Colliders and Luminosity

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Colliders and Luminosity
Fernando Sannibale
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Colliders for high energy (particle) physics
experiments are surely one of the most important
applications of particle accelerators.
Actually, the developments in particle
accelerators and of elementary particle physics
probably represent one of the best examples of
synergy between different physics disciplines.
Colliders can be characterized by the different
nature of the colliding particles (leptons or
hadrons) and by the different acceleration scheme
used (linear or circular)
In existing lepton colliders, electrons collide
with positrons. A significant RD is going on for
the definition of a possible scheme for a muon
collider.
Hadron colliders include, protons colliding with
protons or anti-protons and heavy ion colliders.
Higher collision energies can be achieved with
hadron colliders but cleaner measurements can
be done with lepton colliders.
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In electron-positron collisions the particles
annihilate and all the energy at the center of
mass system is available for the generation of
elementary particles.
Particle generation can happen only if it exists
a particle with rest mass energy equal to the
collision energy at the center of mass system.
The energy of the colliding beams can be tuned on
the rest mass energy of a known particle for
studying its properties, or can be scanned for
the research of unknown particles.
In hadron colliders, are the quarks in the
hadrons to interact during the collision
generating other particles. Because each hadron
is a combination of three quarks, simultanoeus
generation of different particles is possible.
Most of the particles generated during a
collisions usually has a short lifetime and
decays in other particles. Particles detectors
are designed in order to measure the particle
itself when possible or to measure the secondary
particles generated during the decay.
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• Two particles have equal rest mass m0.

Center of Mass Frame (CMF). Velocities are equal
and opposite, total energy is Ecm. By using the
four-vector representation
Laboratory frame (LF)

• The quantity
  is invariant.
• In the CMF, we have
• While in the LF

• After some algebra we obtain for relativistic
  particles

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x, y, z º Lab. Reference Frame
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• Very low currents

• Negligible
• beam-beam effects

• Crossing angle a

• Horizontal vertical
• offset Dx and Dy

• IR position Dt

• Different beta star for the two beams

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For a gaussian charge distribution
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Focusing quadrupole (thin lens)
Beam-Beam Deflection (off-center particles)
Linear beam-beam tune shift
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No analytical solutions for the non-linear
beam-beam case.
Simulation codes
For example LIFETRACK by Shatilov or BBC by
Hirata
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Beam-beam simulations for the DAFNE collider.
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The beam-beam interaction actually sets the
maximum achievable luminosity in practically all
the existing colliders.
No consistent and exhaustive theory exists.
The linear beam-beam parameter is used a measure
of the strength of the beam-beam interaction.
Estimate of the maximum achievable linear tune
shift by

• Simulations

• Statistical analysis of the maximum linear tune
  shifts achieved in existing colliders

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Equal tune shift design
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• Beam-beam interaction in a linear collider is
  basically the same as in a storage ring collider.

• But
• Interaction occurs only once for each bunch
  (single pass) hence very large beam-beam effect
  is acceptable.

• Extremely high charge densities at IP lead to
  very intense fields that can focus the beam at
  the IP with beneficial impact on luminosity.

H enhancement factor
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Few centimeters vertical beta _at_ IP are
routinely obtained.
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In a low beta insertion, the beta function
between the IP and the first quadrupole is given
by
The hourglass effect can limit the luminosity
achievable in low beta schemes.
The use of short bunches can reduce the hourglass
effect on luminosity.
Several schemes are under study for the
minimization of the hourglass effect.
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Large vertical beta functions in quads _at_
IR Larger negative values of vertical
chromaticities Stronger correcting
sextupoles Smaller dynamic aperture Decrease of
beam lifetime
Short bunches for minimizing the hourglass
effect Increase of Touschek effect Decrease of
beam lifetime Higher frequency components in the
beam spectrum Possible coupling with high
frequency Vacuum chamber modes
instabilities Higher peak RF voltages larger
number of cavities RF nonlinearities, stronger
high order modes Coherent synchrotron
radiation with high current per bunch . . . . . .
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Round Beam (k1) A factor 2 of luminosity
gain Both the beta functions _at_ IP must be
small Technically difficult to obtain Large
negative chromaticities in both planes Strong
sextupole correction Small dynamic
aperture Strong beam-beam effects
Flat Beam (kltlt1) A factor 2 of luminosity
loss Chromaticity handling not critical It is
possible to arrange the collider parameters for a
better luminosity performances
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The detector solenoidal field Introduces
coupling between the vertical and horizontal
planes that must be carefully corrected.
Experimental requirements concerning the solid
angle stay clear forces to have permanent IR
quadrupoles and a reduced configuration of beam
diagnostics
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Rotated IR Quadrupoles to correct Coupling
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KEK B-Factory