GyrollaCyclotron Motion / Lorentz ForceSticker

Gyrolla runs a carousel inside a magnet, and her ride has one strange rule: every lap takes the same time.

A charged particle moving across a magnetic field feels a force at right angles to its velocity. The force never speeds it up or slows it down; it just bends the path into a circle, the first line on this page. A faster particle swings out to a wider circle, a slower one stays on a tight inner track. Because the radius grows in proportion to the speed, the time for one lap stays the same. That lap rate is the cyclotron frequency, the second line: for a proton, about 15.2 MHz for every tesla, set only by charge, mass and field.

Ernest Lawrence at Berkeley saw what that meant. If every lap takes the same time, you can kick the particle with an alternating voltage at that fixed beat, twice per lap, across the gap between two hollow D-shaped electrodes. Each kick adds energy, the particle spirals outward, and the timing never has to change. In 1932 he and M. Stanley Livingston reported the production of high-speed light ions without high voltages: protons of more than a million electronvolts, with no million-volt supply anywhere. Lawrence received the 1939 Nobel Prize for the cyclotron.

The rule holds non-relativistically. As a particle approaches light speed, its lap frequency falls by the Lorentz factor and the beat drifts. That is why later machines, the synchrocyclotrons, retune their frequency as the particles speed up.

So Gyrolla taps each rider with her baton every half lap, always on the same beat, and every rider, fast or slow, keeps time.

Bigger circle. Same lap time.