Accelerators: Accelerators: How to go back in time…How to go back in time…
Prof. Robin D. ErbacherUniversity of California, Davis
References: D.H. Perkins, Introduction to High Energy Physics, Ch. 11 World Wide Web Lectures from Roser, Conway, CERN, …
Overview of Accelerators:From CRTs to Colliding Beams
It’s a Simple Idea…
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.
Take the smallest possible particles and give them the highest possible energy.
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.
protons anti-protons
+ E=Mc2 !
Overview-- The Basics
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
Fermilab video of colliding beams
Fermilab video of fixed targets
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.
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.
The advantage: both beams have significant kinetic energy, so a collision between them is more likely toproduce a higher mass particle than would a fixed-target collision at the same energy. These particles have largemomentum (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.
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
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 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 = 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.
Riding the WavesAccelerators 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 1897Investigating 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
alligatorclip
tube
anode
glass tubestand
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 AccelerationConsider how a simple CRT acts as a particle accelerator:
+10 kV 0
e-
E
d
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)
What Do We Accelerate?
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.
Protons: They can easily be obtained by ionizing hydrogen.
Electrons: Heating a metal causes electrons to be ejected. A television, like a cathode ray tube, uses this mechanism.
The Lorentz Forcea 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:
Tesla
GeV/c
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
UC Davis 76 cyclotron
E. O. Lawrence:first cyclotron
80 keV and 32”
Cyclotronscyclotrons are by far the most common type of high
energy particle accelerator, used in hospitals and universities routinely
Particles start in center, andtravel across gap between deeswhere 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 Dipolesthe 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 Acceleratorsname where what when
LHCGeneva,
Switzerlandpp, 14 TeV 2007+
TevatronBatavia, Illinois
pp, 2 TeV 1986-present
LEP 2Geneva,
Switzerlande+e-, 200 GeV 1994-2000
LEP 1Geneva,
Switzerland e+e-, 90 GeV 1989-1994
HERAHamburg, Germany
ep, 30x800 GeV
1992-present
PEP-2Palo Alto,California e+e-, 10 GeV 1998-present
KEK-BTsukuba,
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
Achieved so far:
60 MV/m
If we want 103 GeVwe need ~20 km long machine
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:
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”
• luminosity: number per unit scattering area per unit time
numberof eventsobserved
integratedluminosity
(m-2)
productioncross section
(m2)
efficiency (acceptance)
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