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Cyclotron: Definition, Working Principle, Frequency Formula & Uses

Cyclotron is a type of particle accelerator used to accelerate charged particles to high speeds. It was invented in 1929 by Ernest O. Lawrence. Cyclotrons are widely used in scientific research, medicine, and industry.

The basic principle of a cyclotron involves using a combination of electric and magnetic fields to accelerate charged particles along a circular path. This article covers the basics of cyclotron, including its definition, working, types, and other details related to it.

Table of Content

What is a Cyclotron?

A cyclotron is a type of particle accelerator, a device used to accelerate charged particles to high speeds. Ernest O. Lawrence invented the cyclotron in 1929. Since then, it has become a fundamental tool in various scientific disciplines, including nuclear physics, particle physics, and medicine.

The basic principle of a cyclotron involves the use of electric and magnetic fields to accelerate charged particles in a spiral path. These particles oscillate and gain energy after being subjected to a magnetic field of a specific frequency. This phenomenon is called the ion cyclotron resonance. This depends on the mass and charge of the particle and the strength of the magnetic field. As the particles spiral outward, they gain energy with each revolution.

Cyclotron

Properties of Cyclotron

Cyclotrons have several properties that make them valuable tools in scientific research, medicine, and industry. Some of these properties include:

Acceleration of Charged Particles: Cyclotrons are capable of accelerating charged particles, such as protons or alpha particles, to very high energies. This property is essential for conducting experiments in particle physics, and nuclear physics, and for various practical applications.

High Precision and Control: Cyclotrons can accelerate particles with high precision and control, allowing researchers to manipulate the energy and trajectory of the particles with accuracy.

High Efficiency: Cyclotrons are typically highly efficient in accelerating particles, with a significant fraction of the input energy being transferred to the particles as kinetic energy.

Relatively Compact Size: Compared to other types of particle accelerators, such as linear accelerators or synchrotrons, cyclotrons can be relatively compact.

Continuous Operation: Cyclotrons can operate continuously and this is advantageous for applications such as medical isotope production, where a constant supply of radioisotopes is required.

Versatility: Cyclotrons can accelerate a wide range of charged particles, including protons, deuterons(deuterium nucleus), alpha particles, and heavy ions. This versatility allows researchers to conduct a diverse array of experiments.

Reliability: With proper maintenance and care, cyclotrons can operate for many years, providing consistent access to accelerated particles.

Ion Cyclotron Resonance

Ion Cyclotron Resonance (ICR) is a phenomenon in which charged particles, such as ions, oscillate and gain energy when subjected to a magnetic field of a specific frequency. This resonance occurs when the frequency of the applied magnetic field matches the natural frequency of gyration of the ions around the magnetic field lines.

Components and Operation of a Cyclotron

Cyclotron comprises several key components, each playing a vital role in its operation. Here is an overview of these components and how they function together:

Magnet: Magnet is a crucial component of the cyclotron, providing a uniform and perpendicular magnetic field necessary to bend the path of charged particles.

Dees: Dees are hollow, D-shaped electrodes positioned within the magnetic field. They create an electric field that alternates in polarity as the particles move between them. This alternating electric field serves to accelerate the particles each time they pass through the gap between the dees.

RF (Radio Frequency) Oscillator: RF oscillator generates a high-frequency alternating electric field between the dees.

Vacuum Chamber: Entire cyclotron operates within a vacuum chamber to prevent particles from colliding with air molecules and losing energy.

Charged particles are injected into the central region. As the particles spiral outward due to the magnetic field, they pass through the gap between the dees repeatedly. Each time they cross the gap, they experience an electric field that accelerates them. After reaching the desired energy level, the particles are extracted from the cyclotron for further use.

Working Principle of Cyclotron

Cyclotron operates on the basis of the magnetic Lorentz force experienced by a charged particle travelling normal to a magnetic field. This force is perpendicular to both the particle’s motion and the magnetic field. The particle travels in a circular motion as a result.

Working of a cyclotron is stated below,

  • A charged particle beam is accelerated in a cyclotron’s vacuum chamber by applying a high frequency alternating voltage, between two hollow ‘D’-shaped sheet metal electrodes called Dees. Particles move within the dees because they are positioned face to face with a small gap between them. The central region of this space is filled with particles.
  • The Dees, located between the electromagnet’s poles, applies a static magnetic field B perpendicular to the electrode plane.
  • Because of the Lorentz force which acts perpendicular to the particle’s direction of travel, the magnetic field causes the particle’s path to bend in a circle.
  • An alternating voltage of several thousand volts is supplied between the dees which produces a pulsing sound.
  • The varying electric field created by the voltage in the area between the dees causes the particles to accelerate.
  • The frequency of the voltage is changed such that particles create a single circuit in a single voltage cycle. To satisfy this criterion, the frequency must be tuned to the particle’s cyclotron frequency.

Cyclotron Frequency

Cyclotron frequency, also known as gyrofrequency, denotes the frequency of a charged particle’s motion perpendicular to a uniform magnetic field B, which maintains a constant magnitude and direction. Due to the circular nature of this motion, the cyclotron frequency is determined by the equilibrium between the centripetal force and the Lorentz force

mv2/r = qvB

Where q is the charge,

  • m is the mass,
  • v is the velocity of the particle,
  • r is the radius of the circular path also called gyroradius.

From this,

v/r = qB/m

The cyclotron frequency is related to the angular frequency as fc = ω/2π = v/ 2πr

Now the cyclotron frequency becomes,

fc = qB/2πm

Energy of a Particle

During Ion Cyclotron Resonance, energy can be transferred from the oscillating magnetic field to the ions. As we have calculated in the previous section

v = qBr/m

Kinetic energy therefore becomes,

E = q2B2r2/2m

Types of Cyclotrons

Cyclotrons can be classified into different types based on various criteria such as size, energy range, and application. Here are some common types of cyclotrons:

  • Isochronous cyclotrons are designed to maintain constant particle velocities regardless of the particle’s energy. This is achieved by varying the magnetic field strength as the particles gain energy, compensating for the relativistic increase in mass.
  • Superconducting cyclotrons use superconducting magnets to generate the magnetic field. These magnets can produce much higher magnetic fields than conventional magnets, allowing for higher particle energies.
  • Cyclotrons for Positron Emission Tomography (PET) are specifically designed to produce radioisotopes used in PET imaging. They typically accelerate protons to bombard a target material, producing radioisotopes such as fluorine-18, which are then used to label radiotracers for PET scans.
  • Heavy ion cyclotrons are designed to accelerate heavy ions, such as carbon, nitrogen, or oxygen ions, to high energies. They are used in nuclear physics research to study the properties of atomic nuclei.

Difference between Cyclotron and Betatron

The differences between Cyclotron and Betatron are stated below:

Point of Difference

Cyclotron

Betatron

Definition

A cyclotron is a kind of particle accelerator that uses a spiral path to accelerate particles like electrons.

A betatron is a kind of particle accelerator designed primarily for the purpose of accelerating electrons or beta particles.

Path

It follows semicircular or spiral path.

It follows a circular path.

Type of Particle

It accelerates atomic and subatomic particles.

It accelerates electrons.

Structure

It contains two electrodes called dees attached back to back.

It contains an circular evacuated tube embedded in an electromagnet.

Uses of Cyclotron

The uses of Cyclotron are as follows:

  • Experiments in Nuclear Physics: Atomic nuclei are bombarded by charged particles that are accelerated in cyclotrons.
  • Radiation Treatment: Cancer patients are treated with cyclotrons. Cyclotron ion beams have the ability to enter the body and destroy tumours by radiation damage, with the least amount of damage to healthy tissue.
  • Nuclear Transmutation: The nuclear structure can be altered with the use of cyclotrons.
  • Nuclear Medicine: Medical radioisotopes are created in nuclear medicine cyclotrons. Protons are the charged particles that cyclotron beams in a circular direction.

Advantages of Cyclotron

Cyclotrons offer several advantages over other types of particle accelerators and methods of particle production. Some of the key advantages include:

  • Cyclotrons can achieve high energies in relatively compact designs compared to linear accelerators (linacs) or synchrotrons.
  • Cyclotrons can operate continuously, providing a constant supply of radioisotopes for medical isotope production.
  • Cyclotrons are highly efficient in accelerating particles, with a significant fraction of the input energy being transferred to the particles as kinetic energy.
  • Cyclotrons are often known for their reliability and long operational lifetimes.
  • Cyclotrons are widely used in medicine for various applications, including producing radioisotopes for diagnostic imaging (such as PET scans) and cancer therapy.

Limitations Of Cyclotron

While cyclotrons offer numerous advantages, they also have several limitations and challenges that need to be considered. Some of the key limitations include:

  • Cyclotrons cannot accelerate neutral particles, such as neutrons or atoms, as they do not interact with electric or magnetic fields.
  • Cyclotrons have practical limitations on the maximum energy they can achieve due to relativistic effects. As particles approach the speed of light, their mass increases, requiring stronger magnetic fields to maintain circular orbits.
  • Electrons cannot be efficiently accelerated as they have a much higher charge to mass(e/m) ratio, meaning they are less affected by the magnetic field and experience weaker acceleration in a cyclotron.
  • Achieving high beam intensity can be challenging due to space charge effects, beam losses, and other factors, which can limit the usefulness of cyclotrons for certain applications requiring intense beams of particles.

Conclusion: Cyclotron

Cyclotron is a particle accelerator invented by Ernest O. Lawrence in 1929, used to accelerate charged particles to high speeds by employing electric and magnetic fields. Components of Cyclotron include a magnet, dees, radio oscillator, and vacuum chamber.

Cyclotrons can be classified into various types, such as isochronous cyclotrons, superconducting cyclotrons, cyclotrons for PET, and heavy ion cyclotrons. They offer advantages like achieving high energies in compact designs, efficiency, reliability, making them valuable tools in scientific research and medical applications.

Also Read,

Solved Examples on Cyclotron

Example 1: In a cyclotron the frequency of alternating current is 12 MHz. What should be the operating magnetic field to accelerate protons? Given mass of proton = 1.67 × 10-27 kg.

Solution:

Using formula for Cyclotron Frequency:

f = qB/2πm

Upon rearranging,

B = 2πmf/q

B = 2π × 1.67 × 10-27× 12 × 106/1.6 × 10-19

B = 0.79 T

Example 2: For the above problem, what is the kinetic energy of the proton beam produced by the cyclotron if the radius of the dee is 0.53 m?

Solution:

Using formula for Kinetic Energy:

E = q2B2r2/2m

E = (1.6 × 10-19)2(0.79)2(0.53)2/2 × 1.67 × 10-27

E = 1.34 × 10-12 J

In eV units,

E = 1.34 × 10-12 /1.6 × 10-19

E = 8.38 MeV

Example 3: The magnetic field inside a cyclotron is 0.8 T. At what maximum radius should a proton beam be extracted so that its energy is 10 MeV?

Solution:

Using formula for Kinetic Energy:

E = q2B2r2/2m

Upon rearranging,

r = √2mE/qB

r = √(2 × 1.67 × 10-27 × 107 × 1.6 × 10-19 )/1.6 × 10-19 × 0.8

r = 7.31 × 10-19/1.28 × 10-19

r = 5.71 m

Cyclotron Frequently Asked Questions

What is a cyclotron?

A cyclotron is a type of particle accelerator that utilizes the principles of circular motion and electromagnetic fields to accelerate charged particles to high speeds.

Who invented cyclotron?

Cyclotron was invented by American physicist Ernest O. Lawrence in 1929. This earned him the Nobel Prize in Physics in 1939.

How does a cyclotron work?

Charged particles, injected into the cyclotron, spiral outward due to the magnetic field. Each time they cross the gap between the Ds, they experience an electric field that accelerates them. Once the particles reach the desired energy level, they are extracted from the cyclotron for further use.

What are different types of cyclotrons?

Cyclotrons can be classified into various types, such as

  • Superconducting Cyclotrons
  • PET Cyclotrons
  • Isochronous Cyclotrons
  • Heavy Ion Cyclotrons

 


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