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| New Aircraft | ionic_Engine | Atomic_Model | New Doppler | My Journal | My Articles | Storms | Man's Lightning |
| New Aircraft | ionic_Engine | Atomic_Model | New Doppler | My Journal | My Articles | Storms | Man's Lightning |
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 relatively smaller than a linear accelerator of comparable power (i.e. a linac would have to be extremely long to have the equivalent power of a circular accelerator).
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, never quite attained. 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 circular accelerators were cyclotrons, invented in 1929 by Ernest O. 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. 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. Therefore simple cyclotrons can accelerate protons only to an energy of around 15 million electron volts (15 MeV, corresponding to a speed of roughly 10% of c), because the protons get out of phase with the driving electric field. 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. Cyclotrons are nevertheless still useful for lower energy applications.
There are ways of modifying the classic cyclotron to increase the energy limit. This may be done in a continuous beam, constant frequency, machine by shaping the magnet poles so to increase magnetic field with radius. Then higher energy particles travel a shorter distance in each orbit than they otherwise would, and can remain in phase with the accelerating field. Such machines are called isochronous cyclotrons. Their advantage is that they 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 higher field required at the outer edge.
Another possibility, the synchrocyclotron, accelerates the particles in bunches, in a constant B field, but reduces the RF accelerating field's frequency so as to keep the particles in step as they spiral outward. 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.
Another type of circular accelerator, invented in 1940 for accelerating electrons, is the Betatron. 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.
To reach still higher energies, with relativistic mass approaching or exceeding the rest mass of the particles (for protons, billions of electron volts 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 very much narrower than the diameter of the ring. (The largest cyclotron built in the US had a 184 in dia magnet pole, whereas the diameter of the LEP and LHC is nearly 10 km. The aperture of the beam of the latter is of the order of centimeters.)
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.
Note also a further point about modern synchrotrons: because 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, 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 focusing of the beam is handled independently by specialized quadrupole magnets, while the acceleration itself is accomplished in separate RF sections, rather similar to short linear accelerators. 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.
More complex modern synchrotrons such as the Tevatron, LEP, and LHC may deliver the particle bunches into storage rings of magnets with constant B, where they can continue to orbit for long periods for experimentation or further acceleration. The highest-energy machines such as the Tevatron and LHC are actually accelerator complexes, with a cascade of specialized elements in series, including linear accelerators for initial beam creation, one or more low energy synchrotrons to reach intermediate energy, storage rings where beams can be accumulated or "cooled" (reducing the magnet aperture required and permitting tighter focusing; see beam cooling), and a last large ring for final acceleration and experimentation.
Circular electron accelerators fell somewhat out of favor for particle physics around the time that SLAC was constructed, because their synchrotron losses were considered economically prohibitive and because their beam intensity was lower than for the unpulsed linear machines. The Cornell Electron Synchrotron, built at low cost in the late 1960s, was the first in a series of high-energy circular electron accelerators built for fundamental particle physics, culminating in the LEP at CERN.
A large number of electron synchrotrons have been built in the past two decades, specialized to be synchrotron light sources, of ultraviolet light and X rays; see below.
For some applications, it is useful to store beams of high energy particles for some time (with modern high vacuum technology, up to many hours) without further acceleration. This is especially true for colliding beam accelerators, in which two beams moving in opposite directions are made to collide with each other, with a large gain in effective collision energy. Because relatively few collisions occur at each pass through the intersection point of the two beams, it is customary to first accelerate the beams to the desired energy, and then store them in storage rings, which are essentially synchrotron rings of magnets, with no significant RF power for acceleration.
Some circular accelerators have been built to deliberately generate radiation (called synchrotron light) as X-rays also called synchrotron radiation, for example the Diamond Light Source being built at the Rutherford Appleton Laboratory in England or the Advanced Photon Source at Argonne National Laboratory in Illinois, USA. High-energy X-rays are useful for X-ray spectroscopy of proteins or X-ray absorption fine structure (XAFS) for example.
Synchrotron radiation is more powerfully emitted by lighter particles, so these accelerators are invariably electron accelerators. Synchrotron radiation allows for better imaging as researched and developed at SLAC's SPEAR.
Lawrence's first cyclotron was a mere 4 inches (100 mm) in diameter. Later he built a machine with a 60 in dia pole face, and planned one with a 184-inch dia, which was, however, taken over for World War II-related work connected with uranium isotope separation; after the war it continued in service for research and medicine over many years.
The first large proton synchrotron was the Cosmotron at Brookhaven National Laboratory, which accelerated protons to about 3 GeV. The Bevatron at Berkeley, completed in 1954, was specifically designed to accelerate protons to sufficient energy to create anti-protons, and verify the particle-antiparticle symmetry of nature, then only strongly suspected. The Alternating Gradient Synchrotron (AGS) at Brookhaven was the first large synchrotron with alternating gradient, "strong focusing" magnets, which greatly reduced the required aperture of the beam, and correspondingly the size and cost of the bending magnets. The Proton Synchrotron, built at CERN, was the first major European particle accelerator and generally similar to the AGS.
The Fermilab Tevatron has a ring with a beam path of 4 miles (6 km). The largest circular accelerator ever built was the LEP synchrotron at CERN with a circumference 26.6 kilometers, which was an electron/positron collider. It has been dismantled and the underground tunnel is being reused for a proton/antiproton collider called the LHC, due to start operation in at the end of July 2008. The aborted Superconducting Super Collider (SSC) in Texas would have had a circumference of 87 km. Construction was started in 1991, but abandoned in 1993. Very large circular accelerators are invariably built in underground tunnels a few metres wide to minimize the disruption and cost of building such a structure on the surface, and to provide shielding against intense secondary radiations that may occur. These are extremely penetrating at high energies.
Current accelerators such as the Spallation Neutron Source, incorporate superconducting cryomodules. The Relativistic Heavy Ion Collider, and upcoming Large Hadron Collider also make use of superconducting magnets and RF cavity resonators to accelerate particles.
The output of a particle accelerator can generally be directed towards multiple lines of experiments, one at a given time, by means of a deviating electromagnet. This makes it possible to operate multiple experiments without needing to move things around or shutting down the entire accelerator beam. Except for synchrotron radiation sources, the purpose of an accelerator is to generate high-energy particles for interaction with matter.
This is usually a fixed target, such as the phosphor coating on the back of the screen in the case of a television tube; a piece of uranium in an accelerator designed as a neutron source; or a tungsten target for an X-ray generator. In a linac, the target is simply fitted to the end of the accelerator. The particle track in a cyclotron is a spiral outwards from the centre of the circular machine, so the accelerated particles emerge from a fixed point as for a linear accelerator.
For synchrotrons, the situation is more complex. Particles are accelerated to the desired energy. Then, a fast acting dipole magnet is used to switch the particles out of the circular synchrotron tube and towards the target.
A variation commonly used for particle physics research is a collider, also called a storage ring collider. Two circular synchrotrons are built in close proximity - usually on top of each other and using the same magnets (which are then of more complicated design to accommodate both beam tubes). Bunches of particles travel in opposite directions around the two accelerators and collide at intersections between them. This can increase the energy enormously; whereas in a fixed-target experiment the energy available to produce new particles is proportional to the square root of the beam energy, in a collider the available energy is linear.
At present the highest energy accelerators are all circular colliders, but it is likely that limits have been reached in respect of compensating for synchrotron radiation losses for electron accelerators, and the next generation will probably be linear accelerators 10 times the current length. An example of such a next generation electron accelerator is the 40 km long International Linear Collider, due to be constructed between 2015-2020.
As of 2005, it is believed that plasma wakefield acceleration in the form of electron-beam 'afterburners' and standalone laser pulsers will provide dramatic increases in efficiency within two to three decades. In plasma wakefield accelerators, the beam cavity is filled with a plasma (rather than vacuum). A short pulse of electrons or laser light either constitutes or immediately trails the particles that are being accelerated. The pulse disrupts the plasma, causing the charged particles in the plasma to integrate into and move toward the rear of the bunch of particles that are being accelerated. This process transfers energy to the particle bunch, accelerating it further, and continues as long as the pulse is coherent.[3]
Energy gradients as steep as 200 GeV/m have been achieved over millimeter-scale distances using laser pulsers[4] and gradients approaching 1 GeV/m are being produced on the multi-centimeter-scale with electron-beam systems, in contrast to a limit of about 0.1 GeV/m for radio-frequency acceleration alone. Existing electron accelerators such as SLAC could use electron-beam afterburners to greatly increase the energy of their particle beams, at the cost of beam intensity. Electron systems in general can provide tightly collimated, reliable beams; laser systems may offer more power and compactness. Thus, plasma wakefield accelerators could be used — if technical issues can be resolved — to both increase the maximum energy of the largest accelerators and to bring high energies into university laboratories and medical centres.
In the future, the possibility of black hole (BH) production at the highest energy accelerators may arise if certain predictions of superstring theory[5][6] This and other exotic possibilities have led to public safety concerns that have been widely reported in connection with the LHC, which began operation in 2008. The various possible dangerous scenarios have been assessed as presenting "no conceivable danger" in the latest risk assessment produced by the LHC Safety Assessment Group.[7]. If they are produced, it is thought that BHs would evaporate extremely quickly via Bekenstein-Hawking radiation. While the existence of the Bekenstein-Hawking radiation is unconfirmed and somewhat controversial,[8] if colliders can produce BHs, cosmic rays (and particularly ultra-high-energy cosmic rays, UHECRs) must have been producing them for eons, but they have yet to harm us.[9] It has been argued that to conserve energy and momentum, any BHs created in a collision between an UHECR and local matter would necessarily be produced moving at relativistic speed with respect to the Earth, and should escape into space, as their accretion and growth rate should be very slow, while BHs produced in colliders (with components of equal mass) would have some chance of having a velocity less than Earth escape velocity, 11.2 km per sec, and would be liable to capture and subsequent growth. Yet even on such scenarios the collisions of UHECRs with white dwarfs and neutron stars would lead to their rapid destruction, but these bodies are observed to be common astronomical objects. Thus if stable micro black holes should be produced, they must grow far too slowly to cause any noticeable macroscopic effects within the natural lifetime of the solar system.[10] are accurate.
A cyclotron is a type of particle accelerator. Cyclotrons accelerate charged particles using a high-frequency, alternating voltage (potential difference). A perpendicular magnetic field causes the particles to spiral almost in a circle so that they re-encounter the accelerating voltage many times.
Ernest Lawrence, of the University of California, Berkeley, is credited with the development of the cyclotron in 1929, though others had been working along similar lines at the time.
The electrodes shown at the right would be in the vacuum chamber, which is flat, in a narrow gap between the two poles of a large magnet.
In the cyclotron, a high-frequency alternating voltage applied across the "D" electrodes (also called "dees") alternately attracts and repels charged particles. The particles, injected near the center of the magnetic field, accelerate only when passing through the gap between the electrodes. The perpendicular magnetic field (passing vertically through the "D" electrodes), combined with the increasing energy of the particles forces the particles to travel in a spiral path.
With no change in energy the charged particles in a magnetic field will follow a circular path. In the cyclotron, energy is applied to the particles as they cross the gap between the dees and so they are accelerated (at the typical sub-relativistic speeds used) and will increase in mass as they approach the speed of light. Either of these effects (increased velocity or increased mass) will increase the radius of the circle and so the path will be a spiral.
(The particles move in a spiral, because a current of electrons or ions, flowing perpendicular to a magnetic field, experiences a perpendicular force. The charged particles move freely in a vacuum, so the particles follow a spiral path.)
The radius will increase until the particles hit a target at the perimeter of the vacuum chamber. Various materials may be used for the target, and the collisions will create secondary particles which may be guided outside of the cyclotron and into instruments for analysis. The results will enable the calculation of various properties, such as the mean spacing between atoms and the creation of various collision products. Subsequent chemical and particle analysis of the target material may give insight into nuclear transmutation of the elements used in the target.
For several decades, cyclotrons were the best source of high-energy beams for nuclear physics experiments; several cyclotrons are still in use for this type of research.
Cyclotrons can be used to treat cancer. Ion beams from cyclotrons can be used, as in proton therapy, to penetrate the body and kill tumors by radiation damage, while minimizing damage to healthy tissue along their path.
Cyclotron beams can be used to bombard other atoms to produce short-lived positron-emitting isotopes suitable for PET imaging.
The cyclotron was an improvement over the linear accelerators that were available when it was invented. A linear accelerator (also called a linac) accelerates particles in a straight line through an evacuated tube (or series of such tubes placed end to end). A set of electrodes shaped like flat donuts are arranged inside the length of the tube(s). These are driven by high-power radio waves that continuously switch between positive and negative voltage, causing particles traveling along the center of the tube to accelerate. In the 1920s, it was not possible to get high frequency radio waves at high power, so either the accelerating electrodes had to be far apart to accommodate the low frequency or more stages were required to compensate for the low power at each stage. Either way, higher-energy particles required longer accelerators than scientists could afford.
Modern linacs use high power Klystrons and other devices able to impart much more power at higher frequencies. But before these devices existed, cyclotrons were cheaper than linacs.
Cyclotrons accelerate particles in a spiral path. Therefore, a compact accelerator can contain much more distance than a linear accelerator, with more opportunities to accelerate the particles.
The spiral path of the cyclotron beam can only "synch up" with klystron-type (constant frequency) voltage sources if the accelerated particles are approximately obeying Newton's Laws of Motion. If the particles become fast enough that relativistic effects become important, the beam gets out of phase with the oscillating electric field, and cannot receive any additional acceleration. The cyclotron is therefore only capable of accelerating particles up to a few percent of the speed of light. To accommodate increased mass the magnetic field may be modified by appropriately shaping the pole pieces as in the isochronous cyclotrons, operating in a pulsed mode and changing the frequency applied to the dees as in the synchrocyclotrons, either of which is limited by the diminishing cost effectiveness of making larger machines. Cost limitations have been overcome by employing the more complex synchrotron or linear accelerator, both of which have the advantage of scalability, offering more power within an improved cost structure as the machines are made larger.
The centripetal force is provided by the transverse magnetic field B, and the force on a particle travelling in a magnetic field (which causes it to be angularly displaced, i.e spiral) is equal to Bqv. So,
(Where m is the mass of the particle, q is its charge, v is its velocity and r is the radius of its path.)
The speed at which the particles enter the cyclotron due to a potential difference, V.
Therefore,
v/r is equal to angular velocity, ω, so
And since the angular frequency is
Therefore,
This shows that for a particle of constant mass, the frequency does not depend upon the radius of the particle's orbit. As the beam spirals out, its frequency does not decrease, and it must continue to accelerate, as it is travelling more distance in the same time. As particles approach the speed of light, they acquire additional mass, requiring modifications to the frequency, or the magnetic field during the acceleration. This is accomplished in the synchrocyclotron.
The radius of curvature for a particle moving relativistically in a static magnetic field is
the Lorentz factorNote that in high-energy experiments energy, E, and momentum, p, are used rather than velocity, and both measured in units of energy. In that case one should use the substitution,
The relativistic cyclotron frequency is
,The rest mass of an electron is 511 keV, so the frequency correction is 1% for a magnetic vacuum tube with a 5.11 kV direct current accelerating voltage. The proton mass is nearly two thousand times the electron mass, so the 1% correction energy is about 9 MeV, which is sufficient to induce nuclear reactions.
An alternative to the synchrocyclotron is the isochronous cyclotron, which has a magnetic field that increases with radius, rather than with time. The de-focusing effect of this radial field gradient is compensated by ridges on the magnet faces which vary the field azimuthally as well. This allows particles to be accelerated continuously, on every period of the radio frequency, rather than in bursts as in most other accelerator types. This principle that alternating field gradients have a net focusing effect is called strong focusing. It was obscurely known theoretically long before it was put into practice.
A synchrocyclotron is a cyclotron in which the frequency of the driving RF electric field is varied to compensate for the mass gain of the accelerated particles as their velocity begins to approach the speed of light. This is in contrast to the classical cyclotron, where the frequency was held constant.
It differs from a cyclotron in that it has a single D(ee) instead of two Ds.
Synchrocyclotrons have not been built since the isochronous cyclotron was developed.
Isochronous cyclotrons maintain a constant RF driving frequency and compensate for the relativistic mass gain of the accelerated particles by increasing the magnetic field with radius. Isochronous cyclotrons are capable of producing much greater beam current than synchrocyclotrons.
Isochronous cyclotrons require azimuthal variations in the field strength to provide a strong focusing effect and keep the field captured.
SYNCHROCYCLOTRON
The two fundamental differences between this machine and the orthodox cyclotron are that (1) in this machine, only one dee is used instead of two & (2) the frequency of oscillating electric field is made to decrease continuously instead of keeping it constant so as to maintain the resonance with ion frequency. One terminal of the oscillating electric potential varying periodically is applied to the dee and the other terminal is earthed. The proton or deuterons to be accelerated are made to move in circles of increasing radii. The acceleration of particles takes place as they enter or leave D. at the outer edge, the ion beam can be removed with the aid of electrostatic deflector. It was possible to produce 200MeV deuterons and 400MeV α-particle with the first synchrocyclotron
ADVANTAGES
The chief advantage of the synchrocyclotron is that there is no need to restrict the no of revolutions executed by the ion before its exit. As such, the potential difference supplied between the dees can be much smaller.
The smaller potential difference needed across the gap has the following uses: 1. There is no need for a narrow gap between the dees as in the case of convention cyclotron, because strong electric fields for producing large acceleration are not required. Thus only one dee can be used instead of two, the other end of the oscillating voltage supply being connected to earth.
2. The magnetic pole pieces can be brought closer, thus making it possible to increase greatly the magnetic flux density.
3. The frequency valve oscillator is able to function with much greater efficiency.
The main drawback of this device is that, as a result of the variation in the frequency of the oscillating voltage supply, only a very small fraction of the ions leaving the source are captured in phase-table orbits of maximum radius and energy so that the output beam current is rendered weak. Thus the machine produces high energy ions, though of small intensity.
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field (to turn the particles so they circulate) and the electric field (to accelerate the particles) are carefully synchronized with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant[1]. The honour of the first to publish the idea belongs to Vladimir Veksler, and the first electron synchrotron was constructed by Oliphant's supervisor Edwin McMillan.
While a cyclotron uses a constant magnetic field and a constant-frequency applied electric field (one of these is varied in the synchrocyclotron), both of these fields are varied in the synchrotron. By increasing these parameters appropriately as the particles gain energy, their path can be held constant as they are accelerated. This allows the vacuum chamber for the particles to be a large thin torus. In reality it is easier to use some straight sections between the bending magnets and some bent sections within the magnets giving the torus the shape of a round-cornered polygon. A path of large effective radius may thus be constructed using simple straight and curved pipe segments, unlike the disc-shaped chamber of the cyclotron type devices. The shape also allows and requires the use of multiple magnets to bend the particle beams. Straight sections are required at spacings around a ring for both radiofrequency cavities, and in third generation light sources allow space for insertion devices such as wigglers and undulators.
The maximum energy that a cyclic accelerator can impart is typically limited by the strength of the magnetic field(s) and the minimum radius (maximum curvature) of the particle path.
In a cyclotron the maximum radius is quite limited as the particles start at the center and spiral outward, thus this entire path must be a self-supporting disc-shaped evacuated chamber. Since the radius is limited, the power of the machine becomes limited by the strength of the magnetic field. In the case of an ordinary electromagnet the field strength is limited by the saturation of the core (when all magnetic domains are aligned the field may not be further increased to any practical extent). The arrangement of the single pair of magnets the full width of the device also limits the economic size of the device.
Synchrotrons overcome these limitations, using a narrow beam pipe which can be surrounded by much smaller and more tightly focusing magnets. The ability of this device to accelerate particles is limited by the fact that the particles must be charged to be accelerated at all, but charged particles under acceleration emit photons (light), thereby losing energy. The limiting beam energy is reached when the energy lost to the lateral acceleration required to maintain the beam path in a circle equals the energy added each cycle. More powerful accelerators are built by using large radius paths and by using more numerous and more powerful microwave cavities to accelerate the particle beam between corners. Lighter particles (such as electrons) lose a larger fraction of their energy when turning. Practically speaking, the energy of electron/positron accelerators is limited by this radiation loss, while it does not play a significant role in the dynamics of proton or ion accelerators. The energy of those is limited strictly by the strength of magnets and by the cost.
Particles are injected into the main ring at substantial energies by either a linear accelerator or by an intermediate synchrotron which is in turn fed by a linear accelerator. The "linac" is in turn fed by particles accelerated to intermediate energy by a simple high voltage power supply, typically a Cockcroft-Walton generator.
Starting from an appropriate initial value determined by the injection velocity the magnetic field is then increased. The particles pass through an electrostatic accelerator driven by a high alternating voltage. At particle speeds not close to the speed of light the frequency of the accelerating voltage can be made roughly proportional to the current in the bending magnets. A finer control of the frequency is performed by a servo loop which responds to the detection of the passing of the traveling group of particles. At particle speeds approaching light speed the frequency becomes more nearly constant, while the current in the bending magnets continues to increase. The maximum energy that can be applied to the particles (for a given ring size and magnet count) is determined by the saturation of the cores of the bending magnets (the point at which increasing current does not produce additional magnetic field). One way to obtain additional power is to make the torus larger and add additional bending magnets. This allows the amount of particle redirection at saturation to be less and so the particles can be more energetic. Another means of obtaining higher power is to use superconducting magnets, these not being limited by core saturation.
One of the early large synchrotrons, now retired, is the Bevatron, constructed in 1950 at the Lawrence Berkeley Laboratory. The name of this proton accelerator comes from its power, in the range of 6.3 GeV (then called BeV for billion electron volts; the name predates the adoption of the SI prefix giga-). A number of heavy elements, unseen in the natural world, were first created with this machine. This site is also the location of one of the first large bubble chambers used to examine the results of the atomic collisions produced here.
Another early large synchrotron is the Cosmotron built at Brookhaven National Laboratory which reached 3.3 GeV in 1953.[2]
Until August 2008, the highest energy synchrotron in the world was the Tevatron, at the Fermi National Accelerator Laboratory, in the United States. It accelerates protons and antiprotons to slightly less than 1 TeV of kinetic energy and collides them together. The Large Hadron Collider (LHC), which has been built at the European Laboratory for High Energy Physics (CERN), has roughly seven times this energy. It is housed in the 27 km tunnel which formerly housed the Large Electron Positron (LEP) collider, so it will maintain the claim as the largest scientific device ever built. The LHC will also accelerate heavy ions (such as lead) up to an energy of 1.15 PeV.
The largest device of this type seriously proposed was the Superconducting Super Collider (SSC), which was to be built in the United States. This design, like others, used superconducting magnets which allow more intense magnetic fields to be created without the limitations of core saturation. While construction was begun, the project was cancelled in 1994, citing excessive budget overruns — this was due to naïve cost estimation and economic management issues rather than any basic engineering flaws. It can also be argued that the end of the Cold War resulted in a change of scientific funding priorities that contributed to its ultimate cancellation.
While there is still potential for yet more powerful proton and heavy particle cyclic accelerators, it appears that the next step up in electron beam energy must avoid losses due to synchrotron radiation. This will require a return to the linear accelerator, but with devices significantly longer than those currently in use. There is at present a major effort to design and build the International Linear Collider (ILC), which will consist of two opposing linear accelerators, one for electrons and one for positrons. These will collide at a total center of mass energy of 0.5 TeV.
However, synchrotron radiation also has a wide range of applications (see synchrotron light) and many 2nd and 3rd generation synchrotrons have been built especially to harness it. The largest of those 3rd generation synchrotron light sources are the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, the Advanced Photon Source (APS) near Chicago, USA, and SPring-8 in Japan, accelerating electrons up to 6, 7 and 8 GeV, respectively.
Synchrotrons which are useful for cutting edge research are large machines, costing tens or hundreds of millions of dollars to construct, and each beamline (there may be 20 to 50 at a large synchrotron) costs another two or three million dollars on average. These installations are mostly built by the science funding agencies of governments of developed countries, or by collaborations between several countries in a region, and operated as infrastructure facilities available to scientists from universities and research organisations throughout the country, region, or world. More compact models, however, have been developed, such as the Compact Light Source.
In a betatron, the magnetic field spins the injected electrons and accelerates them at the center where there is a ring-shaped vacuum tube changing the magnetic field and producing an electric field in the vacuum ring.
The stable orbit for the electrons satisfies 
where θ0 is the flux with the orbit at r0 is the radius and H0 is the magnetic field at r0. In other words, the magnetic field at the orbit must be half the average magnetic field over its circular cross section.
Betatrons were historically employed in particle physics experiments to provide high energy beams of electrons—up to about 300 MeV. If the electron beam is directed at a metal plate, the betatron can be used as a source of energetic x-rays or gamma rays; these x-rays may be used in industrial and medical applications (historically in radiation oncology).
The Radiation Center, the first private medical center to treat cancer patients with a betatron was opened by Dr. O. Arthur Stiennon, in a suburb of Madison, Wisconsin in the late 1950s[1].
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