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, …
It’s 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.
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.
E=Mc2 !
+
protons
anti-protons
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
A charged particle such as an electron or a proton is
accelerated by an electric field and collides with a target,
Fermilab video of fixed targets
which can be a solid, liquid, or gas. A detector determines
the charge, momentum, mass, etc. of the resulting particles.
•Colliding Beams: Two beams of particles are made to cross each other
The advantage: both beams have significant kinetic
energy, so a collision between them is more likely to
produce
a higher mass
than would
a fixed-target
Fermilab
videoparticle
of colliding
beams
collision at the same energy. These particles have large
momentum (short wavelengths) and make excellent probes.
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.
•Fixed target
•Injector to a circular accelerator
•Linear collider
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.
•Colliding Beams
•Extracted to Hit a Fixed Target
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 highenergy 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 e+e- machine?
Accelerators 101
How Does an Accelerator work?
Electrically charged objects exert forces on each
other -- opposite charges attract; like charges repel.
•Coulomb’s law F = -K q1 q2 / r2
•Newton’s Law
F=ma
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.
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.
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.
Cathode Ray Tubes (CRT)
cathode
tube
anode
alligator
clip
stand
glass tube
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
CRTs and Acceleration
Consider how a simple CRT acts as a particle accelerator:
e
-
E
10 keV e- to screen
d
+10 kV
0
A charged particle passing
through a potential drop of V
gains kinetic energy qV
1 eV = (1.6x10-19 C)(1 J/C)
What Do We Accelerate?
Electrons: Heating a metal causes electrons to be
ejected. A television, like a cathode ray tube, uses
this mechanism.
Protons: They can easily be obtained by
ionizing hydrogen.
Antiparticles: To get antiparticles, first have
energetic particles hit a target. Then pairs of
particles and antiparticles will be created via
virtual photons or gluons. Magnetic fields can
be used to separate them.
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
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:
GeV/c
Tesla
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
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
Bending Magnets
• uniform magnetic field: dipole magnet
• consider a current-carrying conductor with
circular cross section, but with circular hole
in the conductor:
Bending Dipoles
the Tevatron and LHC superconducting
magnets are based on a cos theta design:
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:
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)
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
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
• world’s 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
Fnal photo
Fermilab Accelerator Complex: The Tevatron
Cern photo
Site of the LHC at CERN in Geneva
Lhc beampipe drawing
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
e+e-, 200 GeV
1994-2000
LEP 1
Geneva,
Switzerland
e+e-, 90 GeV
1989-1994
HERA
Hamburg,
Germany
ep, 30x800
GeV
1992-present
PEP-2
Palo Alto,
California
e+e-, 10 GeV
1998-present
KEK-B
Tsukuba,
Japan
e+e-, 10 GeV
1998-present
Great Colliders
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)
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
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 >> mbeam
Cross Sections and Luminosity
• “fundamental equation of high energy
physics”
efficiency
(acceptance)
number
of events integrated production
observed luminosity cross section
2)
(m
-2
(m )
• luminosity: number per unit scattering area
per unit time
Cross sections -- Geometry
• consider a particle scattering from the repulsive
field of another one:
• suppose all particles going into the annulus between
b and b+db in impact parameter scatter into an angle
between θ and θ+dθ; then:
Cross Sections -- Scattering Angles
• suppose we have, for example hard-sphere
scattering where
• scattering angle is reflection angle from sphere:
Luminosity and Cross Sections
• thus we get
• put this into the differential scattering formula:
Luminosity and Cross Section
• so we prove that the transverse areal projection of a
sphere is πR2 !?
• imagine a beam of particles hitting a thin foil of such
spheres:
cm-2sec-1
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
–e+e- → Z at peak: 30 nb
–top quark pair production at the Tevatron: 7 pb
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
Medical Applications for Accelerators
Neutron Therapy at Fermilab
Proton Therapy at Loma Lina
Light Sources, imaging DNA,
Viruses, proteins
Superconducting magnets
for MRI