Magnetism And Matter

Cyclotron

A cyclotron is a type of particle accelerator that accelerates charged particles using a strong magnetic field. When a strong magnetic field created by two large electromagnets applies to these charged particles, they accelerate and reach a very high speed due to the electromagnetic field. Then, these particles are utilized in experiments where particles with high speed are required. These cyclotrons cannot be utilized to accelerate electrons as the mass of electrons is so small and the application of magnetic field to these electrons increases its speed very high which may go beyond control. As magnetic fields can increase the speed of charged particles only, hence neutrons are the exception to cyclotrons.

The Cyclotron was invented by Ernest O. Lawrence in 1929–1930 at the University of California, Berkeley and got the patent in 1932. He got the Nobel Prize for his invention in 1939.

Cyclotron

Types of Cyclotrons

There are two types of cyclotrons, namely, synchrocyclotrons and isochronous cyclotrons.

Synchrocyclotron

It is a type of particle accelerator and its use is necessary where high energy limits are the requirement of experiment. In this type of particle accelerator, the particles are accelerated in a ring of constant radius. The magnetic field required in this type of particle accelerator where the actual path of the particle lies. Since the particle size is very small, the magnetic path is narrow as compared to the radius of the ring. The drawback of this type of particle accelerator is that it provides the particles in bunches on the target with few seconds of delay in between. This is due to magnetic field adjustment because of constant curvature of the ring as the particle’s momentum increases during acceleration.

Isochronous Cyclotron

It is an alternative to the synchrocyclotron. As stated above that in synchrocyclotrons, the output beams come with a short gap. To avoid this short gap and get a continuous delivery of beam/particles, use of isochronous cyclotrons is necessary. In this structure, the magnetic poles are designed in such a way that the field’s frequency is constant for all particles. This way, all the particles get the acceleration in the isochronous time intervals. The main disadvantage of this cyclotron is the size of magnets which are large and costly. Though the output is continuous but getting the high magnetic field values at the outer edge is a bit difficult.

Principle of Cyclotrons

All the materials in the universe and beyond are made up of molecules and, in turn, atoms are the integral parts of molecules. Electrons and protons are the main constituents of atoms. Electrons are negatively charged particles whereas protons are positively charged particles.  In the atoms, these particles are in such a way that all the electrons are always rotated around the nuclei (a bunch of protons).

When electrons are removed from the atoms, they become positively charged particles and when these charged particles come across the strong magnetic field, in the form of a “D” shape or spiral form, they accelerate and attain a very high speed. This high speed of charged particles can, then, be utilised in several areas like medical treatment, nuclear physics labs, etc.

In the medical area, high-speed protons produced by cyclotron are used in the treatment of cancer. In nuclear physics labs, these high-speed charged particles are the main sources for nuclear disintegration.

The cyclotron consists of two “D” shaped hollow metal plates. These plates are placed in such a manner that their straight sides facing to each other leaving a small gap between them. All these arrangements are inside a vacuum chamber. These two “D”s are then sandwiched between two magnetic plates which create north and south poles. The charged particle is introduced at the centre of Ds. According to the Lorentz principle, the magnetic field directs the motion of the particle in the circular path. The particle’s circular motion becomes spiral motion.

In each circular turn with the increase in speed makes the circular motion a spiral motion. When the particle reaches the exit point of the chamber, it hits the target at a very high speed gives the desired result.

Theory of Motion of the Particle in Cyclotron

A cyclotron consists of two “D” shaped hollow plates which are sandwiched between two magnetic plates. When a charged particle is introduced at the centre of hollow space between these two “D”s, the charged particle goes to one of the Ds with negative potential and starts to accelerate.

As the magnetic field B is perpendicular to the charged particle’s motion, according to the Lorentz’ rule, this motion becomes circular. After completing the half-circle, when this particle goes inside the other “D” with negative potential, it moves in the circular motion due to the magnetic field. In this way, a complete circular motion occurs with a radius r. Therefore, the centripetal force required to keep this particle in the circular path is

\(F_{c}=\frac{mv^{2}}{r}\)

Where v is the velocity and m is the mass of the particle.

The magnetic force produced by the magnetic field B is

\(F_{m}=qvB\)

Where q is the charge on the particle. As these two forces create the circular motion of the particle, at the rim of the “D” or at the exit point of “D” where r = R, these forces will be equal. So at r = R, equating these forces, it gives

\(qvB=\frac{mv^{2}}{R}\)

\(v=\frac{qBR}{m}\)           ………………. (1)

And the kinetic energy E produced by the particle is

\(E=\frac{1}{2}mv^{2}\)   ………………. (2)

Now, replacing the value of v in the above equation from equation (1), we get

\(E=\frac{1}{2}m[\frac{qBR}{m}]^{2}\)

After simplification, we get

\(E=\frac{[qBR]^{2}}{2m}\)

This way, the output energy is proportional to the charge of the particle, magnetic field and radius of “D” and it is inversely proportional to the mass of the particle.

This shows that higher the radius of “D” and a strong magnetic field with a lightweight charged particle can produce a high impact on the target.

FAQs on Cyclotron

Q.1: What is the definition of a particle accelerator?

Answer: Particle accelerators are the devices which utilise electrostatic or electrodynamic fields to accelerate the charged particles to very high speed and energy. There are two types of particle accelerators, namely, Electrostatic Accelerators and Electromagnetic Accelerators. Electrostatic accelerators are the devices which use static electric fields to accelerate the particles. A common example of the electrostatic accelerator is a cathode ray tube (CRT). Ordinary TV sets and old type of computer monitors broadly use these CRTs.

On the other hand, electromagnetic accelerators have known as Cyclotrons use magnetic fields to accelerate the charged particles. The particles accelerate in this type of machines due to the change in a magnetic field. Since particles pass through the same field in a circular manner in multiple times, the magnetic field does not limit the output energy of the particle.

Q.2: Mention the types of cyclotron?

Answer: There are two types of cyclotrons, namely, Synchrocyclotron and Isochronous cyclotrons.

Q.3: How and where the cyclotrons are useful?

Answer: Cyclotrons, the producers of high speed and energy charged particles are in use in the medical field and nuclear physics labs. In the medical field, they are used in particle therapy for treating and curing cancer. Another use of these devices is in proton therapy. In this therapy, an ion beam is used to kill the tumours by penetrating the body and minimising the damage to healthy tissues along the path. On the other hand, in nuclear physics, these devices are useful to calculate various properties of materials like finding the mean spacing between the atoms, creating various collision products, etc.

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