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Ernest Lawrence and M. Stanley Livingston developed repeated acceleration of ions in a cyclotron. An oscillating electric field accelerates a particle each time it crosses the gap between two hollow electrodes; a perpendicular magnetic field bends it back toward the gap. In the nonrelativistic approximation, the orbit period $2\pi m/(|q|B)$ is independent of radius, allowing successive crossings to stay synchronized. Their 1932 report obtained proton energies of $1.22\mathrm{MeV}$ with a maximum applied voltage of $4,000\mathrm{V}$.^[ref]

A physicist.^[ref]

M. Stanley Livingston and Ernest Lawrence developed the cyclotron as a practical source of energetic ions. Their 1932 paper explains how an alternating electric field gives a new acceleration on every gap crossing while the magnetic field supplies the return path. Keeping the half-orbit time synchronized with the field oscillation lets many small energy increments accumulate. The paper also emphasizes beam focusing and magnetic field correction, showing why successful acceleration required control of the trajectories as well as the resonance condition.^[ref]

A physicist.^[ref]