Principle Behind the Working of Cyclotron

A cyclotron is a device used to accelerate a charged particle to a very high speed. It produces very energetic particles. An alternating voltage of high frequency is used in the cyclotron to accelerate the charged particle or ions. The applied voltage causes an oscillating electric field in space, helping accelerate the particles. Cyclotron is used in various nuclear reactions

Construction

It consists of a hollow semi-circular container made up of metal known as dees. Container 1 denotes to D1 and D2 is placed between the two sources of charged particles connected with the high alternating voltage of frequency. Such high-frequency voltage is also known as oscillator. Due to the oscillator, the electric field of the different charge is obtained. As the magnetic field lines travel outwards from the north to south. If a charge from a source of mass m and charge q is; A space is formed in the dees so that the charged particle will eject out from the space.

Working 

The charged particle emits from the source. Initially, the charged particle is positive. It will definitely attract the opposite charged dees. As the particle travels inside the deeds, the electric field on the particle is zero. The electric field does not act between the dees. The charge will accelerate to the D2 and its speed is increased as soon as the q enters the D2.  The electric field is zero. So the speed stops increasing. But the magnetic field acting on the charge forces the charged particle to move in a circle. As the particle executes a circular motion, the electric charge tries to come outwards from the circular space. We have to set a frequency of oscillation so that their charge is changed to the opposite orientation. Due to this, the polarity of the charge gets reversed. The positive charged particle will accelerate towards D1. As it enters D1, the electric field is zero and the magnetic force pushes the charged particle force to move in the circular orbit. 

The process is repeated a number of times, due to which the velocity of the charged particle moving in circular orbit increases. The expression for the charged particle moving in the orbit is given as;

r=mvqB

The above relation shows that as the velocity of the particle is increasing, the radius of the particle will also increase. A point obtained when the velocity of the charged particle is equal to the escape velocity and the particle will come out from the spiral orbit.

The purpose of accelerating the charged particle is achieved.

Final speed and kinetic energy

The radius of the dees is R, so that the radius of the circular orbit in which the charge at the time of exit will be R. So the value of its radius and the velocity is;

R=mvqB 

v=qBRm

  Where, 

q is the positive charge particle 

R is the radius of the orbit at the time of exit

m is the mass of the particle 

B is the magnetic field 

V is the velocity

The kinetic energy of the particle will be;

KE = 12mv2

KE=12m(qBRm)2

KE=q2B2R22m

The above formula shows that all the values are related to the radius.

T is the time required to complete one circle in orbit. In a cyclotron it is known as the time period of orbit. Which is given by the formula ;

T= 2mqB

If the frequency is the inverse of the time period and denoted by f. The frequency of the particle is found as;

f=1T

f=qB2m

One complete charge oscillator circle should give one positive and one negative cycle. Time period to complete one cycle is equal to the time period of the alternating current. So the oscillating frequency is equal to the cyclotron frequency as;

Oscillating frequency = cyclotron frequency =  qB2m

Uses of cyclotron

1. In a nuclear reaction, we need high-speed charge particles so that they can enter the nucleus of the atom. A cyclotron is used to produce such high-speed charge particles.

2. Insert the ions into the solid. These ions are used to change the property of the solids.

3. To stop the radioactive decay.

Conclusion

A cyclotron is a device used to accelerate the charged particle to a very high speed. Cyclotron is used in various nuclear reactions. The article also discussed velocity, kinetic energy, time period and frequency of the particle.