Appendix A2. Particle Accelerators and Detectors

The Large Hadron Collider (LHC) in Geneva, Switzerland on the Border of France.

Prepared by: Arash Akbari-Sharbaf

Why Build Accelerators? Probe deeper From the uncertainty principle large momentum transfers correspond to small distances.

Find new particles Some fundamental particles are short lived and have enormous masses Ex. Top quark has a life time of 5x10-25s and a mass of ~173GeV/c2 (~184u)

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Tandem Van de Graaff Accelerator

The key is to establish a very large voltage A belt carries charge from a source and places it onto the outer surface of a hollow conductor. Ions from an ion source accelerate towards the charged surface and enter the hollow conductor. Inside the hollow conductor the ion beam passes through a stripper foil (ie., carbon foil) and becomes positively ionized. The beam leaves the interior of the conductor and gets accelerated further. This device can achieve a potential of about 30-40MeV for singly-charged ions. It is the most common DC accelerator used.

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The Cyclotron Accelerator

The cyclotron shown consists of two d-shaped hollow conductors with an r.f. Source connected between them. Particles are injected into the center of the apparatus where the electric field in the gap causes them to accelerate. Charges are constrained to move in near-circular orbits due to a magnetic field perpendicular to the plane of motion. The r.f. source is synced with the cyclotron frequency (ω = qB/m for non-relativistic motion) to insure the right polarity of the dees. The largest cyclotron accelerator is 18m in diameter located at the university of British Columbia (TRIUMF) and can produce protons with energies of 500MeV.

AC Linear Accelerator

Particles pass through a series of metal pipes called drift tubes, located in a vacuum vessel. The drift tubes are successively connected to alternate terminals of an r.f. source. The r.f. frequency is adjusted such that when the ions come into the gap between two drift tubes, the potential on both tubes accelerate the ion forward. The increasing length of the tubes insures that the ions reach the gap in-sync with the r.f. frequency as the ions pick up speed. The largest electron linear accelerator (SLAC) in Stanford, USA is 3km long and can attain maximum energy of 50GeV.

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Synchrotron Accelerator Synchrotron accelerators work much like linear accelerators except that the beam path is circular. This is done by arrays of dipole magnets called bending magnets. Acceleration is achieved as the beam repeatedly traverses one or more cavities placed in the ring. Particles traveling in a circular orbit continuously emit radiation (synchrotron radiation) and thus continuously lose energy. The amount of energy radiated per turn by a relativistic particle of mass m is proportional to 1/m4. For electrons the losses are severe. Reducing the curvature of the ion beam reduces energy lose due to radiation. The largest synchrotron accelerator is in Geneva on the border of France and Switzerland. It is 27km in circumference and can produce protons with energy 7TeV and lead nuclei with energy 574TeV

Cyclotron Frequency of Relativistic Particles

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Note that the cyclotron frequency now depends on the speed of the particle. Since the particle is being accelerated the r.f. frequency must be reduced with time or the magnetic field must be increased to keep in sync.

To find the cyclotron frequency we set the centripetal force equal to the Lorentz force

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Using the expression for the relativistic momentum we have

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Available Energy for producing new particles

In particle collision we often want to know what is the available energy for producing new particles. A simple method for finding this value is by considering the following scalar quantity Where is the total relativistic energy of the particle. This scalar quantity is the same in all inertial reference frame. If we consider the center of mass frame, where the total momentum of the two colliding particles is zero, we have Note that in this frame all the energy can be used to produce new particles since the momentum after the collision is zero (no energy is needed to conserve momentum). We see that can be regarded as the rest mass or invariant mass of the two colliding particles.

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Example consider a collision involving a projectile colliding with a fix target particle as observed in the laboratory reference frame. Writing down s in this frame we get Which can be re-expressed as The invariant mass is therefore, For high energies of the incident particle the expression reduces to This is the mass available for converting into new particles. It depends on The rest of the incident energy is used to conserve momentum. To maximize the available energy for producing new particles, beams of equal and opposite momentum are used.

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Particle Detectors

Atlas, one of four detector at the LHC in Geneva, Switzerland.

Gas Detectors (Cloud Chamber) Particles directed into a cloud chamber collide with supersaturated vapours such as water or alcohol and produce ions. These ions act as condensation centers, around which a mist forms, because the mixture is at the point of condensation. The mist allows an observer to visualize the trajectory of particles. This apparatus is typically placed in a magnetic field perpendicular to the plane of motion in order to extract particle momentum from the curvature of its path. This was discuss during cyclotron motion. Apart from the observed curvature, different particles have distinctive track features. For instance alpha particles have thicker tracks as a result of scattering effects.

Gas Detectors (Multiwire Proportional Counter)

These detectors consist of arrays of wires with a large potential across them. Incoming particles ionize inert gas (ex. Ar) atoms in the chamber creating electron-ion pairs. The electric potential on the anodes accelerate the ions and electrons which then collide into other inert atoms causing secondary ionization (Townsend avalanche). The large number of ions produced registers a measurable current on nearby anodes. The output signal at the anode is proportional to the energy lost by the original particle. The trajectory of the particle can be found by noting the locations of the activated anodes. MWPC have spatial resolution of 200μm or less, and time resolutions of about 3ns.

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Particle traversing through suitable materials excite a small fraction of atoms within the medium. Subsequently these atoms de-excite emitting light, which can then be detected by a photo detector. One of the most important examples of a photo detector is the photomultiplier tube shown below. An in coming photon strikes a cathode ejecting an electron due to the photoelectric effect. A large electric potential is set up across a series of dynodes accelerate the electron which then collides with the first dynode producing more electrons as a result of the gained energy. These electron are then accelerated to a second dynode and so on producing an avalanche of electrons, which can then be detected by an ammeter. The most efficient PMTs can detect a single Photon. A scintillation counter can even detect a neutron if the appropriate material is used.

Scintillation Counters

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Identifying Particles Typically, particles are identified by their mass. A particle’s mass can be determined by the simultaneous measurement of its momentum together with some other quantity, such as velocity or energy. The momentum of a particle is usually determined from the curvature of its track in an applied magnetic field. such an apparatus is called a spectrometer. A simple means of measuring the particles velocity is measuring the time of flight of the particle between two points. This can be done by using two scintillation counters placed a distance L apart. The more common apparatus used for measuring velocities of particle is called the Cerenkov counter. When a charged particle with velocity v traverses a dispersive medium faster than the speed of light in that medium, the medium radiates at a characteristic angle θ with respect to the direction of motion. This angle of radiation is related to the velocity of the particle by cos(θ) = c/vn, where n is the refractive index of the medium. An apparatus that detects particle energy is called a calorimeter. Scintillation counters and multiwired proportional counters can be used as calorimeter since these devices can measure energy losses. Calorimeter can also measure energies of neutral particles.

Neutrino Detectors Neutrinos can be detected with extreme difficulty because they interact only weakly with matter. Electron neutrinos and antineutrinos of sufficient energy can be detected by observing the inverse β-decay processes. The probability of these processes occurring is extremely small. The mean free path of a 1MeV neutrino in matter is 106 km. The Super Kamiokande detector is a tank containing about 50 000 metric tons of very pure water buried deep under a mountain in Japan. This protect the detector from cosmic ray muons. The walls of the tank are lined with 11 200 photomultipliers, which detect the presence of electron and muons produced in the weak interaction by detecting the light from Cerenkov radiation.

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