Cyclotron

A modern Cyclotron for radiation therapy

Acyclotronis a type ofparticle acceleratorinvented byErnest Lawrencefrom theUniversity of California, Berkeleyin 1930.It acceleratescharged particlesby whirling them in a circle. The first cyclotrons were the size of a hand. Some modern circular accelerators use a circle as wide as a city.

Cyclotrons use perpendicularmagnetic fieldto bendelectronsandparticlesthrough into a semicircular path by an appliedelectric field.The applied electric field accelerates electrons between the "D" electrodes(also called "dees" ) of the magnetic field region.

The accelerating electric field reverses just at the time the electrons finish their half circle, so that it accelerates them across the gap. With a higher speed, they move in a larger semicircle. After repeating this process several times, they come out the exit port at a high speed.

Cyclotron Frequency

A moving charge in a cyclotron will move in a circular path under the influence of a constant magnetic field. If the time to complete one orbit is calculated:

$T={\frac {2\pi r}{v}}={\frac {2\pi mv}{qBv}}={\frac {2\pi m}{qB}}$.

It is found that the period is independent of the radius. Therefore if asquare waveis applied atangular frequencyqB/m, the charge will spiral outward, increasing in speed.

When a square wave of angular frequency ω=qB/m is applied between the two sides of themagnetic poles,the charge will be boosted again at just the right time to accelerate it across the gap. Thus the constant cyclotronfrequencycan continue to accelerate the charge (so long as it is not relativistic).