Cyclotron is a device used to accelerate positively charged particles like, \(\alpha\) particles, deuterons etc. to acquire enough energy to carry out nuclear disintegration etc. It is based on the fact that the electric field accelerates a charged particle and the magnetic field keeps it revolving in circular orbits of constant frequency.


It consists of two hollow \(D\) – shaped metallic chambers \({{D}_{1}}\) and \({{D}_{2}}\) called dees. The two dees are placed horizontally with a small gap separating them. The dees are connected to the source of high frequency electric field. The dees are enclosed in a metal box containing a gas at a low pressure of the order of \({{10}^{-3}}mm\) mercury. The whole apparatus is placed between the two poles of a strong electromagnet N S as shown in fig. The magnetic field acts perpendicular to the plane of the dees.

1) Cyclotron frequency:  

Time taken by ion to describe a semicircular path is given by, \(t=\frac{\pi r}{v}=\frac{\pi n}{qB}\)

If T = Time period of oscillating electric field then \(T=2t=\frac{2\pi m}{qB}\)

The cyclotron frequency, \(\nu =\frac{1}{T}\frac{Bq}{2\pi m}\)

2) Maximum energy of particle:

Maximum energy gained by the charged particle, \({{E}_{\max }}=\left( \frac{{{q}^{2}}{{B}^{2}}}{2m} \right){{r}^{2}}\)

Where, r = Maximum radius of the circular path followed by the positive ion.