[Physics Class Notes] on Betatron Pdf for Exam

The word “betatron” is a portmanteau of the words “beam” and “cyclotron.” A betatron is a type of cyclic particle accelerator. It is basically a transformer with a magnetic core wrapped by several windings which carry the current required to generate the magnetic field. The betatron is able to accelerate electrons using an alternating potential difference between two D-shaped electrodes spaced apart by about 1 m, known as a vacuum tube. The maximum betatron acceleration voltage is limited to about 10 MeV due to detrimental radiation effects at higher energies. The beam current can be as large as 300 mm and the radius of the beam path inside the D’s was typically 1 cm or so.

Betatrons were developed during World War Two for use in radar sets, and as a result, most were destroyed at the end of the war under orders from Henry A. Wallace, the Secretary of Commerce and future vice-president. Only three working betatrons survived: one at the University of California’s Lawrence Berkeley Laboratory (LBL) in Berkeley, California; another at Harvard University; and a third at Camp Evans. The betatron was developed during World War II as a device to accelerate electrons for use in radar sets. Betatrons were the most powerful accelerators in the world until the late 1950s when they were superseded by the synchrotron and linear accelerator technologies. They were used for scientific research into the structure of nuclei until the late 1970s; the Berkeley and Harvard betatrons ceased operation around 1979, leaving the Camp Evans betatron in New Jersey as the only one still operating until it too shut down in 1982.

Max Steenbeck was a scientist from Germany who had developed a method to accelerate electrons in 1935. However, the concepts are originally adapted from Rolf Widerøe. Since his experiment on the induction accelerator was unsuccessful, he was unable to develop the project. In 1940, the cyclotron was the first particle accelerator discovered by Ernest Lawrence. In this article, we will learn about betatron oscillation, betatron particle accelerator, etc. The first working betatron was developed by Donald Kerst at the University of Illinois at Urbana-Champaign. A year later, Kerst’s team reports having accelerated electrons to 1.22 MeV in a 6-inch diameter device, producing X-rays through breast cancer in 1941, the first medical betatron treatments.

Betatron Oscillation

The oscillation of particles in all circular accelerators about their equilibrium orbits is known as Betatron oscillation. In the horizontal and vertical planes, these oscillations are stable around the equilibrium orbit.

Betatron Accelerator

A Betatron consists of a doughnut-shaped vacuum chamber surrounded by coils. The two ends of the coils are attached to an alternating voltage source. As a result, the coil produces an alternating magnetic field in a direction perpendicular to the doughnut-shaped vacuum chamber.

The working principle of this device is dependent on two phenomena, such as:

1. Lorentz Magnetic Force

2. Electromagnetic Induction

Betatron Particle Accelerator

The Lorentz magnetic force acting on a charged particle starts to move in some external magnetic field. Electromagnetic induction is a phenomenon where an induced EMF is developed in a circle. Also, there is a variation of magnetic flux linked with that circle. 

During the first quarter of the magnetic field cycle, the electrons are injected from the filament into the chamber. At the same time, the magnetic field rapidly starts rising from zero value. The accelerated electrons are created to strike the target during the time of completion of the 1st quarter of the cycle. The velocity of the injection of electrons is kept in a direction perpendicular to the external magnetic field. After that, electrons follow a circular orbit.

Also, due to continuous variation in the magnetic field, an EMF is induced in the chamber due to electromagnetic induction. Here, the induced EMF accelerates the electrons. The arrangements are made in a way that the electrons do not follow a spiral-like path as in the case of cyclotrons. But the electrons follow a circular path in a fixed radius. All this process takes place during the first quarter of the magnetic field cycle. During the second quarter of the magnetic field cycle, there is a decline in the magnetic field from peak value to zero. So, the induced EMF decelerates the electrons. What should we do to avoid the loss of energy during the second quarter of the magnetic field cycle? The accelerated electrons are needed to strike the target just after the completion of the first quarter of the cycle.

Uses of Betatron

Some of the applications of Betatron are mentioned below:

1. Betatron delivers about 300 MeV of highly energized beam electrons.

2. When the electron beam is required to strike on a metal plate, Betatron is used as an X-rays and gamma rays source.

3. X-rays developed from Betatron have huge usage among industries and medical fields.

4. To study the applications of particle physics, high energy of electrons is needed.

5. It can be a possible mechanism to learn about the solar flare.

Limitations of Betatron

Here are some lists that explain the limitations of betatron:

1. The maximum energy of the particle has an impact on the strength of the magnetic field. 

2. The reason for declining in the magnetic field is the physical size of the magnet core and the saturation of iron

3. A betatron acts as a secondary coil of the transformer. 

4. It helps to accelerate the electrons only in a vacuum.

5. The process of acceleration can only be conducted within a circular vacuum tube.

6. Betatron is functional under the conditions of the variable magnetic field and constant electric field.

Now, the experiment is conducted in many industries all around the world. As well as the medical field too can use betatron to treat cancer tumors. The betatron can be used as a substitute for an x-ray tube. There are many companies that are manufacturing betatrons today. They supply the betatrons with various specifications. One can easily buy a betatron from any of these companies online. I hope this article will help you in understanding the betatron concept in detail. Keep practicing.