Typical frequency of the field is about 200 MHz
• Evacuated pipe containing a set of metal drift
  tubes. Drift tubes screen particles from the em
  field for the periods when the
• field has decelerating effect

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• Proton source is continuous , but only those
  protons inside certain time bunch will be
  accelerated
• Lenghts of drift tubes are proportional to
  particles speed.
• If increase in lenght is correctly chosen, then
  as vpincreases, protons in a bunch receive a
  continuous acceleration
• Such proton linacs reach energies of 50 MeV
  (used as injectors for other accelerators)

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CyclicAccelerators Cyclotrons

• The vacuum chamber is
• placed inside a magnetic
• field perpendicular to
• the rotation plane
• Dees (for D) are
• empty boxes working as
• electrodes there is no
• electric field inside them
• Particles accelerated by the high frequency
  field between the dees (maximal energy achieved
  for protons 25 MeV)
• Both the B and RF frequency must increase
• and be synchronized with particles velocity

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Cyclic accelerators Synchrotron

• All modern proton accelerators are circular
• Beam of particles is constrained in a circular
  path by bending
• dipole magnets
• Accelerating cavities are placed along the ring
• For a proton of momentum p in units GeV/c, the
  field must have a
• value B (Tesla)
• where r is the ring radius (m).
• Hence the magnetic field B has to increase given
  that r must be
• constant and the goal is to increase momentum
• Maximal momentum is therefore limited by both the
  maximal
• available magnetic field and by the size of the
  ring

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Layout of a synchrotron
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• There is another problem
• Charged particles which travel in a circular
  orbit with relativistic
• speeds emit synchrotron radiation.
• Amount of energy radiated per turn is
• Here q is electric charge of a particle, b v/c
• (1-b2)-1/2, and r is the radius of the orbit
• For relativistic particles, g E/mc2, hence
  energy loss grows
• dramatically with particle mass decreasing, being
  especially big for
• electrons
• Limits on the amounts of the radio-frequency
  power mean that
• electron synchrotrons can not produce beams with
  energies more
• than 100 GeV

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• Particles are accelerated once or more per
  revolution by RF cavities. Both B and the RFs
  must increas and be synchronized with the
  particle velocity as it increases
• Very precise synchronisation is not requested
  particles behind the radio-frequency phase will
  receive lower momentum increase,
• Therefore all particles in a bunch stay
  basically on the same orbit, slightly oscillating

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• In cyclic accelerators, protons make typically
  105 revolutions,
• receiving an RF kick of the order of a few Mev
  per turn
• To provide focussing (in most machines) two
  types of magnets
• bending magnets produce a uniform vertical
  dipole field over the
• width of the beam pipe and constrain
  protons
• in a circular path
• focussing magnets produce a quadrupole field.
  They are used with
• alternatively reversed pole so that,
  both in
• vertical and horizontal directions one
  obtain
• alternate focussing and defocussing effects.
• Like for a serie of diverging and
  converging
• lenses net effect is focussing in both
  planes

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• Depending on whether beam is deposited onto a
  fixed target or is
• collided with another beam, both linear and
  cyclic accelerators are
• divided in
• fixed-targetmachines
• colliders (or storage rings)
• Much higher energies for protons comparing to
  electrons are
• achieved due to smaller losses caused by
  sinchrotron radiation
• Fixed-target can be used to produce secondary
  beams of neutral or
• unstable particles

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Centre of mass energy, i.e., energy available for
particle production during the collision of a
beam of energy EL with a target is mb and mt
are masses of the beam and target particles
respectively, and increase of EL does not lead
to big gains in ECM More efficiently high
centre-of-mass energies can be achieved by
colliding two beams of energies EA and EB (at an
optional crossing angle q) so that
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Schematic view of the Tevatron (Fermilab)
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• How are proton bunches produced? Tevatron
  Collider at 1.8 TeV (run I)
• - Gaseous H2 is ionised to have H- ions.
• - H- accelerated first with a Cockroft Walton
  accelerator until
• They reach an energy of 750 GeV, and then with a
  linear accelerator
• (Linac) which brings them to 200 MeV
• - After they are focused sent against a thin
  carbon foil. Due to
• this interaction they loose 2 electrons, and
  become protons
• Protons are transferred to a circular
  accelerator (the Booster, a
• synchrotron with 75 m radius) and brought to an
  energy of 8 GeV
• With an accelerating RF, protons are grouped in
  bunches, and
• bunches are injected in the Main Ring,
  synchrotron of the same
• dimension of the Tevatron (R 1 Km), in the same
  tunnel
• Conventional magnets drive bunches until 150
  GeV, then ps are
• transferred to the Tevatron

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• How are anti-proton bunches produced?
• A fraction of protons in the Main Ring , when
  they are at 120 GeV,
• are extracted and sent against a target to
  produce antiprotons
• Goal produce and accumulate large number of
  anti-protons,
• reducing momentum spread and angular divergency.
  In this way,
• can be transferred with high efficiency into the
  Main Ring, and
• after into the Tevatron
• To this purpose, antiprotons are focalized
  through a parabolic
• magnetic lithium lens, and then transferred to
  the Debuncher,
• where the monocromaticity in longitudinal
  momentum is improved.
• Antiprotons are then transferred to the Main
  Ring and stored
• there for thousands of pulses. A stochastic
  cooling system reduces
• the momentum spread in all 3 directions
• When about 6x1011 antiprotons are accumulated,
  6 bunches of
• 4x1010 antiprotons are transferred to the
  Tevatron

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• Stochastic cooling system
• Made of several pickups, amplifiers and
• kickers
• Pickups detect locally a deviation of the
• Antiproton bunches from main orbit in the
• Accumulator
• Signal coming from the pickups is amplified
• and sent to kickers located at opposite
• azimuthal angles along the ring
• Kickers produce an electromagnetic field,
• which corrects the deviation detected by the
• pickups

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Kinematics Colliders
In colliders (Tevatron, LEP, HERA, LHC) head-on
collisions between two counter-rotating
beams. Proton can be roughly thought of
as being about 10-15 m in radius. If bunches are
10-6 m in radius, and only, 10 protons in each
bunch, chance of even one proton-proton
collision when two bunches met would be
extremely small.


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On the other hand, if each bunch had a
billion-billion (1018) protons (entire cross
section filled with protons), every proton from
one bunch would collide with one from the other
bunch, and one would have a billion-billion
collisions Bunch crossing Real situation is in
between these two extremes I.e LHC a few
collisions (up to 20) per bunch crossing, which
requires about a billion protons in each bunch
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Particle interactions with matter

• All particle detecting techniques are based on
  the properties of
• interactions of particles in question with
  different materials
• Short-range interaction with nuclei
• Probability of a particle to interact (with a
  nucleus or another
• particle) is called cross-Section
• Total cross section of a reaction sum over all
  possible processes
• There are two main kinds of scattering processes
• elastic scattering only momentae of incident
  particles are
• changed, for example p-p ? p-p
• inelastic scattering final state particles
  differ from those in
• initial state p-p ?K0L

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• Cross sections of p- on a fixed proton target
• For hadron-hadron scattering, cross sections are
  of the same order
• of the geometrical cross sections of hadrons
• Assuming their sizes are of order 1fm 10-15 m
  ? pr2 30 mb
• For complex nuclei, obviously, cross sections are
  bigger, and elastic
• scattering on one of the nucleons can lead to
  nuclear excitation or
• break-up (quasi-elastic scattering)

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Knowing cross-sections and number of nuclei per
unit volume in a given material n, one can
Introduce two important characteristics collis
ion lenght lc 1/nstot absorption
lenght la 1/nsinel At high energies,
hadrons comprise majority of particles subject to
detection Neutrinos and photons have much
smaller cross sections of interactions with
nuclei, since former interact only weekly and
latter only electromagnetically