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A cyclotron repeatedly passes ions through an alternating electric field between two hollow electrodes called cyclotron dees. A nearly uniform magnetic field perpendicular to their plane bends the charged particles back toward the gap. Inside each cyclotron dee, ideal shielding suppresses the accelerating electric field, so each segment is a constant-speed circular motion. The next gap crossing increases the speed and the radius of curvature. The complete path consists of connected, progressively larger arcs, rather than one circle or a smooth spiral with continuous acceleration everywhere.

The striking feature is a timing cancellation: the longer arc traveled by a faster particle takes the same time. This cyclotron resonance condition lets one fixed radio frequency accelerate many successive gap crossings. The following construction and cyclotron energy and orbit radius example describe an ideal model; the Lawrence-Livingston cyclotron experiment explains what the builders actually measured.

Ernest Orlando Lawrence and Milton Stanley Livingston reported repeated ion acceleration in 1932. Their evacuated brass chamber used one driven hollow cyclotron dee; the grounded box and slotted divider supplied the other electrode. Filament Electrons ionized hydrogen near the gap. A perpendicular magnetic field bent the ions; a high-frequency oscillator drove the gap. Deflecting plates and slits selected particles for a Faraday cup, read by an electrometer.^[ref]

Scanning the magnetic field produced narrow resonance peaks. The optimum deflecting voltage tracked the kinetic energy predicted from field and orbit radius, supporting the reported $1.22\mathrm{MeV}$ protons. Source width and slit geometry limited this check; it was not a direct energy measurement of every particle.^[ref]

This combination distinguishes producing a circulating electric current from establishing its kinetic energy. The electrometer measures collected electric charge per unit time; it cannot by itself tell whether the collected particles are fast. The separate deflection selection supplies a speed-dependent test. Agreement of two consequences of the model, the cyclotron resonance condition and the cyclotron energy and orbit radius relation, makes the inference stronger than either a current signal or a predicted orbit alone.

Milton Stanley Livingston built the early cyclotrons with Ernest Orlando Lawrence; the 1939 Nobel Prize in Physics went to Ernest Orlando Lawrence. His lecture, The evolution of the cyclotron, was delivered on 11 December 1951.^[ref][ref]