ciclotrones

Ciclotrones are a class of particle accelerators in which charged particles are accelerated to high energies by a constant magnetic field and an alternating electric field applied across two D-shaped electrodes, or dees, inside a vacuum chamber. As particles cross the gaps between the dees, they gain energy from the oscillating voltage and follow expanding circular or spiral paths under the magnetic field. For nonrelativistic speeds, the revolution frequency is approximately f = qB/(2πm), which is largely energy-independent, allowing resonance to be maintained as acceleration proceeds. Relativistic effects, however, cause the frequency to drift at higher speeds.

History and development: The cyclotron was invented in the 1930s by Ernest O. Lawrence at the University of California, Berkeley. The first practical cyclotrons began operating in 1931–1932, enabling energetic ion production and rapid radiochemical work. The technology accelerated discoveries in nuclear physics and became a foundation for compact accelerators used in medicine and research.

Variants and limitations: Classical cyclotrons perform well at low-to-moderate energies but relativistic effects limit their use for heavier particles at higher energies. Variants include the synchrocyclotron, which modulates the RF frequency to compensate mass increase, and the azimuthally varying field (AVF) cyclotron, which shapes the magnetic field to maintain isochronous orbits. Modern designs may employ superconducting magnets to reach higher energies.

Applications: Cyclotrons are widely used to produce medical radioisotopes for PET imaging (for example, 18F, 13N, 15O, 68Ga) and, in some configurations, for proton therapy, as well as in basic and applied nuclear physics research. They are valued for relatively compact size and lower cost compared with larger accelerators, though they require substantial shielding and radiation-safety systems.