Accelerators: How to go back in time

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Accelerators How to go back in time
Overview of Accelerators From CRTs to Colliding
Beams

• Prof. Robin D. Erbacher
• University of California, Davis

References D.H. Perkins, Introduction to High
Energy Physics, Ch. 11 World
Wide Web Lectures from
Roser, Conway, CERN,
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Its a Simple Idea
Take the smallest possible particles and
give them the highest possible energy.
From this simple idea has come the science of
high-energy physics, the technology of particle
accelerators, and a revolution in our
understanding of matter, space and time.
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Why Do We Need Accelerators?

• Accelerators solve two problems for physicists
• First, since all particles behave like waves,
  physicists use accelerators to increase a
  particle's momentum, thus decreasing its
  wavelength enough that physicists can use it to
  poke inside atoms. (Resolving power!)
• Second, the energy of speedy particles is used
  to create the massive particles that physicists
  want to study.

EMc2 !
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Overview-- The Basics
Basically, an accelerator takes a particle,
speeds it up using electromagnetic fields, and
bashes the particle into a target or other
particles. Surrounding the collision point are
detectors that record the many pieces of the
event.

• Accelerators for particle physics can be
  classified into two main types
• Fixed Target Shoot a particle at a fixed target
• Colliding Beams Two beams of particles are made
  to cross each other

A charged particle such as an electron or a
proton is accelerated by an electric field and
collides with a target, which can be a solid,
liquid, or gas. A detector determines the
charge, momentum, mass, etc. of the resulting
particles.
Fermilab video of fixed targets
The advantage both beams have significant
kinetic energy, so a collision between them is
more likely to produce a higher mass particle
than would a fixed-target collision at the same
energy. These particles have large momentum
(short wavelengths) and make excellent probes.
Fermilab video of colliding beams
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Types of Accelerators
Accelerators basically fall into two different
categories Linear Accelerators (Linacs)
Particle is shot like a bullet from a gun.
Used for fixed-target experiments, as injectors
to circular accelerators, or as linear
colliders. Circular Accelerator
(Synchrotron) Used for colliding-beam
experiments or extracted from the ring for
fixed-target experiments. Large magnets tweak the
particle's path enough to keep it in the circular
accelerator.

• Fixed target
• Injector to a circular accelerator
• Linear collider

• Colliding Beams
• Extracted to Hit a Fixed Target

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Pros and Cons

• Advantage of a circular accelerator over a
  linear one
• Particles in a circular accelerator
  (synchrotron) go around many times, getting
  multiple kicks of energy each time around.
  Therefore, synchrotrons can provide very
  high-energy particles without having to be of
  tremendous length.
• The fact that the particles go around many
  times means that there are many chances for
  collisions at those places where particle beams
  are made to cross.

• Advantage of a linear accelerator over a
  circular one
• Linear accelerators are much easier to build
  than circular accelerators-- they don't need the
  large magnets required to coerce particles into
  going in a circle. Circular accelerators also
  need an enormous radii in order to get particles
  to high enough energies, so they are expensive to
  build.
• When a charged particle is accelerated, it
  radiates away energy. At high energies the
  radiation loss is larger for circular
  acceleration than for linear acceleration.

Why are we planning to build a Linear Collider
for the next ee- machine?
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Accelerators 101

• How Does an Accelerator work?
• Electrically charged objects exert forces on each
  
• other -- opposite charges attract like charges
  repel.
• Coulombs law F -K q1 q2 / r2
• Newtons Law F m a
• A particle with a positive or negative charge
  experiences a force
• when it is in the presence of an electric field.
  When a net force acts
• on an object, the object accelerates.

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Riding the Waves
Accelerators speed up charged particles by
creating large electric fields which attract or
repel the particles. This field is then moved
down the accelerator, "pushing" the particles
along.
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Back to the Beginning
J.J. Thomson discovered the electron in
1897 Investigating cathode rays using a highly
evacuated discharge tube he was able to use the
calculated velocity and deflection of the beam to
calculate the ratio of electric charge to mass of
the cathode ray. This was found to be constant
regardless of the gas used in the tube and the
metal of the cathode and was approximately 1000
times less than the value calculated for hydrogen
ions in the electrolysis of liquids.
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Cathode Ray Tubes (CRT)
A cathode (electron emitter) which is a heated
filament spits out electrons that travel through
a vacuum to an anode (electron acceptor). The
voltage difference in the direction from the
cathode to the anode is known as the forward bias
and is the normal operating mode. TV Tube e-
beam is guided by Electrostatics to a particular
spot on the Screen. The beam is moved so very
quickly, that the eye can see not just one
particular spot, but all the spots on the screen
at once, forming a variable picture
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CRTs and Acceleration
Consider how a simple CRT acts as a particle
accelerator
10 keV e- to screen
A charged particle passing through a potential
drop of V gains kinetic energy qV 1 eV
(1.6x10-19 C)(1 J/C)
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What Do We Accelerate?
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The Lorentz Force

• a charged particle experiences a force
• in general, in a uniform magnetic field, the
  particle will move in a helix with radius such
  that
• this condition holds, clearly, for particles
  travelling in a circle

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Relativistic Motion in Magnetic Field

• this relation holds in the relativistic case if
  we replace mv by the particle momentum
• if we employ usual high-energy physics units, we
  find a simple rule of thumb relation for a
  particle with charge e

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Cyclotron Frequency

• the angular frequency of circular motion for a
  non-relativistic particle in a uniform magnetic
  field is
• the independence of the cyclotron frequency on
  velocity leads to the possibility of accelerators
  called cyclotrons

80 keV and 32
E. O. Lawrence first cyclotron
UC Davis 76 cyclotron
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Cyclotrons
cyclotrons are by far the most common type of
high energy particle accelerator, used in
hospitals and universities routinely
Particles start in center, and travel across gap
between dees where they are accelerated by the
voltage difference between the two halves.
Typical particle energies 100 MeV
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Bending Magnets

• uniform magnetic field dipole magnet
• consider a current-carrying conductor with
  circular cross section, but with circular hole in
  the conductor

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Bending Dipoles
the Tevatron and LHC superconducting magnets are
based on a cos theta design
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Focusing Magnets

• a quadupole focuses in one dimension, and
  defocuses in the other dimension
• particles on axis are unaffected!
• a train of focusing and defocusing magnets has a
  net focusing effect

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Synchrotrons

• synchrotron is a circular ring of magnets in a
  repeating series
• at one or more points on the ring, insert a
  cavity in which there is an oscillating RF
  electromagnetic field
• set RF frequency such that every time the
  particles pass, they are accelerated in the
  direction of the field (hence the name
  synchrotron)

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Synchrotrons

• the RF in a synchrotron keeps particles in a
  bunch which experiences the field at a certain
  phase point in the RF
• two competing effects faster with more energy,
  but longer path with more energy!
• critical energy transition energy peculiar to
  machine

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Where We Get Accelerated Particles

• particles in a synchrotron which are off the main
  axis (or orbit) experience focusing/defocusing
  quadrupole fields
• after many cycles the particles radiate away
  their off-axis-ness
• worlds highest energy machine the Tevatron at
  Fermilab 960 GeV protons and antiprotons
• in 2007 the LHC at CERN will begin operating at 7
  TeV ( 7000 GeV) colliding protons and antiprotons

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Fnal photo
Fermilab Accelerator Complex The Tevatron
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Cern photo
Site of the LHC at CERN in Geneva
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Lhc beampipe drawing
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Global Accelerators
name where what when
LHC Geneva, Switzerland pp, 14 TeV 2007
Tevatron Batavia, Illinois pp, 2 TeV 1986-present
LEP 2 Geneva, Switzerland ee-, 200 GeV 1994-2000
LEP 1 Geneva, Switzerland ee-, 90 GeV 1989-1994
HERA Hamburg, Germany ep, 30x800 GeV 1992-present
PEP-2 Palo Alto, California ee-, 10 GeV 1998-present
KEK-B Tsukuba, Japan ee-, 10 GeV 1998-present
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Great Colliders
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Synchrotron Radiation

• a particle moving in a circular orbit in a
  magnetic field radiates away energy in the form
  of photons
• for highly relativistic particles we find that
  the energy loss per orbit is
• for protons, the E4 term is much smaller than for
  electrons
• probably no electron synchrotron will be built
  larger than LEP (27 km circumference)

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Linear Accelerators
If we arrange a series of RF cavities with
longitudinal field wave phased to travel at the
speed of light, a charged particle will ride down
it
Achieved so far 60 MV/m If we want 103 GeV we
need 20 km long machine
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Fixed Target v. Collider (redux)

• why colliders?
• can get more bang for the buck in terms of
  center of mass energy with colliding beams
• can get more collisions with fixed-target (beam
  on target) experiments
• relativistic calculation initial momentum p,
  target mass m, E gtgt mbeam

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Cross Sections and Luminosity

• fundamental equation of high energy physics
• luminosity number per unit scattering area per
  unit time

efficiency (acceptance)
number of events observed
production cross section (m2)
integrated luminosity (m-2)
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Cross sections -- Geometry

• consider a particle scattering from the repulsive
  field of another one
• suppose all particles going into the annulus
  between b and bdb in impact parameter scatter
  into an angle between ? and ?d? then

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Cross Sections -- Scattering Angles

• suppose we have, for example hard-sphere
  scattering where
• scattering angle is reflection angle from sphere

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Luminosity and Cross Sections

• thus we get
• put this into the differential scattering formula

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Luminosity and Cross Section

• so we prove that the transverse areal projection
  of a sphere is pR2 !?
• imagine a beam of particles hitting a thin foil
  of such spheres

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Cross Sections at Colliders

• the usual units of cross section are barns
• 1 barn 1 b 10-24 cm2 10-28 m2
• typical cross sections
• p-pbar total elastic at 1.96 TeV 1x1010 b
• pp total scattering at 10 GeV cm energy 40 mb
• ee- ? Z at peak 30 nb
• top quark pair production at the Tevatron 7 pb

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Luminosities at Colliders

• integrated luminosity is measured in the inverse
  units of cross section
• inverse barns (b-1)
• typical luminosities
• Tevatron 1032 cm-2s-1
• LHC 1033 cm-2s-1 (later 1034 cm-2s-1)
• can see online display of Tevatron operations at
• http//www-bd.fnal.gov/notifyservlet/www
• rule of thumb year 107 seconds, so
• 1032 cm-2s-1 1 fb-1/year

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Medical Applications for Accelerators