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In an X-ray generator, the target itself is one of the electrodes. A low-energy particle accelerator called an ion implanter is used in the manufacture of integrated circuits. At lower energies, beams of accelerated nuclei are also used in medicine as particle therapy , for the treatment of cancer. DC accelerator types capable of accelerating particles to speeds sufficient to cause nuclear reactions are Cockcroft-Walton generators or voltage multipliers , which convert AC to high voltage DC, or Van de Graaff generators that use static electricity carried by belts.

Historically, the first accelerators used simple technology of a single static high voltage to accelerate charged particles. The charged particle was accelerated through an evacuated tube with an electrode at either end, with the static potential across it. Since the particle passed only once through the potential difference, the output energy was limited to the accelerating voltage of the machine. While this method is still extremely popular today, with the electrostatic accelerators greatly out-numbering any other type, they are more suited to lower energy studies owing to the practical voltage limit of about 1 MV for air insulated machines, or 30 MV when the accelerator is operated in a tank of pressurized gas with high dielectric strength , such as sulfur hexafluoride.

In a tandem accelerator the potential is used twice to accelerate the particles, by reversing the charge of the particles while they are inside the terminal. This is possible with the acceleration of atomic nuclei by using anions negatively charged ions , and then passing the beam through a thin foil to strip electrons off the anions inside the high voltage terminal, converting them to cations positively charged ions , which are accelerated again as they leave the terminal.

The two main types of electrostatic accelerator are the Cockcroft-Walton accelerator , which uses a diode-capacitor voltage multiplier to produce high voltage, and the Van de Graaff accelerator , which uses a moving fabric belt to carry charge to the high voltage electrode. Although electrostatic accelerators accelerate particles along a straight line, the term linear accelerator is more often used for accelerators that employ oscillating rather than static electric fields.

Due to the high voltage ceiling imposed by electrical discharge, in order to accelerate particles to higher energies, techniques involving dynamic fields rather than static fields are used. Electrodynamic acceleration can arise from either of two mechanisms: non-resonant magnetic induction , or resonant circuits or cavities excited by oscillating RF fields.

Magnetic induction accelerators accelerate particles by induction from an increasing magnetic field, as if the particles were the secondary winding in a transformer. The increasing magnetic field creates a circulating electric field which can be configured to accelerate the particles. Induction accelerators can be either linear or circular. Linear induction accelerators utilize ferrite-loaded, non-resonant induction cavities. Each cavity can be thought of as two large washer-shaped disks connected by an outer cylindrical tube. Between the disks is a ferrite toroid. A voltage pulse applied between the two disks causes an increasing magnetic field which inductively couples power into the charged particle beam.

The linear induction accelerator was invented by Christofilos in the s. They have been used to generate X-rays for flash radiography e. The Betatron is circular magnetic induction accelerator, invented by Donald Kerst in for accelerating electrons. These machines, like synchrotrons, use a donut-shaped ring magnet see below with a cyclically increasing B field, but accelerate the particles by induction from the increasing magnetic field, as if they were the secondary winding in a transformer, due to the changing magnetic flux through the orbit.

Achieving constant orbital radius while supplying the proper accelerating electric field requires that the magnetic flux linking the orbit be somewhat independent of the magnetic field on the orbit, bending the particles into a constant radius curve. These machines have in practice been limited by the large radiative losses suffered by the electrons moving at nearly the speed of light in a relatively small radius orbit.

In a linear particle accelerator linac , particles are accelerated in a straight line with a target of interest at one end. They are often used to provide an initial low-energy kick to particles before they are injected into circular accelerators. SLAC is an electron - positron collider. Linear high-energy accelerators use a linear array of plates or drift tubes to which an alternating high-energy field is applied.

PARTICLE ACCELERATOR PHYSICS. - Tome 1, Basic de Helmut Wiedemann - Livre - Decitre

As the particles approach a plate they are accelerated towards it by an opposite polarity charge applied to the plate. As they pass through a hole in the plate, the polarity is switched so that the plate now repels them and they are now accelerated by it towards the next plate. Normally a stream of "bunches" of particles are accelerated, so a carefully controlled AC voltage is applied to each plate to continuously repeat this process for each bunch.

As the particles approach the speed of light the switching rate of the electric fields becomes so high that they operate at radio frequencies , and so microwave cavities are used in higher energy machines instead of simple plates. Linear accelerators are also widely used in medicine , for radiotherapy and radiosurgery.

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The electrons can be used directly or they can be collided with a target to produce a beam of X-rays. The reliability, flexibility and accuracy of the radiation beam produced has largely supplanted the older use of cobalt therapy as a treatment tool.

In the circular accelerator, particles move in a circle until they reach sufficient energy. The particle track is typically bent into a circle using electromagnets. The advantage of circular accelerators over linear accelerators linacs is that the ring topology allows continuous acceleration, as the particle can transit indefinitely. Another advantage is that a circular accelerator is smaller than a linear accelerator of comparable power i. Depending on the energy and the particle being accelerated, circular accelerators suffer a disadvantage in that the particles emit synchrotron radiation.

When any charged particle is accelerated, it emits electromagnetic radiation and secondary emissions. As a particle traveling in a circle is always accelerating towards the center of the circle, it continuously radiates towards the tangent of the circle. This radiation is called synchrotron light and depends highly on the mass of the accelerating particle.

For this reason, many high energy electron accelerators are linacs. Certain accelerators synchrotrons are however built specially for producing synchrotron light X-rays. Since the special theory of relativity requires that matter always travels slower than the speed of light in a vacuum , in high-energy accelerators, as the energy increases the particle speed approaches the speed of light as a limit, but never attains it. Therefore, particle physicists do not generally think in terms of speed, but rather in terms of a particle's energy or momentum , usually measured in electron volts eV.

An important principle for circular accelerators, and particle beams in general, is that the curvature of the particle trajectory is proportional to the particle charge and to the magnetic field, but inversely proportional to the typically relativistic momentum.

The earliest operational circular accelerators were cyclotrons , invented in by Ernest Lawrence at the University of California, Berkeley. Cyclotrons have a single pair of hollow 'D'-shaped plates to accelerate the particles and a single large dipole magnet to bend their path into a circular orbit.


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It is a characteristic property of charged particles in a uniform and constant magnetic field B that they orbit with a constant period, at a frequency called the cyclotron frequency , so long as their speed is small compared to the speed of light c. This means that the accelerating D's of a cyclotron can be driven at a constant frequency by a radio frequency RF accelerating power source, as the beam spirals outwards continuously. The particles are injected in the centre of the magnet and are extracted at the outer edge at their maximum energy. Cyclotrons reach an energy limit because of relativistic effects whereby the particles effectively become more massive, so that their cyclotron frequency drops out of synch with the accelerating RF.

If accelerated further, the beam would continue to spiral outward to a larger radius but the particles would no longer gain enough speed to complete the larger circle in step with the accelerating RF. To accommodate relativistic effects the magnetic field needs to be increased to higher radii as is done in isochronous cyclotrons.

The advantage of such a cyclotron is the maximum achievable extracted proton current which is currently 2. The energy and current correspond to 1. A classic cyclotron can be modified to increase its energy limit. The historically first approach was the synchrocyclotron , which accelerates the particles in bunches. This approach suffers from low average beam intensity due to the bunching, and again from the need for a huge magnet of large radius and constant field over the larger orbit demanded by high energy. The second approach to the problem of accelerating relativistic particles is the isochronous cyclotron.

In such a structure, the accelerating field's frequency and the cyclotron resonance frequency is kept constant for all energies by shaping the magnet poles so to increase magnetic field with radius.

Particle accelerator

Thus, all particles get accelerated in isochronous time intervals. Higher energy particles travel a shorter distance in each orbit than they would in a classical cyclotron, thus remaining in phase with the accelerating field. The advantage of the isochronous cyclotron is that it can deliver continuous beams of higher average intensity, which is useful for some applications.

The main disadvantages are the size and cost of the large magnet needed, and the difficulty in achieving the high magnetic field values required at the outer edge of the structure. To reach still higher energies, with relativistic mass approaching or exceeding the rest mass of the particles for protons, billions of electron volts or GeV , it is necessary to use a synchrotron. This is an accelerator in which the particles are accelerated in a ring of constant radius.

An immediate advantage over cyclotrons is that the magnetic field need only be present over the actual region of the particle orbits, which is much narrower than that of the ring. The largest cyclotron built in the US had a inch-diameter 4. The aperture of the two beams of the LHC is of the order of a centimeter. However, since the particle momentum increases during acceleration, it is necessary to turn up the magnetic field B in proportion to maintain constant curvature of the orbit.

In consequence, synchrotrons cannot accelerate particles continuously, as cyclotrons can, but must operate cyclically, supplying particles in bunches, which are delivered to a target or an external beam in beam "spills" typically every few seconds. Since high energy synchrotrons do most of their work on particles that are already traveling at nearly the speed of light c , the time to complete one orbit of the ring is nearly constant, as is the frequency of the RF cavity resonators used to drive the acceleration.

In modern synchrotrons, the beam aperture is small and the magnetic field does not cover the entire area of the particle orbit as it does for a cyclotron, so several necessary functions can be separated. Instead of one huge magnet, one has a line of hundreds of bending magnets, enclosing or enclosed by vacuum connecting pipes. The design of synchrotrons was revolutionized in the early s with the discovery of the strong focusing concept. Also, there is no necessity that cyclic machines be circular, but rather the beam pipe may have straight sections between magnets where beams may collide, be cooled, etc.

This has developed into an entire separate subject, called "beam physics" or "beam optics". This specific ISBN edition is currently not available. View all copies of this ISBN edition:. Synopsis About this title Rare Book "synopsis" may belong to another edition of this title. From the Back Cover : Particle Accelerator Physics is an in-depth and comprehensive introduction to the field of high-energy particle acceleration and beam dynamics. Synopsis : This work is designed to serve as an introduction to the field of high-energy particle accelerator physics and particle-beam dynamics.

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