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