# Betatron Oscillation Applications Limitations

## Introduction

Betatron oscillation is executed by electron in a particle accelerator. There are a large number of situations we come across in the realm of science wherein, we need subatomic particles to be accelerated to very high velocities. For example, high energy electrons are used in the production of various types of nanomaterials. X-rays are generated via bombardment of metals with very high energy electrons. Particle accelerators also find usage in cancer treatment.

Unfortunately, subatomic particles aren’t naturally as energetic as we need them to be. This is where particle accelerators come in. Simply put, a particle accelerator is an apparatus that we can use to accelerate subatomic particles to very high velocities. Typically, they use electric or electromagnetic fields to achieve this. Various designs for particle accelerators have been proposed over the years, and each one has its own merits and demerits. In this article, we will discuss a type of particle accelerator known as the Betatron.

## What is Betatron?

Particle accelerators are of various types and the Betatron belongs to a class of particle accelerators known as cyclic accelerators.

Nicolae Coman, Schema betatron, CC BY-SA 3.0

In the simplest of terms, a Betatron is made by using a transformer with the secondary coil replaced by a vacuum tube in the shape of a torus. A Betatron is based on the principle of electromagnetic induction that was given by Faraday. We know that an alternating magnetic field gives to an EMF given by the following equation −

$$\mathrm{\varepsilon=-\frac{d\phi}{dt}}$$

Due to changing current in the primary coil of the transformer in Betatron, a changing magnetic field arises. This variable magnetic field accelerates the electrons that are present in the vacuum tube. The electrons revolve around the tube and rapidly gain velocity, which is equivalent to gaining kinetic energy.

## Betatron Oscillation

In some particle accelerators, the charged particle’s radius increases or decreases with its energy. However, it is possible to create accelerators where the radius remains constant, i.e., the orbit remains stable. For that to happen, the following equation must be satisfied −

$$\mathrm{\Phi=2\pi r^2 H}$$

Here, $\mathrm{ϕ}$ is the flux passing through the circular area generated by the radius of the orbit, which is given by r, and H is the value of the magnetic field at a distance r from the centre.

An Irish scientist the name of Ernest Walton studied the behaviour of electrons in a magnetic field and observed an interesting result. He saw that if the electron was deflected from this stable orbit, it would experience a force-directed opposite to the direction of deflection. That is, the electron tended to return to its stable orbit. This force generated by the deflection of an electron in circular particle accelerators caused the electron to oscillate about its stable orbit. These oscillations were termed Betatron oscillations.

## Betatron Accelerator

The acceleration of particles in Betatron occurs via the application of electromagnetic force. This force is generated via a changing magnetic field. Depending on the strength of the field applied, the Betatron can accelerate electrons to very high velocities.

During the time of its inception, the first Betatron could give the electron's energy of 2.5 MeV, which was enormous at the time. Over time, this limit was increased further. In 1942, German scientists created a 6 MeV Betatron and in 1962, the University of Melbourne purchased a 35 MeV Betatron for photonuclear research.

## Betatron Particle Accelerator

The Betatron particle accelerator wasn’t initially called the Betatron. Indeed, it is said that initially, there was a heated debate regarding what to call the apparatus. Some of the names that were proposed included terms like Rheotron, induction accelerator, etc.

## Applications of Betatron

There are multiple areas in which a Betatron can be used. A few are listed below −

• In particle physics, high-energy electrons are required for various experiments and studies. They can be generated via Betatron.

• High energy electrons, when bombarded with metals, generate X-rays. X-rays have an almost unlimited number of applications.

• Around 1960, a private medical center was opened in Wisconsin which utilized Betatron for cancer treatment.

## Limitations of Betatron

A Betatron has one major drawback, which was later overcome by using synchrotrons. This limitation is encountered due to the strength of the magnetic field we can use in a Betatron. For very large magnetic fields, we would need to utilize a correspondingly large magnetic core. However, in practicality, the size of the magnetic core is limited. Thus, there is an upper limit to how much we can accelerate electrons via a Betatron.

## Conclusion

Various situations arise in scientific experiments wherein, high-energy subatomic particles are required. These are generated via the use of particle accelerators, which allow us to accelerate subatomic particles. Broadly, they are classified into linear and cyclic types. A Betatron is a particle accelerator belonging to the cyclic particle accelerators class. It was first proposed in the 1920s, and the first working model was created in 1940. By design, it is just a transformer wherein, the secondary coil is replaced by a vacuum tube in the shape of a torus.

The Betatron utilizes Faraday’s law of electromagnetic induction to increase the speed of electrons that are moving in the vacuum tube. Electrons that revolve at a fixed orbit in particle accelerators tend to oscillate about their stable orbit when deflected. This oscillation is known as Betatron oscillation. While the Betatron has enormous uses in nuclear research, X-ray generation, and cancer treatment, the speed up to which we can accelerate the electrons is limited due to the amount of magnetic field practically possible.

## FAQs

Q1. Where does the name Betatron come from?

Ans. The term “beta” is a nod to beta particles, which are high-velocity electrons. When created, there was a lot of debate about what to name it but finally, scientists settled on the simple name we know it by today.

Q2. Is a Betatron different from a Cyclotron?

Ans. Yes. A Cyclotron utilizes spiral orbits, D-shaped chambers, and alternating electric fields, while a Betatron utilizes magnetic fields and fixed orbits.

Q3. What kind of accelerator is a betatron?

Ans. A Betatron is an electrodynamic particle accelerator, i.e., it uses dynamic fields in place of static ones, which allows for higher energies to be achieved.

Q4. Are there dangers associated with Betatron?

Ans. As long as basic safety protocols are followed, Betatron is very safe. The energies achieved via Betatron aren’t high enough to pose cataclysmic threats.

Q5. What is the highest energy we have achieved via Betatron?

Ans. Currently, Betatron can accelerate electrons up to an energy of about 300 MeV.

Updated on: 26-Apr-2023

149 Views