Cyclotron

Cyclotron

Cyclotron is a machine to accelerate charged particles or ions to high energies. It was invented by E.O Lawrence and M.S Livingston.

• Cyclotron uses both electric and magnetic fields in combination to increase the energy of charged particles.
• The electric and magnetic fields are perpendicular to each other ( and called as crossed fields)
• Principle:- the frequency of revolution of the charged particle in a magnetic field is independent of its energy.

Working:

o   The particles move most of the time inside two semi circular disc –like metal containers, D₁   and D₂ , which are called ‘dees’  ( as they look like the letter ‘D’)

o   Inside the metal boxes, the particle is shielded and is not acted on by the electric field.

o   The magnetic field acts on the particle and makes it go round in a circular path inside the dee.

o   Every time the particle moves from one dee to another, it is acted upon by the electric field.

o   The sign of the electric field is changed alternately in tune with the circular motion of the particle.

o   Thus, the particle is always accelerated by the electric field

o   Each time, the acceleration increases the energy of the particle.

o   As energy increases, the radius of the circular path also increases. So, the path is a spiral one.

o   The whole assembly is evacuated to minimize collisions between the ions and the air molecules.

o   A high frequency a.c voltage is applied to the dees.

In the fig, positive ions or positively charged particles (protons) are released at the centre P. They move in a semi-circular path in one of the dees and arrive in the gap between the dees in a time interval T/2.

T- period of revolution.

T=1/f_C = 2πm/qB

Or , f_C = qB/2 πm

f_C – Cyclotron frequency

f_a – frequency of applied voltage

At resonance, f_C = f_a

• The phase of the supply is adjusted so that when the positive ions arrive at the edge of D_1,   the dee D₂ is at a lower potential and the ions are accelerated across the gap.
• Inside the dees, the particles travel in a region free of the electric field.
• The increase in their K.E = qV each time they cross from one dee to another.
• (V= the voltage across the dees at that time)
• Thus, radius of the path increases each time they cross the dees.
• The ions are repeatedly accelerated across the dees until they have the required energy to have a radius approximately equal to that of the dees.
• They are then deflected by a magnetic field and leave the system via an exit slip.

From  

Applications

1. Used to bombard nuclei with energetic particles to accelerate nuclei and study the resulting nuclear reactions
2. Used to implant ions in to solids and modify their properties. Or to synthesize new materials.
3. Used in hospitals to produce radio active substances that can be used in diagnosis and treatment.