## Cyclotron

The **cyclotron** is a machine to accelerate charged particles or ions to high energies. The cyclotron uses both
electric and magnetic fields in combination to increase the energy of charged particles. As the fields are
perpendicular to each other they are called **crossed fields**.

### Working

**Cyclotron** uses the fact that the frequency of
revolution of the charged particle in a magnetic field is independent of its energy and speed. The particles move most of the time inside two semicircular disc like metal containers, D_{1} and D_{2}, which are called **dees** as they
look like the letter D. Figure shows a schematic view of the cyclotron. Inside the metal boxes the particle is
shielded and is not acted on by the electric field. The magnetic field, however, acts on the particle and makes
it go round in a circular path inside a dee. Every time the particle moves from one dee to another it is acted
upon by the electric field. The sign of the electric field is changed alternately in tune with the circular motion
of the particle.

This ensures that the particle is always accelerated by the electric field. Each time the charge enters the gap, the electric field increases the energy of the particle. As energy increases, the radius of the circular path increases. So the path is a spiral one.

The whole assembly is evacuated to minimize collisions between the ions and the air molecules. A high frequency alternating voltage is applied to the dees. In the sketch shown in figure, positive ions or positively charged particles (e.g., protons) are released at the centre P. They move in a semicircular path in one of the dees and arrive in the gap between the dees in a time interval T/2; where T is the period of revolution, given by

`T=\frac{1}{f_c}=\frac{2\pi m}{qB}`

`f_{c}=\frac{qB}{2\pi m}`

This frequency is called the **cyclotron frequency** for obvious reasons and is denoted by f_{c}.

### Operating Principle

The frequency f_{a} of the applied voltage is adjusted so that the polarity of the dees is reversed in the same
time that it takes the ions to complete one half of the revolution. The requirement f_{a} = f_{c} is called the **resonance condition**. The phase of the supply is adjusted so that when the positive ions arrive at the edge of D_{1}, then D_{2} is at a lower potential and the ions are accelerated across the gap. Inside the dees the particles
travel in a region free from the electric field.

The increase in their kinetic energy is qV each time they move from one dee to another. As radius is directly proportional to speed, the radius of their path goes on increasing each time their kinetic energy increases. The ions are repeatedly accelerated across the dees until they have the required energy to have a radius approximately that of the dees. They are then deflected by a magnetic field and leave the system via an exit slit. We have

`v=\frac{qBR}{m}`

where R is radius of the trajectory at exit, and equals the radius of a dee.

Hence, kinetic energy of the ions is,

`\frac{1}{2}mv^2=\frac{q^{2}B^{2}R^{2}}{2m}`

The operation of a cyclotron is based on the fact that the time for one revolution of an ion is independent of its speed or radius of its orbit.

### Applications

The

**cyclotron**is used to bombard nuclei with energetic particles and study the resulting nuclear reactions.It is also used to implant ions into solids and modify their properties or even synthesise new materials.

It is used in hospitals to produce radioactive substances which can be used in diagnosis and treatment.