Cyclotron

Introduction

In 1934, E.O. Lawrence and M.S. Livingston invented the cyclotron, a device known to accelerate the charged particles or ions to high energies. For the acceleration of the particles, both electric and magnetic fields are used. During the insertion of charged particles in a cyclotron, the static magnetic field and direction of motion are always perpendicular to each other. Though both the forces act in the cyclotron, their uses are different. Let’s understand other major facts about cyclotrons such as their principle, construction, working, uses, and limitations.

Principle of Cyclotron

A charged particle that moves normally to the magnetic field tends to experience magnetic Lorentz force. Because of the presence of the force, the charged particle starts moving in a circular path. A static magnetic field holds the particles to the spiral trajectory, and the varying electric field present accelerates the charged particle. Both magnetic and electric fields are known as cross fields because they act perpendicular to each other.

Also read: What is Magnetic Field Intensity?

Construction of Cyclotron

Cyclotron consists of a hollow metal cylinder that is equipped with two different sections represented by D1 and D2. These D1 and D2 sections are known as dees and are covered under an evacuated chamber. Both the dees have some distance between them that is filled with a source of ions. A strong electromagnet covers the dees, and the magnetic field thus produced acts at right angles to the dees’ planes. To complete the construction, a high-frequency alternating voltage or oscillator connects the dees, D1 and D2.

Working Principle of Cyclotron

A source that emits a positive charge, q, and the mass of the particle, m, always accelerates towards the dees. The particle gets accelerated and moves towards the dee with negative potential at that moment. The normal magnetic field acting on the system makes the ion move in a circular path. As they move in a circular path, a time arrives when the ions reach the gap present in the dees. Till then, the polarity of the dees is reversed, and the particle reached again moves in another dee. But this time, the ion is accelerated at a high velocity and in a greater radius of the circle. The process continues, and when the accelerated particle reaches the edge, a deflector plate is used to take out the accelerated particle. This time the accelerated particle has high energy and is allowed to hit the target. Thus, this is the working principle of the cyclotron.

Expression for Cyclotron Frequency

The theory of cyclotron is based on the interaction of electric and magnetic fields with the charged particle. When a charged particle, q, moves with the velocity, v, due to the presence of a uniform magnetic field, B, the magnetic force is calculated by the formula:

F = qv x B

When the velocity of the moving particle and the uniform magnetic field are at right angles to each other, the magnitude of the magnetic force becomes:

F = qvB sin 90°

where sin 90° = 1 and by substitution of value in the above equation, we get:

F = qvB

Thus, in this case, the acting force is always at a right angle to velocity as well as the magnetic field applied.

A circular path of charged particle: When the magnetic force serves as the required centripetal force of the circular path, it leads to the rotation of the particle. Here is the expression for the centripetal force with Fc as the magnitude:

Fc = mν2 / r

where ‘m’ is the mass of the particle that is accelerated or moving, and ‘r’ is the radius of the circular path in which the particle is moving. Hence, both the forces (centripetal force and magnetic force) are equal to each other.

Fc = F

mν2 / r = qνB

ν = qBr / m

As we know, the angular velocity or, more precisely, cyclotron angular velocity is represented by,

ω = ν / r

On substituting the values in the above expression, we get,

ω = qB / m

Hence, the formula of cyclotron frequency is given by,

f = ω / 2π

f = qB / 2Ï€m

Thus, the above equation is known as the expression for cyclotron frequency.

Uses of Cyclotron

Cyclotrons hold plenty of benefits in comparison to linear accelerators. First, they require less space, and second, they can accelerate particles multiple times in a single setup. Here are a few applications or uses of a cyclotron:

• Multiple nuclear physics experiments use cyclotrons to accelerate the charged particles
• The bombardment of atomic nuclei also uses cyclotrons
• Treatment of cancer that involves radiation therapy utilizes cyclotron
• During the transformation of nuclear structure, most precisely known as nuclear transmutation, cyclotrons are used

Limitations of Cyclotron

Besides the uses of cyclotrons, they have a few limitations too:

• Neutrons don’t get accelerated by the use of cyclotrons
• The reason is that such particles don’t have any charge, meaning they don’t intersect with magnetic or electric fields
• Electrons, also, don’t get accelerated by using cyclotrons
• The reason is that they have a small mass, which rapidly increases the speed. The rapid increase in speed leads to losing the particle during motion
• It’s quite hard to maintain a uniform magnetic field over a vast area of the dees

Conclusion

Cyclotrons accelerate the charged particles by using a high-frequency alternating voltage, but they come with certain limitations, as stated above. We hope this article helped you understand the major facts about cyclotron including its working, principle, construction, uses, and limitations.