CBSE Class 12 · 2019 · Magnetic Effects of CurrentShort Answer

Principle: a positive ion can be given large energy using a modest alternating voltage by making it cross the same accelerating gap again and again, in step with its circular motion maintained by a magnetic field.
Working: two hollow D-shaped electrodes (dees) sit in a uniform magnetic field perpendicular to their plane and are connected to a high-frequency oscillator. Inside a dee the magnetic force provides the centripetal force,

so the path is a semicircle; each time the ion crosses the gap the field has reversed and accelerates it, and $r$ grows with speed while the time per semicircle stays the same.
Time for one semicircle $=\frac{\pi m}{qB}$, so the period is $T=\frac{2\pi m}{qB}$ and the cyclotron frequency is

which is independent of the speed (or energy) and radius of the particle.