= Cyclotron
{wiki}
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.
\Image[/cyclotron-dees-gap-and-readout.png]
{title=Cyclotron bending, gap kicks, and a separate beam readout}
{description=Original functional schematic, with illustrative dimensions only. The orbit is constructed from exact semicircles of successively increased speed in the zero-width-gap model; the white gap band marks where the finite-gap electric field would act. The architecture shows two ideal dees, not a scale reconstruction of the one-driven-dee 1932 apparatus. Extraction and readout are shown as a separate functional chain.}
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