THE PHYSICS OF ACCELERATORS

Porter Johnson


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The great advances in building accelerators in the twentieth century are extensions of the advances in vacuum technology, which began during the latter part of the nineteenth century.  Particles were accelerated in electric fields through an evacuated region of space, such as the interior of a vacuum tube. A beam of particles passing through air would quickly get destroyed through scattering and absorption, so that vacuum technology necessarily preceded the development of accelerators.

The natural unit of energy of an elementary particle, such as an electron or a proton, is the electron Volt (eV), the energy given to a particle of unit charge (e =1.6 ´ 10-19 Coulombs) in traveling through a potential difference of one Volt: 1 eV = 1.6 ´ 10-19 Joules.  The energies available in electron and proton accelerators have steadily increased over the years, and today machines are being operated at energies of about 1 Tera electron Volt (TeV)  = 1012 eV.

The use of particle accelerators to produce, identify, and study the elementary constituents of matter has revolutionized our conception of matter. Particle accelerators have also stimulated a wide variety of technological applications throughout the twentieth century, which continue at an increasing pace today.

Types of Accelerators
Cathode Ray Tubes
The original vacuum tube was invented by Heinrich Geissler in the 1850s, but it was perfected as a laboratory device by Sir William Crookes and exhibited in 1879.  Actually, Crookes combined his development of vacuum tubes with his pursuit of spiritualism, believing that the ghostly images of light coming from vacuum tubes, evocative of the Northern Lights, were a manifestation of the soul.  The vacuum tube was used by J J Thompson to discover the electron and proton, and to measure their charge-to-mass ratios by deflecting the beams in a magnetic field.  The X-ray tube was developed by accelerating electrons to a few kilo electron Volts (keV), to strike a suitably dense metallic target. The X-ray tube was quickly employed for basic research, as well as for practical applications in medical diagnostics.  The ordinary vacuum tube spearheaded the development of  radio and television, and stimulated the growth of the telecommunications industry. 

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Linear Accelerators
The simplest type of accelerator is the Cockroft-Walton machine, in which ions are passed through sets of aligned electrodes that are staged to operate at successively higher fixed potentials.  A source of ions (e.g., hydrogen gas) is located at one end, electrodes in the middle, and perhaps a target at the other end.  These machines are limited to energies of about 1 MeV, because at higher energies Voltage breakdown and discharge will occur.  Cockroft-Walton machines are often employed as high current injectors -- about 1 mA (milli-Ampère) -- in the first step in the multi-stage process of accelerating ions to higher energies.

The Van de Graaff accelerator is a similar machine that also involves a DC voltage. A charge sprayer sends ions onto a conveyer belt, which carries positive charges up to a metallic dome, where they reside on the outside.  Positively charged ions are also produced in an ion source within the dome, and then dropped down through an accelerating tube that produces a uniform downward acceleration.  The singly charged ions strike a target at the bottom of the tube with an energy of up to 12 MeV.  As a variation, the Tandem Van de Graaff accelerator uses negative ions, which are first accelerated into the dome, then stripped to become positive ions, and finally accelerated onward (out of the dome to ground potential), thereby doubling the energy available.

In the linear accelerator (Linac) particles are sent through a sequence of metallic drift tubes, in which longitudinal electric fields oscillate at radio frequencies [MHz].  The oscillation of the fields in a particular drift tube is timed to accelerate the particles while they are inside that tube, and the position of the tubes is coordinated to produce an accelerating beam.  Linacs are preferred for accelerating electrons and positrons, in order to reduce the amount of synchrotron radiation.  The longest Linac, 3 kilometers long, is located at the Stanford Linear Accelerator Center (SLAC) in California.  It produces an electron beam of up to 50 GeV.

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Cyclotrons
The cyclotron was invented by the American physicist E O Lawrence in 1929.  A beam of particles of mass m, charge Q, and speed v moves in a uniform circular orbit of radius R in a uniform magnetic field B perpendicular to the plane of motion, under the condition
Ftot  = m acent = m v2 / R = Q v B
Or
w = v / R = Q B / m .
In other words, the angular velocity of the particles is determined by the external field, the charge, and the mass of the particle.  The idea to increase the speed of the particles by reversing the direction of an external field in the plane of motion every half-cycle.  The particles thus spiral outward into orbits or larger radius, until the reach the edge of the cyclotron and are extracted.  Actually, the cyclotron works very well until particles are traveling at a significant fraction of the velocity of light.  In such a circumstances, the frequency of revolution actually decreases, since the effective inertia (mass) of the particles increases, because of relativity.  The synchrocyclotron was develop to compensate partially for the effects of relativity, taking protons up to a kinetic energy of 700 MeV.    Go To Top of Page
Synchrotrons
In contrast to a cyclotron, the particles in a synchrotron move in a (roughly circular) orbit of fixed size.  The beam particles are confined in orbit by a magnetic field, which gradually increases in strength as the particles get higher energies of translation.  An oscillating electric field produces the increase in energy for particles in the "beam bunch".  It is very difficult to maintain a stable beam upon acceleration of the particles in the beam, it would naturally break apart because of the spread in speeds of the particles.  A form of dynamic stability, which was called strong focusing, was developed.  The particles in the beam undergo both longitudinal and transverse oscillations, and beam stability is maintained.   The principle of strong focusing was developed independently in the early 1950s by Nicholas Christofolos, and by the research team of Earnest Courant, Stanley Livingston, and Harland Snyder.  It was first applied in the construction of the 30 GeV Alternating Gradient Synchrotron at Brookhaven National Laboratory in the late 1950s.  Incidentally, charged particles moving in circular orbits emit synchrotron radiation.  The amount of radiation is proportional to the square of the particle charge, and it increases quite rapidly as the particle speed approaches the speed of light.  Because electrons of a given energy are moving much more quickly than protons of the same energy, they generally emit much more synchrotron radiation.  Thus, synchrotrons are more naturally applied to accelerate protons than  to accelerate electrons.

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Storage Rings  
The storage ring was first developed in 1961 at Frascati Laboratory (Italy) by Bruno Touschek, a Jewish student of Werner Heisenberg who spent time in a concentration camp during World War II.  The idea was to accelerate electrons and positrons in the same ring, the particles moving with the same speed in opposite directions.  The particles and antiparticles interact at the intersection points of the beams. The advantage of the storage ring is that the particles have higher center of mass energies in a storage ring, since when an ultra-relativistic beam hits a fixed target, most of the beam energy goes into energy of motion of the decay fragments, rather than in energy of interaction. The Large Electron Positron collider (LEP) at CERN produces beam energies as large as 200 GeV,  The beam at LEP lies underground along the France-Switzerland border; its circumference is about 27 kilometers.

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X-ray Sources
When electrons are knocked out of atom by an energetic beam of particles, X-rays of definite energies are emitted as the atomic electrons are rearranged.  For example, in an ionized atom of atomic number Z, the Ka emission line corresponds to an energy of (Z-1)2 ´ 10.2 eV.  Thus, for Z > 10, X-rays in the kilo-Volt (keV) range are emitted.  These X-rays may be used to locate particular elements in a sample in, for example, medical diagnostic tests.  In addition, X-rays in the kilo-Volt range may be used to study the regular pattern of atoms in a crystalline solid, through Bragg Scattering.from various planes of atoms in the lattice. Because of the precision of this technique, small crystals have been prepared using many naturally non-crystalline substances, to determine the underlying molecular structure through X-ray diffraction.  The most famous and important of these investigations involved determination of the double-helical structure of DNA by Watson and Crick.  Because of the wide variety of applications in imaging, X-ray sources of greater and greater intensities have been developed over the years.  The original  X-ray tubes involved crashing kilo-Volt electron beams against large Z metallic targets.  More recently, sources have been developed to produce synchrotron radiation, which is emitted by charged particles in circular accelerators.  At first this synchrotron radiation was considered as a nuisance that merely robs energy from the particles in the beam, but it gradually came to be appreciated in its own right, as a well-collimated, polarized, tunable source of X-rays.  At first, synchrotron radiation was studied in "parisitic mode" at synchrotrons dedicated to acceleration of charged particles, but today there are many machines dedicated completely to synchrotron radiation. The electrons circulate in the beam and are never extracted; their sole purpose is to emit synchrotron radiation.

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Free Electron Laser
Excerpt from the University of California Santa Barbara website on its Free Electron Laser: http://sbfel3.ucsb.edu/www/vl_fel.html:
"A Free Electron Laser generates tunable, coherent, high power radiation, currently spanning wavelengths from millimeter to visible and potentially ultraviolet to x-ray. It can have the optical properties characteristic of conventional lasers such as high spatial coherence and a near diffraction limited radiation beam. It differs from conventional lasers in using a relativistic electron beam as its lasing medium, as opposed to bound atomic or molecular states, hence the term free-electron."

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Cosmic Acceleration
Lightning is an electrical discharge in the earth's atmosphere, in which electrons may acquire a kinetic energy of a few hundred MeV [Mega electron Volts].  Indeed, a beam of charged particles in that energy range may be shot upward from the ground in order to induce such an electrical discharge.  In addition, the Northern Lights are produced by electrons trapped in the Van Allen Belts in the earth's ionosphere, which preferentially discharge in the polar regions.

An even more energetic form of charged particles were discovered by Victor Hess in 1912, as a result of a daring balloon flight from Vienna to Berlin.  Traveling with a radiation counter (gold leaf electroscope) to a height of 5300 meters (17500 feet) above sea level without oxygen, he noted that the amount of radiation increased as the balloon rose in the atmosphere.  He concluded that this radiation was from outer space, and it came to be called "cosmic radiation".

Cosmic rays consist mostly of charged particles, with less than 1% being photons (gamma rays).  The energies range from a 109 to 1020 eV, so that cosmic rays must originate from a celestial accelerator, with much more energy than the terrestrial variety.  Cosmic rays of lower energies are quite plentiful (many thousand striking the earth per square meter per second), becoming increasingly rare with increasing energies (one per square kilometer per century at the highest energy range).

While some of the lower energy cosmic rays come from the sun, it has been clear for a long time that the more energetic ones arise from outside our solar system.  The source and mechanism of cosmic rays remains somewhat of a mystery, despite important insights gained through intense investigations. There should be a natural cutoff in cosmic rays at an energy a little above 1020 eV, as a result of inelastic scattering from the 2.7K cosmic microwave background, which was discovered by Penzias and Wilson in 1966.

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References

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