Discuss the working of cyclotron in detail.

Explanation

Cyclotron: Cyclotron is a device used to accelerate the charged particles to gain large kinetic energy. It is also called as high energy accelerator. It was invented by Lawrence and Livingston in 1934.
Principle: When a charged particle moves normal to the magnetic field, it experiences magnetic Lorentz force.
Construction: The particles are allowed to move in between two semicircular metal containers called Dees (hollow D-shaped objects), Dees are enclosed in an evacuated chamber and it is kept in a region with uniform magnetic field controlled by an electromagnet. The direction of magnetic field is normal to the plane of the Dees. The two Dees are kept separated with a gap and the source S (which ejects the particle to be accelerated) is placed at the center in the gap between the Dees. Dees are connected to high frequency alternating potential difference.

Working: Let us assume that the ion ejected from source S is positively charged. As soon as ion is ejected, it is accelerated towards a Dee (say, Dee - 1) which has negative potential at that time. Since the magnetic field is normal to the plane of the Dees, the ion undergoes circular path. After one semi-circular path in Dee-1, the ion reaches the gap between Dees. At this time, the polarities of the Dees are reversed so that the ion is now accelerated towards Dee-2 with a greater velocity. For this circular motion, the centripetal force of the charged particle q is provided by Lorentz force.
`(mv^2)/r = qvB rArr r=m/(qB) v rArr r prop v`
From the equation, the increase in velocity increases the radius of circular path. This process continues and hence the particle undergoes spiral path of increasing radius. Once it reaches near the edge, it is taken out with the help of deflector plate and allowed to hit the target T. Very important condition in cyclotron operation is the resonance condition. It happens when the frequency f at which the positive ion circulates in the magnetic field must be equal to the constant frequency of the electrical oscillator `f_"osc"` From equation
`f_"osc"=(qB)/(2pim) rArr T=1/f_"osc"`
The time period of oscillation is `T=(2pim)/(qB)`
The kinetic energy of the charged particle is `KE=1/2 mv^2 =(q^2B^2r^2)/(2m)`
Limitations of cyclotron
(a) the speed of the ion is limited
(b) electron cannot be accelerated
(c) uncharged particles cannot be accelerated.