Physicists use particle accelerators to study the nature of matter and energy. The massive machines accelerate charged particles (ions) through an electric field in a hollow, evacuated tube, eventually colliding each ion with a stationary target or another moving particle. Scientists analyze the results of the collisions, attempting to probe the interactions governing the subatomic world. (The collision point is usually located in a bubble chamber, a device that records the tracks of ionizing particles as rows of tiny bubbles in a liquid-filled chamber.) The paths of the accelerating particles may be straight, spiral, or circular. Both the cyclotron(spiral path) and the synchrotron (circular path) use an increasingly strong magnetic field to control the paths of particles. Although smashing particles may initially appear to be an odd technique of studying them, particle accelerators have enabled scientists to learn more about the subatomic world than any other device. Particle Accelerators are devices used to accelerate charged elementary particles or ions to high energies. Particle accelerators today are some of the largest and most expensive instruments used by physicists. They all have the same three basic parts:

Charged particles can be accelerated by an electrostatic field. For example, by placing electrodes with a large potential difference at each end of an evacuated tube, British scientists John D. Cockcroft and Ernest Walton were able to accelerate protons to 250,000 eV .Another electrostatic accelerator is the Van de Graaff accelerator, which was developed in the early1930s by the American physicist Robert Jemison Van de Graaff. This accelerator uses the same principles as the Van de Graaff Generator. The Van de Graaff accelerator builds up a potential between two electrodes by transporting charges on a moving belt.Van de Graaff accelerators can accelerate particles to energies as high as 15 MeV (15 million electron volts).

Here are the different types of accelerator:


Another machine, first conceived in the late 1920s, is the linear accelerator, or linac, which uses alternating voltages of high magnitude to push particles along in a straight line. Particles pass through a line of hollow metal tubes enclosed in an evacuated cylinder. An alternating voltage is timed so that a particle is pushed forward each time it goes through a gap between two of the metal tubes. Theoretically, a linac of any energy can be built. The largest linac in the world, at Stanford University, is 3.2 km (2 mi) long. It is capable of accelerating electrons to an energy of 50 GeV (50 billion, or giga, electron volts). Stanford's linac is designed to collide two beams of particles accelerated on different tracks of the accelerator.


The American physicist Ernest O. Lawrence won the 1939 Nobel Prize in physics for a breakthrough in accelerator design in the early 1930s. He developed the cyclotron, the first circular accelerator. A cyclotron is somewhat like a linac wrapped into a tight spiral. Instead of many tubes, the machine has only two hollow vacuum chambers, called dees, that are shaped like capital letter Ds back to back .A magnetic field, produced by a powerful electromagnet, keeps the particles moving in a circle. Each time the charged particles pass through the gap between the dees, they are accelerated. As the particles gain energy, they spiral out toward the edge of the accelerator until they gain enough energy to exit the accelerator.

Q1) Explain why the particles are accelerated as the move across the gap but move at constant radius in either dee.

Q2) Show that the maximum speed a proton could have in a dee of radius R and strength B is given by (ignoring relativistic effects.)

vm = BeR / mp

Q3)Evaluate this for protons in a 1.20m diameter cyclotron of field strength 0.50T. Hence show that the frequency of the alternating p.d must be 7.61 MHz.

When nuclear particles in a cyclotron gain an energy of 20 MeV or more, they become appreciably more massive, as predicted by the theory of relativity. This tends to slow them down and throws the acceleration pulses at the gaps between the dees out of phase. The solution, the synchrocyclotron, is sometimes called the frequency modulated cyclotron. In this instrument, the oscillator (radio-frequency generator) that accelerates the particles around the dees is automatically adjusted to stay in step with the accelerated particles; as the particles gain mass, the frequency of accelerations is lowered slightly to keep in step with them. As the maximum energy of a synchrocyclotron increases, so must its size, for the particles must have more space in which to spiral.


When electrons are accelerated, they undergo a large increase in mass at a relatively low energy. At 1 MeV energy, an electron weighs two and one-half times as much as an electron at rest. Synchrocyclotrons cannot be adapted to make allowance for such large increases in mass.

Q4) Using the relativistic formula for mass, calculate the speed of an electron that has a mass two and a half times its rest mass.

Therefore, another type of cyclic accelerator, the betatron, is employed to accelerate electrons. The betatron consists of a doughnut-shaped evacuated chamber placed between the poles of an electromagnet. The electrons are kept in a circular path by a magnetic field called a guide field. By applying an alternating current to the electromagnet, the electromotive force induced by the changing magnetic flux through the circular orbit accelerates the electrons. During operation, both the guide field and the magnetic flux are varied to keep the radius of the orbit of the electrons constant.


The synchrotron is the most recent and most powerful member of the accelerator family. A synchrotron consists of a tube in the shape of a large ring through which the particles travel; the tube is surrounded by magnets that keep the particles moving through the center of the tube. The particles enter the tube after already having been accelerated to several million electron volts. Particles are accelerated at one or more points on the ring each time the particles make a complete circle around the accelerator. To keep the particles in a rigid orbit, the strengths of the magnets in the ring are increased as the particles gain energy. In a few seconds, the particles reach energies greater than 1 GeV and are ejected, either directly into experiments or toward targets that produce a variety of elementary particles when struck by the accelerated particles. The synchrotron principle can be applied to either protons or electrons, although most of the large machines are proton-synchrotrons.


Q5) Show that the radius of curvature of the path of particles of momentum p and
charge q in a synchrotron is given by the formula R = p / q B where B is the field strength.

Q6) A synchrotron of radius R has four straight sections of length L each. If the period of the radio frequency oscillator corresponds to the time of one revolution,show that

(a) The speed of the particles must be

v = ( 2pR + 4L ) f

(b) by considering the relativistic momentum of particles of mass M , that the magneticfield strength of the synchrotron is given by

In synchrotrons a computer is used to maintain this relation between magnetic field and oscillator frequency.

By the early 1980s, the two largest proton-synchrotrons were a 500-GeV device at CERN and a similar one at the Fermi National Accelerator Laboratory (Fermilab) near Batavia, Illinois. The capacity of the latter, called Tevatron, was increased to a potential 1 TeV (trillion, or tera, eV) in 1983 by installing superconducting magnets, making it the most powerful accelerator in the world. In 1989, CERN began operating the Large-Electron Positron Collider (LEP), a 27-km (16.7-mi) ring that can accelerate electrons and positrons to an energy of 50 GeV.


A storage ring collider accelerator is a synchrotron that produces more energetic collisions between particles than a conventional synchrotron, which slams accelerated particles into a stationary target. A storage ring collider accelerates two sets of particles that rotate in opposite directions in the ring, then collides the two sets of particles. CERN's Large Electron-Positron Collider is a storage ring collider. In 1987, Fermilab converted the Tevatron into a storage ring collider and installed a three-story-high detector that observed and measured the products of the head-on particle collisions.


Accelerators are used to explore atomic nuclei, thereby allowing nuclear scientists to identify new elements and to explain phenomena that affect the entire nucleus. Machines exceeding 1 GeV are used to study the fundamental particles that compose the nucleus.
Several hundred of these particles have been identified. High-energy physicists hope
to discover rules or principles that will permit an orderly arrangement of the proportion of subnuclear particles. Such an arrangement would be as useful to nuclear science as the periodic table of the chemical elements is to chemistry. Fermilab's accelerator and collider detector permit scientists to study violent particle collisions that mimic thestate of the universe when it was just microseconds old. Continued study of their findings should increase scientific understanding of the structure of the universe.

Collision Problem based on the decay scheme below: