cyclotron

A cyclotron is a type of particle accelerator that uses a perpendicular magnetic field and an alternating electric field to accelerate charged particles along a spiral path. The device consists of two hollow, semicircular electrodes called dees placed in a vacuum chamber. A uniform magnetic field causes charged particles to move in circular orbits within the dees, and an alternating voltage between the dees accelerates the particles each time they cross the gap between them.

Principle and design: When a charged particle enters the magnetic field, it experiences a Lorentz force that bends its trajectory into a circle. The orbital frequency in a uniform field is approximately independent of the particle’s speed (non-relativistic case), given by f = qB/(2πm), where q is the charge, B the magnetic field strength, and m the particle’s mass. The radius of the orbit is r = mv/(qB), so as the particle gains speed it follows a spiral path outward until reaching the electrostatic gap and gaining energy with each crossing. The accelerating voltage is synchronized to the particle’s revolution frequency.

History and variants: The cyclotron was developed in the early 1930s by Ernest O. Lawrence and M. S. Livingston at the University of California, Berkeley. Limitations arise as particles become relativistic, increasing mass and changing the frequency. Variants such as the synchrocyclotron (varying RF frequency) and the isochronous cyclotron (adjusting field to keep timing constant) were devised to address this.

Uses: Cyclotrons are used for fundamental research, production of medical isotopes, and certain forms of proton therapy and materials science applications. Modern compact cyclotrons remain common in medical facilities for PET isotope production, while larger machines evolved into other accelerator types for high-energy physics.