Cyclotron 2026-10-18
View more
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.
Figure 1.
Cyclotron bending, gap kicks, and a separate beam readout
. 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. Details.
Read the full article