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A cyclotron is a type of particle accelerator invented by Ernest Lawrence in 1929–1930 at the University of California, Berkeley,<ref>{{#invoke:citation/CS1|citation
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|{{US patent|123456|link text}}}} Lawrence, Ernest O. Method and apparatus for the acceleration of ions, filed: January 26, 1932, granted: February 20, 1934</ref><ref name="Lawrence">Template:Cite journal</ref> A cyclotron accelerates charged particles outwards from the center of a flat cylindrical vacuum chamber along a spiral path.<ref name="Nave">{{#invoke:citation/CS1|citation
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}}</ref><ref name="Close">Template:Cite book</ref> The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying electric field. Lawrence was awarded the 1939 Nobel Prize in Physics for this invention.<ref name="Close"/><ref>{{#invoke:citation/CS1|citation
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The cyclotron was the first "cyclical" accelerator.<ref name="Serway" /> The primary accelerators before the development of the cyclotron were electrostatic accelerators, such as the Cockcroft–Walton generator and the Van de Graaff generator. In these accelerators, particles would cross an accelerating electric field only once. Thus, the energy gained by the particles was limited by the maximum electrical potential that could be achieved across the accelerating region. This potential was in turn limited by electrostatic breakdown to a few million volts. In a cyclotron, by contrast, the particles encounter the accelerating region many times by following a spiral path, so the output energy can be many times the energy gained in a single accelerating step.<ref name="Lawrence"/>
Cyclotrons were the most powerful particle accelerator technology until the 1950s, when they were surpassed by the synchrotron.<ref name="Bryant">Template:Cite conference</ref> Nonetheless, they are still widely used to produce particle beams for nuclear medicine and basic research. As of 2020, close to 1,500 cyclotrons were in use worldwide for the production of radionuclides for nuclear medicine and ultimately, for the production of radiopharmaceuticals.Template:R In addition, cyclotrons can be used for particle therapy, where particle beams are directly applied to patients.<ref name="itnonline">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
HistoryEdit
OriginsEdit
A key limitation of the earliest charged particle accelerators was that increasing the particle energy required extending the length of the acceleration path, which was only feasible and practical up to a certain point. In 1927, while a student at Kiel, German physicist Max Steenbeck was the first to formulate the concept of the cyclotron, but he was discouraged from pursuing the idea further.<ref>Lawrence and His Laboratory - II — A Million Volts or Bust 81–82 in Heilbron, J. L., and Robert W. Seidel Lawrence and His Laboratory: A History of the Lawrence Berkeley Laboratory', Volume I. (Berkeley: University of California Press, 2000)</ref> In late 1928 and early 1929, Hungarian physicist Leo Szilárd filed patent applications in Germany for the linear accelerator, cyclotron, and betatron.<ref name="Dannen-20012">Template:Cite journal</ref> In these applications, Szilárd became the first person to discuss the resonance condition for a circular accelerating apparatus. However, neither Steenbeck's ideas nor Szilard's patent applications were ever published and therefore did not contribute to the development of the cyclotron.<ref>Template:Cite journal</ref>
Several months later, in the early summer of 1929, Ernest Lawrence independently conceived the cyclotron concept after reading a paper by Rolf Widerøe describing a drift tube accelerator.<ref>Template:Cite journal</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref>Template:Cite conference</ref> He published a paper in Science in 1930 (the first published description of the cyclotron concept), after a student of his built a crude model in April of that year.<ref>Template:Cite journal</ref> He patented the device in 1932.<ref name="Lawrence2">Template:Cite journal</ref><ref name="Physics2">Template:Cite book</ref>
To construct the first such device, Lawrence used large electromagnets recycled from obsolete arc converters provided by the Federal Telegraph Company.<ref>Template:Cite journal</ref> He was assisted by a graduate student, M. Stanley Livingston. Their first working cyclotron became operational on January 2, 1931. This machine had a diameter of Template:Convert, and accelerated protons to an energy up to 80 keV.<ref name="aipexhibit2">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name="c609">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
At the Radiation Laboratory on the campus of the University of California, Berkeley (now the Lawrence Berkeley National Laboratory), Lawrence and his collaborators went on to construct a series of cyclotrons which were the most powerful accelerators in the world at the time; a Template:Convert 4.8 MeV machine (1932), a Template:Convert 8 MeV machine (1937), and a Template:Convert 16 MeV machine (1939). Lawrence received the 1939 Nobel Prize in Physics for the invention and development of the cyclotron and for results obtained with it.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
The first European cyclotron was constructed in 1934 in the Soviet Union by Mikhail Alekseevich Eremeev, at the Leningrad Physico-Technical Institute. It was a small design based a prototype by Lawrence, with a 28 cm diameter capable of achieving 530 keV proton energies. Research quickly refocused around the construction of a larger MeV-level cyclotron, in the physics department of the V.G. Khlopin Radium Institute in Leningrad, headed by Template:Interlanguage link multi. This instrument was first proposed in 1932 by George Gamow and Template:Interlanguage link multi and was installed and became operative in March 1937 at 100 cm (39 in) diameter and 3.2 MeV proton energies.<ref>Template:Cite journal</ref><ref name="h373">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name="chronology">V. G. Khlopin Radium Institute. Chronology Template:Webarchive. Retrieved 25 February 2012.</ref>
The first Asian cyclotron was constructed at the Riken laboratory in Tokyo, by a team including Yoshio Nishina, Sukeo Watanabe, Tameichi Yasaki, and Ryokichi Sagane. Yasaki and Sagane had been sent to Berkeley Radiation Laboratory to work with Lawrence. The device had a 26 in diameter and the first beam was produced on April 2, 1937, at 2.9 MeV deuteron energies.<ref name="h349">Template:Cite journal</ref><ref name="x344">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
During World War IIEdit
Cyclotrons played a key role in the Manhattan Project. The published 1940 discovery of neptunium and the withheld 1941 discovery of plutonium both used bombardment in the Berkeley Radiation Laboratory's 60-inch cyclotron.<ref name="EL93">Template:Cite journal</ref><ref name="SeaborgStory">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Furthermore Lawrence invented the calutron (California University cyclotron)Template:Efn, which was industrially developed at the Y-12 National Security Complex from 1942. This provided the bulk of the uranium enrichment process, taking low-enriched uranium (<5% uranium-235) from the S-50 and K-25 plants and electromagnetically separating isotopes up to 84.5% highly enriched uranium (HEU). This was the first production of HEU in history, and was shipped to Los Alamos and used in the Little Boy bomb dropped on Hiroshima, and its precursor Water Boiler and Dragon test reactors.<ref name="m226">Template:Cite journal</ref>
In France, Frédéric Joliot-Curie constructed a large 7 MeV cyclotron at the Collège de France in Paris, achieving the first beam in March 1939. With the Nazi occupation of Paris in June 1940 and an incoming contingent of German scientists, Joliot ceased research into uranium fission, and obtained an understanding with his German former colleague Wolfgang Gentner that no research of military use would be carried out. In 1943 Gentner was recalled for weakness, and a new German contingent attempted to operate the cyclotron. However, it is likely that Joliot, a member of French Communist Party and in fact president of the National Front resistance movement, sabotaged the cyclotron to prevent its use to the Nazi German nuclear program.<ref name="d249">Template:Cite book</ref><ref name="l813">Template:Cite journal</ref>
In Nazi Germany, one cyclotron was built in Heidelberg, under the supervision of Walther Bothe and Wolfgang Gentner, with support from the Heereswaffenamt. At the end of 1938, Gentner was sent to Berkeley Radiation Laboratory and worked most closely with Emilio Segrè and Donald Cooksey, returning before the start of the war. Construction was slowed by the war and completed in January 1944, but difficulties in testing made it unusable until the war's end.<ref name="g387">Template:Cite book</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref>Template:Cite book</ref>
In Japan, the large Riken cyclotron was used to bombard uranium processed in their Clusius tube gaseous diffusion device. The experiment indicated that no enrichment of the uranium-235 content had occurred.<ref name="y213">Template:Cite journal</ref> Following the occupation of Japan, American forces, fearing continuation of the Japanese nuclear weapons program, dissembled the Riken laboratory's cyclotron and dumped it in Tokyo Bay. During the disassembly, Yoshio Nishina begged otherwise, saying "This is ten years of my life ... It has nothing to do with bombs." Secretary of War Robert P. Patterson later admitted the decision was a mistake.<ref name="h349" />
Post-warEdit
By the late 1930s it had become clear that there was a practical limit on the beam energy that could be achieved with the traditional cyclotron design, due to the effects of special relativity.<ref>Template:Cite journal</ref> As particles reach relativistic speeds, their effective mass increases, which causes the resonant frequency for a given magnetic field to change. To address this issue and reach higher beam energies using cyclotrons, two primary approaches were taken, synchrocyclotrons (which hold the magnetic field constant, but decrease the accelerating frequency) and isochronous cyclotrons (which hold the accelerating frequency constant, but alter the magnetic field).<ref name="craddock2">Template:Cite conference</ref>
Lawrence's team built one of the first synchrocyclotrons in 1946. This Template:Convert machine eventually achieved a maximum beam energy of 350 MeV for protons. However, synchrocyclotrons suffer from low beam intensities (< 1 μA), and must be operated in a "pulsed" mode, further decreasing the available total beam. As such, they were quickly overtaken in popularity by isochronous cyclotrons.Template:R
The first isochronous cyclotron (other than classified prototypes) was built by F. Heyn and K.T. Khoe in Delft, the Netherlands, in 1956.<ref name="heyn2">Template:Cite journal</ref> Early isochronous cyclotrons were limited to energies of ~50 MeV per nucleon, but as manufacturing and design techniques gradually improved, the construction of "spiral-sector" cyclotrons allowed the acceleration and control of more powerful beams. Later developments included the use of more compact and power-efficient superconducting magnets and the separation of the magnets into discrete sectors, as opposed to a single large magnet.Template:R
Principle of operationEdit
A cyclotron is essentially a linear particle accelerator wrapped in a circle. A uniform magnetic field perpendicular to the plane of particle motion causes the particles to orbit. During each orbit the particles are accelerated by electric fields.<ref name="Klaus-2000">Template:Cite book</ref>Template:Rp
Cyclotron principleEdit
In a particle accelerator, charged particles are accelerated by applying an electric field across a gap. The force on a particle crossing this gap is given by the Lorentz force law:
<math display="block">\mathbf{F} = q [\mathbf{E} + (\mathbf{v} \times \mathbf{B})]</math>
where Template:Mvar is the charge on the particle, Template:Math is the electric field, Template:Math is the particle velocity, and Template:Math is the magnetic flux density. It is not possible to accelerate particles using only a static magnetic field, as the magnetic force always acts perpendicularly to the direction of motion, and therefore can only change the direction of the particle, not the speed.<ref name="conte">Template:Cite book</ref>
In practice, the magnitude of an unchanging electric field which can be applied across a gap is limited by the need to avoid electrostatic breakdown.<ref name="edwards">Template:Cite book</ref>Template:Rp As such, modern particle accelerators use alternating (radio frequency) electric fields for acceleration. Since an alternating field across a gap only provides an acceleration in the forward direction for a portion of its cycle, particles in RF accelerators travel in bunches, rather than a continuous stream. In a linear particle accelerator, in order for a bunch to "see" a forward voltage every time it crosses a gap, the gaps must be placed further and further apart, in order to compensate for the increasing speed of the particle.<ref name="wilson">Template:Cite book</ref>
A cyclotron, by contrast, uses a magnetic field to bend the particle trajectories into a spiral, thus allowing the same gap to be used many times to accelerate a single bunch. As the bunch spirals outward, the increasing distance between transits of the gap is exactly balanced by the increase in speed, so a bunch will reach the gap at the same point in the RF cycle every time.Template:R
The frequency at which a particle will orbit in a perpendicular magnetic field is known as the cyclotron frequency, and depends, in the non-relativistic case, solely on the charge and mass of the particle, and the strength of the magnetic field:
<math display="block">f = \frac{qB}{2\pi m}</math>
where Template:Mvar is the (linear) frequency, Template:Mvar is the charge of the particle, Template:Mvar is the magnitude of the magnetic field that is perpendicular to the plane in which the particle is travelling, and Template:Mvar is the particle mass. The property that the frequency is independent of particle velocity is what allows a single, fixed gap to be used to accelerate a particle travelling in a spiral.Template:R
Particle energyEdit
Each time a particle crosses the accelerating gap in a cyclotron, it is given an accelerating force by the electric field across the gap, and the total particle energy gain can be calculated by multiplying the increase per crossing by the number of times the particle crosses the gap.<ref name="seidel" />
However, given the typically high number of revolutions, it is usually simpler to estimate the energy by combining the equation for frequency in circular motion:
<math display="block">f = \frac{v}{2 \pi r}</math>
with the cyclotron frequency equation to yield:
<math display="block">v = \frac{q B r}{m}</math>
The kinetic energy for particles with speed Template:Mvar is therefore given by:
<math display="block">E = \frac{1}{2}m v^2 = \frac{q^2 B^2 r^2}{2 m}</math>
where Template:Mvar is the radius at which the energy is to be determined. The limit on the beam energy which can be produced by a given cyclotron thus depends on the maximum radius which can be reached by the magnetic field and the accelerating structures, and on the maximum strength of the magnetic field which can be achieved.<ref name="Serway">Template:Cite book</ref>
K-factorEdit
In the nonrelativistic approximation, the maximum kinetic energy per atomic mass for a given cyclotron is given by:
<math display="block">\frac{T}{A} = \frac{(e B r_{\max})^2}{2 m_a}\left(\frac{Q}{A}\right)^2 = K \left(\frac{Q}{A}\right)^2</math>
where <math>e</math> is the elementary charge, <math>B</math> is the strength of the magnet, <math>r_{\max}</math> is the maximum radius of the beam, <math>m_a</math> is an atomic mass unit, <math>Q</math> is the charge of the beam particles, and <math>A</math> is the atomic mass of the beam particles. The value of K
<math display="block">K = \frac{(e B r_{\max})^2}{2 m_a}</math>
is known as the "K-factor", and is used to characterize the maximum kinetic beam energy of protons (quoted in MeV). It represents the theoretical maximum energy of protons (with Q and A equal to 1) accelerated in a given machine.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
Particle trajectoryEdit
While the trajectory followed by a particle in the cyclotron is conventionally referred to as a "spiral", it is more accurately described as a series of arcs of constant radius. The particles' speed, and therefore orbital radius, only increases at the accelerating gaps. Away from those regions, the particle will orbit (to a first approximation) at a fixed radius.<ref name="Chautard">Template:Cite journal</ref>
Assuming a uniform energy gain per orbit (which is only valid in the non-relativistic case), the average orbit may be approximated by a simple spiral. If the energy gain per turn is given by Template:Math, the particle energy after Template:Mvar turns will be: <math display="block">E(n) = n \Delta E</math> Combining this with the non-relativistic equation for the kinetic energy of a particle in a cyclotron gives: <math display="block">r(n) = {\sqrt{2 m \Delta E} \over q B} \sqrt{n}</math> This is the equation of a Fermat spiral.
Stability and focusingEdit
As a particle bunch travels around a cyclotron, two effects tend to make its particles spread out. The first is simply the particles injected from the ion source having some initial spread of positions and velocities. This spread tends to get amplified over time, making the particles move away from the bunch center. The second is the mutual repulsion of the beam particles due to their electrostatic charges.<ref>Template:Cite conference</ref> Keeping the particles focused for acceleration requires confining the particles to the plane of acceleration (in-plane or "vertical"Template:Efn focusing), preventing them from moving inward or outward from their correct orbit ("horizontal"Template:Efn focusing), and keeping them synchronized with the accelerating RF field cycle (longitudinal focusing).<ref name="Chautard" />
Transverse stability and focusingEdit
The in-plane or "vertical"Template:Efn focusing is typically achieved by varying the magnetic field around the orbit, i.e. with azimuth. A cyclotron using this focusing method is thus called an azimuthally-varying field (AVF) cyclotron.<ref name="sylee014">Template:Cite book</ref> The variation in field strength is provided by shaping the steel poles of the magnet into sectors<ref name="Chautard" /> which can have a shape reminiscent of a spiral and also have a larger area towards the outer edge of the cyclotron to improve the vertical focus of the particle beam.<ref>Template:Cite journal</ref> This solution for focusing the particle beam was proposed by L. H. Thomas in 1938<ref name="sylee014"/> and almost all modern cyclotrons use azimuthally-varying fields.<ref>Template:Cite book</ref>
The "horizontal"Template:Efn focusing happens as a natural result of cyclotron motion. Since for identical particles travelling perpendicularly to a constant magnetic field the trajectory curvature radius is only a function of their speed, all particles with the same speed will travel in circular orbits of the same radius, and a particle with a slightly incorrect trajectory will simply travel in a circle with a slightly offset center. Relative to a particle with a centered orbit, such a particle will appear to undergo a horizontal oscillation relative to the centered particle. This oscillation is stable for particles with a small deviation from the reference energy.<ref name="Chautard" />
Longitudinal stabilityEdit
The instantaneous level of synchronization between a particle and the RF field is expressed by phase difference between the RF field and the particle. In the first harmonic mode (i.e. particles make one revolution per RF cycle) it is the difference between the instantaneous phase of the RF field and the instantaneous azimuth of the particle. Fastest acceleration is achieved when the phase difference equals 90° (modulo 360°).Template:R Poor synchronization, i.e. phase difference far from this value, leads to the particle being accelerated slowly or even decelerated (outside of the 0–180° range).
As the time taken by a particle to complete an orbit depends only on particle's type, magnetic field (which may vary with the radius), and Lorentz factor (see Template:Slink), cyclotrons have no longitudinal focusing mechanism which would keep the particles synchronized to the RF field. The phase difference, that the particle had at the moment of its injection into the cyclotron, is preserved throughout the acceleration process, but errors from imperfect match between the RF field frequency and the cyclotron frequency at a given radius accumulate on top of it.Template:R Failure of the particle to be injected with phase difference within about ±20° from the optimum may make its acceleration too slow and its stay in the cyclotron too long. As a consequence, half-way through the process the phase difference escapes the 0–180° range, the acceleration turns into deceleration, and the particle fails to reach the target energy. Grouping of the particles into correctly synchronized bunches before their injection into the cyclotron thus greatly increases the injection efficiency.Template:R
Relativistic considerationsEdit
In the non-relativistic approximation, the cyclotron frequency does not depend upon the particle's speed or the radius of the particle's orbit. As the beam spirals outward, the rotation frequency stays constant, and the beam continues to accelerate as it travels a greater distance in the same time period. In contrast to this approximation, as particles approach the speed of light, the cyclotron frequency decreases due to the change in relativistic mass. This change is proportional to the particle's Lorentz factor.Template:R
The relativistic mass can be written as:
<math display="block">m = \frac{m_0}{\sqrt{1-\left(\frac{v}{c}\right)^2}} = \frac{m_0}{\sqrt{1-\beta^2}} = \gamma {m_0},</math>
where:
- <math>m_0</math> is the particle rest mass,
- <math>\beta = \frac{v}{c}</math> is the relative velocity, and
- <math>\gamma=\frac{1}{\sqrt{1-\beta^2}}=\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}}</math> is the Lorentz factor.Template:R
Substituting this into the equations for cyclotron frequency and angular frequency gives:
<math display="block">\begin{align} f & = \frac{q B}{2\pi \gamma m_0} \\[6pt] \omega & = \frac{q B}{\gamma m_0} \end{align}</math>
The gyroradius for a particle moving in a static magnetic field is then given by:Template:R <math display="block">r = \frac{\gamma \beta m_0 c}{q B} = \frac{\gamma m_0 v}{q B} = \frac{m_0}{q B \sqrt{v^{-2} - c^{-2}}}</math>
Expressing the speed in this equation in terms of frequency and radius <math display="block">v = 2\pi f r</math> yields the connection between the magnetic field strength, frequency, and radius: <math display="block">\left(\frac{1}{2\pi f}\right)^2 = \left(\frac{m_0}{q B}\right)^2 + \left(\frac{r}{c}\right)^2</math>
Approaches to relativistic cyclotronsEdit
| CitationClass=web
}}</ref> |
Relativistic | Accelerating field | Bending magnetic field strength |
Orbit radius variation | |||
|---|---|---|---|---|---|---|---|
| Origin | Frequency vs timeTemplate:Efn |
vs timeTemplate:Efn | vs radius | ||||
| Template:Small | |||||||
| Classical cyclotron | No | Electrostatic | Constant | Constant | Constant | Large | |
| Isochronous cyclotron |
Yes | Electrostatic | Constant | Constant | Increasing | Large | |
| Synchrocyclotron | Yes | Electrostatic | Decreasing | Constant | ConstantTemplate:Efn | Large | |
| Template:Small | |||||||
| FFA | Yes | Electrostatic | DDTemplate:Efn | Constant | DDTemplate:Efn | Small | |
| Synchrotron | Yes | Electrostatic | Increasing, finite limit |
Increasing | N/ATemplate:Efn | None | |
| Betatron | Yes | Induction | Increasing, finite limit |
Increasing | N/ATemplate:Efn | None | |
SynchrocyclotronEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Since <math>\gamma</math> increases as the particle reaches relativistic velocities, acceleration of relativistic particles requires modification of the cyclotron to ensure the particle crosses the gap at the same point in each RF cycle. If the frequency of the accelerating electric field is varied while the magnetic field is held constant, this leads to the synchrocyclotron.Template:R
In this type of cyclotron, the accelerating frequency is varied as a function of particle orbit radius such that:
<math display="block">f(r) = \frac{1}{2\pi \sqrt{\left(\frac{m_0}{q B}\right)^2 + \left(\frac{r}{c}\right)^2}}</math>
The decrease in accelerating frequency is tuned to match the increase in gamma for a constant magnetic field.Template:R
Isochronous cyclotronEdit
If instead the magnetic field is varied with radius while the frequency of the accelerating field is held constant, this leads to the isochronous cyclotron.Template:R
<math display="block">B(r) = \frac{m_0}{q \sqrt{\left(\frac{1}{2\pi f}\right)^2 - \left(\frac{r}{c}\right)^2}}</math>
Keeping the frequency constant allows isochronous cyclotrons to operate in a continuous mode, which makes them capable of producing much greater beam current than synchrocyclotrons. On the other hand, as precise matching of the orbital frequency to the accelerating field frequency is the responsibility of the magnetic field variation with radius, the variation must be precisely tuned.
Fixed-field alternating gradient accelerator (FFA)Edit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}}
An approach which combines static magnetic fields (as in the synchrocyclotron) and alternating gradient focusing (as in a synchrotron) is the fixed-field alternating gradient accelerator (FFA). In an isochronous cyclotron, the magnetic field is shaped by using precisely machined steel magnet poles. This variation provides a focusing effect as the particles cross the edges of the poles. In an FFA, separate magnets with alternating directions are used to focus the beam using the principle of strong focusing. The field of the focusing and bending magnets in an FFA is not varied over time, so the beam chamber must still be wide enough to accommodate a changing beam radius within the field of the focusing magnets as the beam accelerates.<ref>Template:Cite journal</ref>
ClassificationsEdit
Cyclotron typesEdit
There are a number of basic types of cyclotron:<ref name="Chao">Template:Cite book</ref>
Template:Glossary Template:Term Template:Defn Template:Term Template:Defn Template:Term Template:Defn Template:Term Template:Defn Template:Term Template:Defn Template:Glossary end
Beam typesEdit
The particles for cyclotron beams are produced in ion sources of various types.
Template:Glossary Template:Term Template:Defn Template:Term Template:Defn Template:Term Template:Defn Template:Glossary end
Target typesEdit
To make use of the cyclotron beam, it must be directed to a target.<ref>Template:Cite conference</ref>
Template:Glossary Template:Term Template:Defn Template:Term Template:Defn Template:Glossary end
UsageEdit
Basic researchEdit
For several decades, cyclotrons were the best source of high-energy beams for nuclear physics experiments. With the advent of strong focusing synchrotrons, cyclotrons were supplanted as the accelerators capable of producing the highest energies.<ref name="wilson" />Template:R However, due to their compactness, and therefore lower expense compared to high energy synchrotrons, cyclotrons are still used to create beams for research where the primary consideration is not achieving the maximum possible energy.Template:R Cyclotron based nuclear physics experiments are used to measure basic properties of isotopes (particularly short lived radioactive isotopes) including half life, mass, interaction cross sections, and decay schemes.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
Medical usesEdit
Radioisotope productionEdit
Cyclotron beams can be used to bombard other atoms to produce short-lived isotopes with a variety of medical uses, including medical imaging and radiotherapy.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Positron and gamma emitting isotopes, such as fluorine-18, carbon-11, and technetium-99m<ref>Template:Cite news</ref> are used for PET and SPECT imaging. While cyclotron produced radioisotopes are widely used for diagnostic purposes, therapeutic uses are still largely in development. Proposed isotopes include astatine-211, palladium-103, rhenium-186, and bromine-77, among others.<ref>Template:Cite book</ref>
Beam therapyEdit
The first suggestion that energetic protons could be an effective treatment method was made by Robert R. Wilson in a paper published in 1946<ref>Template:Cite journal</ref> while he was involved in the design of the Harvard Cyclotron Laboratory.<ref>Template:Cite book</ref>
Beams from cyclotrons can be used in particle therapy 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.
As of 2020, there were approximately 80 facilities worldwide for radiotherapy using beams of protons and heavy ions, consisting of a mixture of cyclotrons and synchrotrons. Cyclotrons are primarily used for proton beams, while synchrotrons are used to produce heavier ions.<ref>Template:Cite book</ref>
Advantages and limitationsEdit
The most obvious advantage of a cyclotron over a linear accelerator is that because the same accelerating gap is used many times, it is both more space efficient and more cost efficient; particles can be brought to higher energies in less space, and with less equipment. The compactness of the cyclotron reduces other costs as well, such as foundations, radiation shielding, and the enclosing building. Cyclotrons have a single electrical driver, which saves both equipment and power costs. Furthermore, cyclotrons are able to produce a continuous beam of particles at the target, so the average power passed from a particle beam into a target is relatively high compared to the pulsed beam of a synchrotron.<ref name="peach">Template:Cite journal</ref>
However, as discussed above, a constant frequency acceleration method is only possible when the accelerated particles are approximately obeying Newton's laws of motion. If the particles become fast enough that relativistic effects become important, the beam becomes out of phase with the oscillating electric field, and cannot receive any additional acceleration. The classical cyclotron (constant field and frequency) is therefore only capable of accelerating particles up to a few percent of the speed of light. Synchro-, isochronous, and other types of cyclotrons can overcome this limitation, with the tradeoff of increased complexity and cost.Template:R
An additional limitation of cyclotrons is due to space charge effects – the mutual repulsion of the particles in the beam. As the amount of particles (beam current) in a cyclotron beam is increased, the effects of electrostatic repulsion grow stronger until they disrupt the orbits of neighboring particles. This puts a functional limit on the beam intensity, or the number of particles which can be accelerated at one time, as distinct from their energy.<ref>Template:Cite journal</ref>
Notable examplesEdit
| Template:Abbr | Country | Date | Template:Abbr | Template:Abbr | Diameter | In use? | Comments | Template:Abbr | |
|---|---|---|---|---|---|---|---|---|---|
| Lawrence 4.5-inch Cyclotron | Template:Flagicon United States | 1931 | Template:Convert | Protons | Template:Convert | Template:No | First working cyclotron | Template:R | |
| Leningrad cyclotron | Template:Flagicon Soviet Union | 1934 | 530 keV | Protons | Template:Convert | Template:No | First cyclotron outside Berkeley | <ref name="g778">Template:Cite journal</ref><ref name="b194">Template:Cite book</ref> | |
| Lawrence 184-inch Cyclotron | Template:Flagicon United States | 1946 | 380 MeV | Alpha particles, deuterium, protons | Template:Convert | Template:No | First synchrocyclotron and largest single-magnet cyclotron ever constructed | Template:R | |
| TU Delft Isochronous Cyclotron | Template:Flagicon Netherlands | 1958 | 12 MeV | Protons | Template:Convert | Template:No | First isochronous cyclotron | Template:R | |
| Lawrence Berkeley National Laboratory 88-inch Cyclotron | Template:Flagicon United States | 1961 | 60 MeV | Protons, Alpha Particles, Neutrons, Heavy Ions | Template:Convert | Template:Yes | Oldest continuously operated large cyclotron in existence; Lawrence's last cyclotron | citation | CitationClass=web
}}</ref> |
| PSI Ring Cyclotron | Template:Flagicon Switzerland | 1974 | 590 MeV | Protons | Template:Convert | Template:Yes | Highest beam power of any cyclotron | <ref>Template:Cite conference</ref> | |
| TRIUMF 520 MeV | Template:Flagicon Canada | 1976 | 520 MeV | H− | Template:Convert | Template:Yes | Largest normal conducting cyclotron ever constructed | citation | CitationClass=web
}}</ref> |
| Michigan State University K500 | Template:Flagicon United States | 1982 | 500 MeV/u | Heavy Ion | Template:Convert | Template:Yes<ref name="MSUrefurb">{{#invoke:citation/CS1|citation | CitationClass=web
}}</ref> |
First superconducting cyclotron | <ref name="Blosser-2004">Template:Cite conference</ref><ref name="MSUrefurb" /> |
| RIKEN Superconducting Ring Cyclotron | Template:Flagicon Japan | 2006 | 400 MeV/u | Heavy Ion | Template:Convert | Template:Yes | K-value of 2600 is highest ever achieved | <ref>Template:Cite conference</ref> |
Superconducting cyclotron examplesEdit
A superconducting cyclotron uses superconducting magnets to achieve high magnetic field in a small diameter and with lower power requirements. These cyclotrons require a cryostat to house the magnet and cool it to superconducting temperatures. Some of these cyclotrons are being built for medical therapy.<ref name="craddock">Template:Cite conference</ref>Template:Rp
| Template:Abbr | Country | Date | Template:Abbr | Template:Abbr | Diameter | In use? | Template:Abbr | |
|---|---|---|---|---|---|---|---|---|
| Michigan State University K500 | Template:FlagiconUnited States | 1982 | 500 MeV/u | Heavy Ion | Template:Convert | Template:Yes<ref name="MSUrefurb"/> | <ref name="Blosser-2004"/><ref name="MSUrefurb"/> | |
| Texas A&M University Cyclotron Institute K500 | Template:FlagiconUnited States | 1987 | 70 MeV (protons), 15 MeV/u | Protons, Heavy Ions | Template:Convert | Template:Yes | citation | CitationClass=web
}}</ref> |
| Template:Interlanguage link K800 | Template:FlagiconItaly | 1994 | 80 MeV | Protons, Heavy ions | Template:Convert | Template:Yes | citation | CitationClass=web
}}</ref> |
| University Medical Center Groningen AGOR | Template:FlagiconNetherlands | 1996 | 120-190 MeV (protons), 30-90 MeV/u (Heavy Ions) | Protons, Light ions, Heavy ions | Template:Convert | Template:Yes | citation | CitationClass=web
}}</ref> |
| Variable Energy Cyclotron Centre K500 | Template:FlagiconIndia | 2009 | 80 MeV/u (Light Ions), 5-10 MeV/u (Heavy Ions)<ref>Template:Cite journal</ref> | Protons, dueterons, Alpha particles, Heavy ions | Template:Convert | Template:Yes | citation | CitationClass=web
}}</ref> |
| Ionetix ION-12SC | Template:FlagiconUnited States | 2016 | 12.5 MeV | Proton | Template:Convert | Template:Yes | <ref>Template:Cite journal</ref> |
Related technologiesEdit
The spiraling of electrons in a cylindrical vacuum chamber within a transverse magnetic field is also employed in the magnetron, a device for producing high frequency radio waves (microwaves). In the magnetron, electrons are bent into a circular path by a magnetic field, and their motion is used to excite resonant cavities, producing electromagnetic radiation.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
A betatron uses the change in the magnetic field to accelerate electrons in a circular path. While static magnetic fields cannot provide acceleration, as the force always acts perpendicularly to the direction of particle motion, changing fields can be used to induce an electromotive force in the same manner as in a transformer. The betatron was developed in 1940,<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> although the idea had been proposed substantially earlier.<ref name="Dannen-2001">Template:Cite journal</ref>
A synchrotron is another type of particle accelerator that uses magnets to bend particles into a circular trajectory. Unlike in a cyclotron, the particle path in a synchrotron has a fixed radius. Particles in a synchrotron pass accelerating stations at increasing frequency as they get faster. To compensate for this frequency increase, both the frequency of the applied accelerating electric field and the magnetic field must be increased in tandem, leading to the "synchro" portion of the name.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
In fictionEdit
The United States Department of War famously asked for dailies of the Superman comic strip to be pulled in April 1945 for having Superman bombarded with the radiation from a cyclotron.<ref>Template:Cite book</ref>
In the 1984 film Ghostbusters, a miniature cyclotron forms part of the proton pack used for catching ghosts.<ref>Template:Cite book</ref>
See alsoEdit
- Cyclotron radiation – radiation produced by non-relativistic charged particles bent by a magnetic field
- Fast neutron therapy – a type of beam therapy that may use accelerator produced beams
- Microtron – an accelerator concept similar to the cyclotron which uses a linear accelerator type accelerating structure with a constant magnetic field.
- Radiation reaction force – a braking force on beams that are bent in a magnetic field
NotesEdit
ReferencesEdit
Further readingEdit
- Template:Cite journal
- Template:Cite magazine About a neighborhood cyclotron in Anchorage, Alaska.
- {{#invoke:citation/CS1|citation
|CitationClass=web }} An experiment done by Fred M. Niell, III his senior year of high school (1994–95) with which he won the overall grand prize in the ISEF.
External linksEdit
Template:Sister project Template:Sister project
Current facilitiesEdit
- The 88-Inch Cyclotron at Lawrence Berkeley National Laboratory
- PSI Proton Accelerator – the highest beam current cyclotron in the world.
- The Superconducting Ring Cyclotron at the RIKEN Nishina Center for Accelerator Based Science – the highest energy cyclotron in the world
- Rutgers Cyclotron – Students at Rutgers University built a Template:Convert 1 MeV cyclotron as an undergraduate project, which is now used for a senior-level undergraduate and a graduate lab course.
- TRIUMF – the largest single-magnet cyclotron in the world.
Historic cyclotronsEdit
- Ernest Lawrence's Cyclotron A history of cyclotron development at the Berkeley Radiation Laboratory, now Lawrence Berkeley National Laboratory
- National Superconducting Cyclotron Laboratory of the Michigan State University – Home of coupled K500 and K1200 superconducting cyclotrons; the K500, the first superconducting cyclotron, and the K1200, formerly the most powerful in the world.