Cyclotron

For other uses, see Cyclotron (disambiguation).

A French cyclotron, produced in Zurich, Switzerland in 1937

A modern cyclotron for radiation therapy

A cyclotron is a compact type of particle accelerator in which charged particles in a static magnetic field are travelling outwards from the center along a spiral path and get accelerated by radio frequency electromagnetic fields.

The cyclotron was invented by Leó Szilárd and first manufactured and patented by Ernest Lawrence, of the University of California, Berkeley who started operating it in 1932. Lawrence read an article about the concept of a drift tube linac by Rolf Widerøe, who had also been working along similar lines with the betatron concept. The first European cyclotron was constructed in Leningrad in the physics department of the Radium Institute, headed by Vitali Khlopin. This instrument was first proposed in 1932 by George Gamow and Lev Mysovskii and was installed and running by 1937.

TRIUMF, 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 while a 23 MHz 94 kV 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, Vancouver, Canada.

Principle of operation

Diagram of cyclotron operation from Lawrence's 1934 patent. The "D" shaped electrodes are enclosed in a flat vacuum chamber, which is installed in a narrow gap between the two poles of a large magnet.

Beam of electrons moving in a circle. Lighting is caused by excitation of gas atoms in a bulb.

Cyclotrons accelerate charged particle beams using a high frequency alternating voltage which is applied between two "D"-shaped electrodes (also called "dees"). An additional static magnetic field B is applied in perpendicular direction to the electrode plane, enabling particles to re-encounter the accelerating voltage many times at the same phase. To achieve this, the voltage frequency must match the particle's cyclotron resonance frequency

$f = \frac{q B}{2\pi m}$,

with the relativistic mass m and its charge q. This frequency is given by equality of centripetal force and magnetic Lorentz force. The particles, injected near the center of the magnetic field, increase their kinetic energy only when recirculating through the gap between the electrodes; thus they travel outwards along a spiral path.

Their radius will increase until the particles hit a target at the perimeter of the vacuum chamber, or leave the cyclotron using a beam tube, enabling their use e.g. for particle therapy. Various materials may be used for a target, and the collisions will create secondary particles which may be guided outside of the cyclotron and into instruments for analysis.

Relativistic considerations

In classical approximation, the frequency does not depend upon the radius of the particle's orbit, since the particles mass is constant. 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.

In contrast to this approximation, as particles approach the speed of light, their relativistic mass increases, requiring either modifications to the frequency, leading to the synchrocyclotron, or the magnetic field during the acceleration, leading to the isochronous cyclotron. The relativistic cyclotron frequency can be rewritten as

$f = \frac{q B}{2\pi \gamma m_0} = \frac{f_0}{\gamma}$,

where

$\gamma=1 / \sqrt{1-\left(\frac{v}{c}\right)^2}$ is the Lorentz factor

m₀ is the particle rest mass

f₀ would be the cyclotron frequency in classical approximation.

The gyroradius for a particle moving in a static magnetic field is then given by

$r = \frac{\gamma \beta m_0 c}{q B}$,

where β = v / c is the relative velocity.

Synchrocyclotron

Main article: 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. This is in contrast to the classical cyclotron, where the frequency was held constant, thus leading to the synchrocyclotron operation frequency being

$f = \frac{f_0}{\gamma} = f_0 \; \sqrt{1-\beta^2}$,

where f₀ is the classical cyclotron frequency, and β = v / c again is the relative velocity of the particle beam.

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.

Isochronous cyclotron

An alternative to the synchrocyclotron is the isochronous cyclotron, which has a magnetic field that increases with radius, rather than with time. Isochronous cyclotrons are capable of producing much greater beam current than synchrocyclotrons, but require azimuthal variations in the field strength to provide a strong focusing effect and keep the particles captured in their spiral trajectory.

Recalling the relativistic gyroradius

$r = \frac{\gamma m_0 v}{q B}$

and the relativistic cyclotron frequency f = f₀ / γ, one can choose B to be proportional to the Lorentz factor, B = γB₀. This results in the relation

$r = \frac{m_0 v}{q B_0}$

which again only depends on the velocity v, like in the non-relativistic case. Also, the cyclotron frequency is constant in this case.

The transverse 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 (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. It was obscurely known theoretically long before it was put into practice.^{[citation needed]}

Usage

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. The results 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.

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. Cyclotron beams can be used to bombard other atoms to produce short-lived positron-emitting isotopes suitable for PET imaging.

More recently cyclotrons currently installed at hospitals for particle therapy have been retrofitted to enable them to produce technetium-99. Technetium-99 is a diagnostic isotope in short supply due to difficulties at Canada's Chalk River facility.

Advantages and Limitations

60-inch cyclotron, circa 1939, showing a beam of accelerated ions (likely protons or deuterons) escaping the accelerator and ionizing the surrounding air causing a blue glow

The cyclotron was an improvement over the linear accelerators (linacs) that were available when it was invented, being more cost- and space-effective due to its iterated interaction with the accelerating field. In the 1920s, it was not possible to generate high power high-frequency radio waves which are used in modern linacs (generated by Klystrons), thus requiring unpractically long linac structures for higher-energy particles. The compactness of the device reduces other costs, such as its foundations, radiation shielding, and the enclosing building.

Cyclotrons have a single electrical driver, which saves both money and power, since more expense may be allocated to increasing efficiency. Furthermore , cyclotrons are able to produce a continuous stream of particles at the target, so the average power passed from a particle beam into a target is relatively high.

The magnet portion of a 27" cyclotron. The gray object is the upper pole piece, routing the magnetic field in two loops through a similar part below. The white canisters held conductive coils to generate the magnetic field. The D electrodes are contained in a vacuum chamber that was inserted in the central field gap.

The spiral 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. 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 classical 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 modern, klystron-driven linear accelerators, both of which have the advantage of scalability, offering more power within an improved cost structure as the machines are made larger.

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 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.

See also

• Beamline
• Cyclotron radiation
• Synchrotron light
• Bremsstrahlung (radiation)
• Electron cyclotron resonance
• Gyroradius
• Gyrotron
• Ion cyclotron resonance
• Linear accelerator
• Particle accelerator
• Storage ring
• Synchrocyclotron
• Synchrotron
• TRIUMF - largest cyclotron in the world
• Radiation reaction

External links

• 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, 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
• Wired news article about a neighborhood cyclotron in Anchorage, Alaska
• The Cyclotron Kids A pair of high school students building their own 2.3 MeV cyclotron for experimentation.
• 2010 Small Cyclotron Conference Amateur cyclotron builders gathered for the first Small Cyclotron Conference on April 24, 2010.
• TSL - The Svedberg laboratory, center for proton therapy and radiation testing, Uppsala, Sweden.
• Oak Ridge Isochronous Cyclotron
• Web site of company IBA
• Advanced Cyclotron Systems Inc Commercial manufacturer of high output medical cyclotrons.