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. protons anti-protons + E=Mc2 !

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

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. The trick in a proton accelerator is to keep applying the force to accelerate protons in the same direction until they are going at almost the speed of light.

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. The trick in a proton accelerator is to keep applying the force to accelerate protons in the same direction until they are going at almost the speed of light.

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) alligator clip tube anode glass tube stand 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

E e- d +10 kV CRTs and Acceleration 10 keV e- to screen Consider how a simple CRT acts as a particle accelerator: +10 kV 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? 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: current density proportional to cosθ: “cos theta design”
current density proportional to cosθ: “cos theta design”

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 (final exam: calculate it in certain case)

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 a puzzle for discussion: if bending magnets are all set to a certain field, how does the beam energy ever chang
e?

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 e+e-, 200 GeV 1994-2000 LEP 1 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

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 GeV 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” luminosity: number per unit scattering area per unit time efficiency (acceptance) number of events observed production cross section (m2) integrated luminosity (m-2)

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