# Cyclotron

## Cyclotron

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.