Cyclotron

Introduction

A cyclotron is one of the earliest particle accelerators that utilises electromagnetic fields to push charged particles to exceptionally high speeds and energies along a spiral path. The charged particles were accelerated along a spiral path by quickly shifting radiofrequency. It is used to deliver radioisotopes, a vital source for cancer treatment. There are around 1500 cyclotrons across the globe producing radionuclides. Ernest O. Lawrence, an American nuclear scientist, devised this machine in 1919-1930 and was awarded the Nobel Prize in Physics in 1939 for this invention.

Working Principle of Cyclotron

A high-frequency alternating voltage accelerates the charged particle beam in a cyclotron. The dees (D-shaped electrodes) inside the vacuum chamber are placed to create a spiral path for the beam to pass. The particles are then placed into the centre of this space. The dees are arranged between a large electromagnet’s north and south poles. As the Lorentz force is perpendicular to charged particles’ direction, the magnetic field forces the particle’s motion. This results in the circular path of the charged particle.

An alternating voltage of several thousand volts is introduced to accelerate the charged particle speed. The frequency of charged particles and the cycle of voltage is set proportional to each other. To achieve this, the frequency should match the particle’s frequency. Each time the particles cross the next dee terminal, the polarity of the RF voltage inverts. In this way, each time the particles cross the gap from one dee to the next, the electric field speeds them up. The particles’ speeding up because of these pushes makes them move in a bigger span circle with every revolution, so the particles move in a spiral way outward from the middle to the edge of the dees. At the point when they arrive at the edge, a small voltage on a metal plate redirects the beam, so it leaves the dees through a little hole among them and hits an object situated at the exit point at the edge of the chamber. Hence, the working principle of cyclotron is that a charged particle normally moving to a magnetic field experiences magnetic force because of which the particle moves in a circular path.

Expression for Cyclotron Frequency

The expression for cyclotron frequency of the charged particles concerning the uniform magnetic field is known as the frequency of the cyclotron. As the motion is always circular here, the frequency is calculated by comparing the centripetal force to the Lorentz Force.

Hence the equation is:

m v2r= q v B

Here, 

m = particle’s mass, 

v = particle’s velocity, 

r = radius of the circular path,

q = particle’s electric charge,

B = magnetic field strength (constant magnitude and direction) 

The angular speed is, = vr=q Bm

Hence, the formula for expression of cyclotron frequency is: f= 2=q B2m

From the equation, it is clear that the cyclotron frequency is not dependent on the radius and velocity of the particles. Hence it is concluded that the frequency of a cyclotron is independent of the kinetic energy of the charged particles.

Apart from the classic one, there are other types of particle accelerators:

Synchrocyclotron

A synchrocyclotron is a cyclotron where the frequency of the driving RF electric field differs from making up for relativistic impacts as the particles’ speed approaches the speed of light. This is opposite to the old style cyclotron, where the frequency was held constant, subsequently prompting the synchrocyclotron frequency:

      f= fo=fo 1-2

where,

 fo = classical cyclotron frequency, 

 β = relative velocity

 γ =  Lorentz factor

Isochronous cyclotron

In contrast to the synchrocyclotron, an option is an isochronous cyclotron, which has a magnetic field that increments with radius rather than time. Isochronous cyclotrons are equipped for creating a much more noteworthy beam current than synchrocyclotron, yet require azimuthal variation in the field to give a substantial focusing impact and keep the particles caught in their spiral trajectory. Hence, an isochronous cyclotron is likewise called an azimuthal varying field cyclotron.

So the relativistic gyroradius is; r=m vq B0

The expression of frequency is also constant here.

Uses of Cyclotron

Cyclotrons are considerably more compelling than linear accelerators. This is because, in a linear accelerator, the output energy is limited to the accelerating voltage. In contrast, the output energy in a cyclotron is many times greater than the accelerating voltage. Also, because of the hollow space, a cyclotron requires less space. Therefore, the uses of cyclotron and its application are:

• Nuclear physics experiments 

The high energy produced by a cyclotron enables one to research at the molecular level. For example, experimenting with the properties of atoms and creating new products by bombardments. 

• Treatment of cancer 

The High energy beam can be used to kill the tumours without damaging the body’s healthy tissue.  

• Nuclear transmutation 

Uses of cyclotrons can also be to change the properties and the behaviour of the proton or neutron present inside a nucleus.  

Limitation of Cyclotrons

Neutral particles like neutrons don’t communicate with electric or magnetic fields. Thus, cyclotrons can’t be utilised to speed them up.

Since electrons have a tiny mass, their speed increases quickly, and soon the reverberation between the high voltage and the molecule becomes lost. Thus, a cyclotron can’t speed up electrons.

In the non-relativistic regime, cyclotrons can speed up particles to speeds significantly less than the speed of light.

Radioisotopes produced by this machine do not stay radioactive for a longer period of time. So, the medical facility or laboratory where the medicine is created and the hospital where it will be used must be closer to each other. 

To sum  it up

The cyclotron is a powerful machine and has been serving humanity since the day it was invented. Due to the iterative nature of the molecules with the accelerating field, this machine’s output is huge compared to linear ones. The working principle of a cyclotron is to accelerate charged particles to high energies. So this is basically an improved version of linacs (Linear Accelerators). In the modern era, these machines are still operating worldwide. It has advantages as well as limitations. Other modern particle accelerators are:

• Magnetron (produces high-frequency microwaves)
• Synchrotron
• Betatron

In various science fiction movies, series, and comics, this machine is used for purposes such as creating an earthquake, obtaining superhuman ability, or catching a ghost. Here are a few recommendations:

• The Flash (DC Entertainment)
• Atom Man vs Superman, Lex Luthor (DC comics)
• Ghostbusters