Cyclotron
Overview

In technology
Technology
Technology is the making, usage, and knowledge of tools, machines, techniques, crafts, systems or methods of organization in order to solve a problem or perform a specific function. It can also refer to the collection of such tools, machinery, and procedures. The word technology comes ;...

, a cyclotron is a type of particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

. In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the cyclotron frequency or gyrofrequency is the frequency of a charged particle
Charged particle
In physics, a charged particle is a particle with an electric charge. It may be either a subatomic particle or an ion. A collection of charged particles, or even a gas containing a proportion of charged particles, is called a plasma, which is called the fourth state of matter because its...

moving perpendicularly to the direction of a uniform magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

, i.e. a magnetic field of constant magnitude and direction. Since that motion is always circular, the cyclotron frequency is well defined.

Cyclotrons accelerate charged particle
Charged particle
In physics, a charged particle is a particle with an electric charge. It may be either a subatomic particle or an ion. A collection of charged particles, or even a gas containing a proportion of charged particles, is called a plasma, which is called the fourth state of matter because its...

s using a high-frequency, alternating voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

(potential difference).
Encyclopedia
In technology
Technology
Technology is the making, usage, and knowledge of tools, machines, techniques, crafts, systems or methods of organization in order to solve a problem or perform a specific function. It can also refer to the collection of such tools, machinery, and procedures. The word technology comes ;...

, a cyclotron is a type of particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

. In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the cyclotron frequency or gyrofrequency is the frequency of a charged particle
Charged particle
In physics, a charged particle is a particle with an electric charge. It may be either a subatomic particle or an ion. A collection of charged particles, or even a gas containing a proportion of charged particles, is called a plasma, which is called the fourth state of matter because its...

moving perpendicularly to the direction of a uniform magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

, i.e. a magnetic field of constant magnitude and direction. Since that motion is always circular, the cyclotron frequency is well defined.

Cyclotrons accelerate charged particle
Charged particle
In physics, a charged particle is a particle with an electric charge. It may be either a subatomic particle or an ion. A collection of charged particles, or even a gas containing a proportion of charged particles, is called a plasma, which is called the fourth state of matter because its...

s using a high-frequency, alternating voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

(potential difference). A perpendicular magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

causes the particles to spiral
Spiral
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.-Spiral or helix:...

almost in a circle so that they re-encounter the accelerating voltage many times.

The cyclotron was invented by Leo Szilárd
Leó Szilárd
Leó Szilárd was an Austro-Hungarian physicist and inventor who conceived the nuclear chain reaction in 1933, patented the idea of a nuclear reactor with Enrico Fermi, and in late 1939 wrote the letter for Albert Einstein's signature that resulted in the Manhattan Project that built the atomic bomb...

and first manufactured by Ernest Lawrence
Ernest Lawrence
Ernest Orlando Lawrence was an American physicist and Nobel Laureate, known for his invention, utilization, and improvement of the cyclotron atom-smasher beginning in 1929, based on his studies of the works of Rolf Widerøe, and his later work in uranium-isotope separation for the Manhattan Project...

, of the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...

who started operating it in 1932. Others had been working along similar lines at the time. The first European cyclotron was constructed in Leningrad
Leningrad is the former name of Saint Petersburg, Russia.Leningrad may also refer to:- Places :* Leningrad Oblast, a federal subject of Russia, around Saint Petersburg* Leningrad, Tajikistan, capital of Muminobod district in Khatlon Province...

in the physics department of the Radium Institute, headed by Vitali Khlopin. This instrument was first proposed in 1932 by George Gamow
George Gamow
George Gamow , born Georgiy Antonovich Gamov , was a Russian-born theoretical physicist and cosmologist. He discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis, cosmic microwave...

and Lev Mysovskii and was installed and running by 1937.

TRIUMF
TRIUMF
TRIUMF is Canada’s national laboratory for particle and nuclear physics. Its headquarters are located on the south campus of the University of British Columbia in Vancouver, British Columbia. TRIUMF houses the world's largest cyclotron, source of 500 MeV protons, which was named an IEEE Milestone...

, Canada's national laboratory for nuclear and particle physics, houses the world's largest cyclotron. The 18m diameter, 4,000 tonne main magnet produces a field of 0.46 T
Tesla (unit)
The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...

while a 23 MHz 94 kV
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

electric field is used to accelerate the 300 μA beam. TRIUMF is run by a consortium of sixteen Canadian universities and is located at the University of British Columbia
University of British Columbia
The University of British Columbia is a public research university. UBC’s two main campuses are situated in Vancouver and in Kelowna in the Okanagan Valley...

How the cyclotron works

The electrode
Electrode
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit...

s shown at the right would be in the vacuum chamber
Vacuum chamber
A vacuum chamber is a rigid enclosure from which air and other gases are removed by a vacuum pump. The resulting low pressure, commonly referred to as a vacuum, allows researchers to conduct physical experiments or to test mechanical devices which must operate in outer space...

, which is flat, in a narrow gap between the two poles
Magnetic pole
Magnetic pole may refer to:* One of the two ends of a magnet* The magnetic poles of astronomical bodies, a special case of magnets, two special cases of which are the Geomagnetic poles:...

of a large magnet.
In the cyclotron, a high-frequency alternating voltage
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

applied across the "D" electrodes (also called "dees") alternately attracts and repels charged particle
Charged particle
In physics, a charged particle is a particle with an electric charge. It may be either a subatomic particle or an ion. A collection of charged particles, or even a gas containing a proportion of charged particles, is called a plasma, which is called the fourth state of matter because its...

s. The particles, injected near the center of the magnetic field, increase in speed (and therefore energy) only when passing through the gap between the electrodes. The perpendicular magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

(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 force perpendicular to its direction of motion
Right-hand rule
In mathematics and physics, the right-hand rule is a common mnemonic for understanding notation conventions for vectors in 3 dimensions. It was invented for use in electromagnetism by British physicist John Ambrose Fleming in the late 19th century....

. 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
Nuclear transmutation
Nuclear transmutation is the conversion of one chemical element or isotope into another. In other words, atoms of one element can be changed into atoms of other element by 'transmutation'...

of the elements used in the target.

Uses of the cyclotron

For several decades, cyclotrons were the best source of high-energy beams for nuclear physics
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...

experiments; several cyclotrons are still in use for this type of research.
Cyclotrons can be used to treat cancer
Cancer
Cancer , known medically as a malignant neoplasm, is a large group of different diseases, all involving unregulated cell growth. In cancer, cells divide and grow uncontrollably, forming malignant tumors, and invade nearby parts of the body. The cancer may also spread to more distant parts of the...

. Ion beams from cyclotrons can be used, as in proton therapy
Proton therapy
Proton therapy is a type of particle therapy which uses a beam of protons to irradiate diseased tissue, most often in the treatment of cancer. The chief advantage of proton therapy is the ability to more precisely localize the radiation dosage when compared with other types of external beam...

, to penetrate the body and kill tumors by radiation damage
Acute radiation syndrome also known as radiation poisoning, radiation sickness or radiation toxicity, is a constellation of health effects which occur within several months of exposure to high amounts of ionizing radiation...

, while minimizing damage to healthy tissue along their path.
Cyclotron beams can be used to bombard other atoms to produce short-lived positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

-emitting isotopes suitable for PET imaging.

Problems solved by the cyclotron

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 Klystron
Klystron
A klystron is a specialized linear-beam vacuum tube . Klystrons are used as amplifiers at microwave and radio frequencies to produce both low-power reference signals for superheterodyne radar receivers and to produce high-power carrier waves for communications and the driving force for modern...

s 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.

• Cyclotrons have a single electrical driver, which saves both money and power, since more expense may be allocated to increasing efficiency.
• Cyclotrons produce a continuous stream of particles at the target, so the average power is relatively high.
• The compactness of the device reduces other costs, such as its foundations, radiation shielding, and the enclosing building.

Limitations of the cyclotron

The spiral
Spiral
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.-Spiral or helix:...

path of the cyclotron beam can only "sync up" with klystron-type (constant frequency) voltage sources if the accelerated particles are approximately obeying Newton's Laws of Motion
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...

. If the particles become fast enough that relativistic
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

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 cyclotron
Isochronous cyclotron
In particle accelerators an Isochronous cyclotron is a cyclotron that maintains a constant RF driving frequency, and compensates for the relativistic mass gain of the accelerated particles by alternating field gradient in space but constant in time...

s, operating in a pulsed mode and changing the frequency applied to the dees as in the synchrocyclotron
Synchrocyclotron
A synchrocyclotron is a cyclotron in which the frequency of the driving RF electric field is varied to compensate for relativistic effects as the particles' velocity begins to approach the speed of light...

s, 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
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...

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.

Non-relativistic

The centripetal force
Centripetal force
Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...

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, B the magnetic field strength, 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,

The frequency of the driving voltage is simply the inverse of this frequency so that the particle crosses between the dees at the same point in the voltage cycle.

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
Synchrocyclotron
A synchrocyclotron is a cyclotron in which the frequency of the driving RF electric field is varied to compensate for relativistic effects as the particles' velocity begins to approach the speed of light...

.

Relativistic

The radius of curvature for a particle moving relativistically in a static magnetic field is
where is the Lorentz factor
Lorentz factor
The Lorentz factor or Lorentz term appears in several equations in special relativity, including time dilation, length contraction, and the relativistic mass formula. Because of its ubiquity, physicists generally represent it with the shorthand symbol γ . It gets its name from its earlier...

Note 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,
where this is in Natural units
Natural units
In physics, natural units are physical units of measurement based only on universal physical constants. For example the elementary charge e is a natural unit of electric charge, or the speed of light c is a natural unit of speed...

The relativistic cyclotron frequency is
,
where is the classical frequency, given above, of a charged particle with velocity circling in a magnetic field.

The rest mass of an electron is 511 keV/c2, so the frequency correction is 1% for a magnetic vacuum tube with a 5.11 keV/c2 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
Isochronous cyclotron
In particle accelerators an Isochronous cyclotron is a cyclotron that maintains a constant RF driving frequency, and compensates for the relativistic mass gain of the accelerated particles by alternating field gradient in space but constant in time...

, 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
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...

(RF), 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
Strong focusing
In accelerator physics strong focusing or alternating-gradient focusing is the principle that the net effect on a particle beam of charged particles passing through alternating field gradients is to make the beam converge...

. It was obscurely known theoretically long before it was put into practice.

Related technologies

• 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).

• The Synchrotron
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...

moves the particles through a path of constant radius, allowing it to be made as a pipe and so of much larger radius than is practical with the cyclotron and synchrocyclotron. The larger radius allows the use of numerous magnets, each of which imparts angular momentum and so allows particles of higher velocity (mass) to be kept within the bounds of the evacuated pipe. The magnetic field strength of each of the bending magnets is increased as the particles gain energy in order to keep the bending angle constant.

• Beamline
Beamline
In particle physics, a beamline is the line in a linear accelerator along which a beam of particles travels. It may also refer to the line of travel within a bending section such as a storage ring or cyclotron, or an external beam extracted from a cyclic accelerator.In materials science, physics,...

Cyclotron radiation is electromagnetic radiation emitted by moving charged particles deflected by a magnetic field. The Lorentz force on the particles acts perpendicular to both the magnetic field lines and the particles' motion through them, creating an acceleration of charged particles that...

• Synchrotron light
Synchrotron light
A synchrotron light source is a source of electromagnetic radiation produced by a synchrotron, which is artificially produced for scientific and technical purposes by specialized particle accelerators, typically accelerating electrons...

• Bremsstrahlung
Bremsstrahlung
Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

• Electron cyclotron resonance
Electron cyclotron resonance
Electron cyclotron resonance is a phenomenon observed both in plasma physics and condensed matter physics. An electron in a static and uniform magnetic field will move in a circle due to the Lorentz force...

• Gyrotron
Gyrotron
Gyrotrons are high powered vacuum tubes which emit millimeter-wave beams by bunching electrons with cyclotron motion in a strong magnetic field. Output frequencies range from about 20 to 250 GHz, covering wavelengths from microwave to the edge of the terahertz gap. Typical output powers range from...

• Ion cyclotron resonance
Ion cyclotron resonance
Ion cyclotron resonance is a phenomenon related to the movement of ions in a magnetic field. It is used for accelerating ions in a cyclotron, and for measuring the masses of an ionized analyte in mass spectrometry, particularly with Fourier transform ion cyclotron resonance mass spectrometers...

• Linear accelerator
• Particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

• Storage ring
Storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating for a long period of time, up to many hours. Storage of a particular particle depends upon the mass, energy and usually charge of the particle being stored...

• Synchrocyclotron
Synchrocyclotron
A synchrocyclotron is a cyclotron in which the frequency of the driving RF electric field is varied to compensate for relativistic effects as the particles' velocity begins to approach the speed of light...

• Synchrotron
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...

• TRIUMF
TRIUMF
TRIUMF is Canada’s national laboratory for particle and nuclear physics. Its headquarters are located on the south campus of the University of British Columbia in Vancouver, British Columbia. TRIUMF houses the world's largest cyclotron, source of 500 MeV protons, which was named an IEEE Milestone...

- largest cyclotron in the world

• Tech Marvels: The Cyclotron — slideshow by Life magazine
• Advanced Cyclotron Systems Inc Commercial manufacturer of high output medical cyclotrons.
• TRIUMF
TRIUMF
TRIUMF is Canada’s national laboratory for particle and nuclear physics. Its headquarters are located on the south campus of the University of British Columbia in Vancouver, British Columbia. TRIUMF houses the world's largest cyclotron, source of 500 MeV protons, which was named an IEEE Milestone...

-- The University of British Columbia, Vancouver, Canada & National Research Council of Canada\Conseil national de recherches Canada -- Method and apparatus for the acceleration of ions
• Indiana University Cyclotron Facility MPRI treats first patient using robotic gantry system.
• "The 88-Inch Cyclotron at LBNL"
• "The NSCL at Michigan State University" Home of coupled K500 and K1200 cyclotrons; the K500, being the first superconducting cyclotron and the K1200 currently the most powerful in the world.
• Rutgers Cyclotron and "Building a Cyclotron on a Shoestring" Tim Koeth, now a graduate student at Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...

, built a 12-inch 1 MeV cyclotron as an undergraduate project, which is now used for a senior-level undergraduate and a graduate lab course.
• "Resonance Spectral Analysis with a Homebuilt Cyclotron" 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.
• Relativistic accelerator physics PDF