What is Cyclotron?

A Cyclotron is a type of particle accelerator in which charged particles accelerate outwards from the centre along a spiral path. These particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying electric field.

**Working of cyclotron**

A cyclotron accelerates a charged particle beam using a high frequency alternating voltage which is applied between two hollow “D”-shaped sheet metal electrodes called “dees” inside a vacuum chamber.

The dees are placed face to face with a narrow gap between them, creating a cylindrical space within them for the particles to move. Then, the particles are injected into the center of this space. The magnetic field causes the particles path to bend in a circle due to the Lorentz force perpendicular to their direction of motion.

**Uses of cyclotron**

For several decades, these were the best sources of high-energy beams for nuclear physics experiments. However, these are still in use for this type of research.

**Treat Cancer**: Cyclotrons can be used in particle therapy to treat cancer, using the ion beams from cyclotrons can be used to penetrate the body and kill tumors by radiation damage.

**Cyclotron Frequency**

The frequency is given by :

\(\large n = \frac{qB}{2 \pi m}\)

Where,

*q* is charge of particle,

*B* is magnetic field used in cyclotron,

*M* is mass of the charged particle.

Consider a particle of charge *q* revolving in the path of radius r with a velocity v. Now for circular motion:

Centripetal force = Lorentz force due to magnetic field B

\(i.e., \frac{mv^{2}}{r}=qvB\)

\(\frac{v}{r}=\frac{qB}{m}\)

Therefore Angular velocity\((\omega ) = \frac{v}{r}\)

\(\omega = \frac{qB}{m}\)

\(Time\; Period (T)= \frac{2\pi}{\omega}\)

\(T = \frac{2\pi m}{qB}\)

\(Cyclotron\; frequency(n) = \frac{1}{T}\)

\(n = \frac{\omega}{2\pi}\)

\(n = \frac{qB}{2\pi m}\)

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