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 f_c = ω/2π = v/ 2πr

Now the cyclotron frequency becomes,

f_c = 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

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.