Cyclotron: It is a device used to accelerate charged particles like protons, deuterons, α particles, etc. to very high energies.

Principle: A charged particle passes through the perpendicular electric and magnetic field, it is accelerated to very high energies.

Construction: It consists of following main parts:

(i) It consists of two small, hollow, metallic half cylinders D₁ and D₂, called dees.

(ii) They are mounted inside a vacuum chamber between the poles of a powerful electromagnet.

(iii) The des are connected to the source of high frequency alternating voltage of few hundred kilovolts.

(iv) The beam of charged particles to be accelerated is injected in to dees near their centre, in a plane perpendicular to the magnetic field.

(v) The charged particles are pulled out of the dees by a deflecting plate, (which is negatively charged) through a window w.

Theory: Let a particle of charge q and mass m enters a region of magnetic field B with velocity v, normal to the field B.

The necessary centripetal force being provided by the magnetic field. Therefore, magnetic force on charge q = centripetal force on charge q

qvB sinθ = mv²/r

r = mv/qB

Period of revolution of the charged particles is given by

T = 2πr/v = (2π/v).(mv/qB) = 2πm/qB

And frequency

F_C = 1/T = qB/2πm

Clearly, this frequency is independent of both the velocity of the particle and radius of the orbit and is called cyclotron frequency.

Working: Suppose the positive ion, say a proton enters a gap between the two dees and finds dee D₁ to be negative. It gets accelerated towards D₁. As it enters the dee D₁, it does not experience any electric force due to shielding effect of the metallic dee. The perpendicular magnetic field throws it in the circular path. At the instant the proton comes out of dee D₁, it find D₁ is positive and D₂ is negative. It now get accelerated towards D₂. It moves faster through D₂ describing a larger semicircle than before. Thus if the frequency of the applied voltage is kept exactly the same as the frequency of revolution of the proton, then every time the proton reaches the gap between the dees, the electric field is reversed and proton revives a push and finally it acquire very high energy. This is called cyclotron resonance condition. The proton follows a spiral path. The accelerated proton is ejected through a window by a deflecting voltage and hits the target.

Maximum kinetic energy of the accelerated ions: If v₀ is the maximum velocity acquired by the ions and r₀ is the radius of the dess, then

m(v₀)²/r₀ = qv₀B

v₀ = qBr₀/m

the maximum K.E. of the ions will be

K₀ = (1/2)m(v₀)² = (1/2)m (qBr₀/m)² = q²B²(r₀)²/2m

Limitations of cyclotron:

(i) Electrons cannot accelerated in a cyclotron. A large increase in their energy increases their velocity to a very large extent. This follows the electrons out of step with the oscillating field.

(ii) Neutrons, being electrically neutral, cannot be accelerated in a cyclotron.

Uses of cyclotron:

(i) Used to bombard nuclei and study the resulting nuclear reactions.

(ii) The high energy particles are used to produce other high energy particles, such as Neutrons, by collision.

(iii) Used to implane ions in to solids.

(iv) Used to produce radioactive isotopes.