A cyclotron is a form of particle accelerator, invented by Ernest Lawrence in the early 1930s, which is useful both for low-to-medium-energy subatomic physics experiments and for commercial isotope production. It is based on the behavior of charged particles under crossed electric and magnetic fields.

The basic situation in a cyclotron is of a charged particle moving in a plane, under a constant uniform magnetic field directed perpendicular to that plane. The particle will move in a circle, with angular frequency qB/m, where q is the charge of the particle, m is the mass of the particle, and B is the magnetic field strength. (see cyclotron frequency for details) This frequency is independent of velocity, which is very important. If the particle is accelerated by some other force, the radius of its path will increase to maintain the constant frequency. In a cyclotron, this acceleration is provided by an oscillating electric field between two semi-circular plates called 'dees'. If the frequency of the oscillating electric potential is an integer multiple of the cyclotron frequency qB/m, then the particle sees a potential difference of the same sign every time it crosses the gap between the dees. The net result is that the particle accelerates in an outward spiral until its radius exceeds the radius of the cyclotron, at which point it leaves tangentially.

The cyclotron can, in theory, accelerate any charged particle to a velocity qBr/m, where r is the radius of the cyclotron. In practice, it is used mainly to accelerate protons and light ions, although use of a cyclotron to accelerate heavy ions is not unheard of. Light particles are used because their charge-to-mass ratio is relatively large, so lower magnetic fields and/or smaller radii are necessary to acheive a desired energy.

The largest cyclotron in the world is found at TRIUMF, in Vancouver, British Columbia. It produces a 520 MeV proton beam at a relatively high current. A clever method is used to extract proton beams with various energies in the 60-520 MeV range. Instead of accelerating protons (H+ ions), the accelerator accelerates H- ions, consisting of a proton and two electrons. Thin foils are placed inside the accelerator which strip the electrons from the H- ions, converting them to bare protons. Since the charge changes sign, the proton begins to circulate in the opposite direction and leaves the accelerator via a beam pipe at the edge. This method can be used to produce three separate beams simultaneously, which the TRIUMF lab takes full advantage of.

There are several disadvantages to the cyclotron design. The main disadvantage is the relatively low practical limit on beam energies. A cyclotron requires a circular disc shape to operate and a uniform magnetic field throughout the entire disc. Generating such a field is subject to immense practical problems; the TRIUMF accelerator uses an unusual design with pinwheel-shaped poles. A related problem is the ability for other accelerator designs, mainly synchrotrons, to have vastly larger accelerator sizes due to only requiring an accelerator ring and not an accelerator disc. Synchrotron rings of diameters measured in kilometers have been built, but the TRIUMF cyclotron, largest in the world, isn't even 20 meters in diameter. Nevertheless, there is no more practical design for a small accelerator due to its simplicity of operation.

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This writeup is copyright 2003-2004 D.G. Roberge and is released under the Creative Commons Attribution-NoDerivs-NonCommercial licence. Details can be found at http://creativecommons.org/licenses/by-nd-nc/2.0/ .