What are the Factors that Affect Cyclotron?

In the year 1929-30, scientist Lawrence invented a particle accelerator device called the cyclotron. A cyclotron contains a hollow cylinder. This cylinder has two Dees in a vacuum chamber. An electric field accelerates the charged particles along a spiral path in this cylinder.

Principle of Cyclotron

The working principle of a cyclotron is that the electric field accelerates the charged particle. A force known as the Lorentz force acts on this charged particle.

F=Bqv

Here, q is the charge on the particle. E is the electric field that influences the acceleration of the charged particle. B is the static magnetic field on the particle. v is the velocity of the charged particle.

Working of the Cyclotron

Cyclotron consists of a hollow cylinder divided into two parts called Dees. A vacuum chamber encompasses these Dees. Now, we connect high-frequency oscillators to this dee. When the source releases the positive charge having a mass of m, the negatively charged dee attracts the particle; now, the Lorentz force acts on the particle, which moves the particle in a spiral path.

When the charged particle reaches the gap between the dees, there is a change in the polarity of the dees. As a result, the dee just in front of the moving charged particle now becomes negative and attracts the particle and accelerates the particle. The change in polarity repeats when the charged particle again comes to the gap between the dees. Thus, by continuing to change the polarity of the dees, the charged particle is accelerated in the cyclotron. All this happens under the Lorentz force.

Frequency of the Charged Particle

The Lorentz force acting on a charged particle moving in a circular path will be equal to the centripetal force acting on the particle.

Bqv=1  ⁄ 2mv²

v=√2Bqv ⁄ m

Thus, we can calculate the velocity of the charged particle by the above formula.

Now again, from the above equation

Bqv=1 ⁄ 2mv²

v ⁄ r=Bq ⁄ m

Now time for a half-circle is given as:

t=πr ⁄ v

t=πm ⁄ Bq

The total time period of the accelerated particle 

T=2πm ⁄ Bq

So the frequency of the charged particle will be

f=Bq ⁄ 2πm

From the above formula, we can see the frequency of the particle depends upon the following factors:

1. The frequency of a cyclotron depends upon the charge present on the particle.
2. The frequency of the cyclotron depends upon the magnetic field that influences the acceleration of the charged particle.
3. The frequency of charged particles in a cyclotron also depends upon the mass of the particle. The frequency will be higher for the lower masses.
4. The frequency of the particle does not depend upon the radius and the speed of the accelerated particles.

Limitations of the Cyclotrons:

1. We cannot use cyclotrons to accelerate the neutrons because they are neutral. Hence, there will not be any effect of magnetic or electric field on this particle.
2. The cyclotrons can not accelerate electrons because the electrons have a very small mass; their speed increases rapidly, by which the resonance between the voltage and the particle is lost.
3. It is not easy to maintain a uniform electric field over a large area of the dees.

Conclusion

In this article, we studied factors affecting the frequency of cyclotrons and the limitations of the cyclotrons. A cyclotron contains a hollow cylinder. This cylinder has two Dees in a vacuum chamber. An electric field accelerates the charged particles along a spiral path in this cylinder. The working principle of a cyclotron is that the electric field accelerates the charged particle. We found that the frequency does not depend upon the radius and the velocity. And the cyclotron does not accelerate the electrons due to their lighter weight.