# 0.9 Cyclotron

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High speed charged particles are required for nuclear and atomic investigations. Cyclotron is one of the devices popularly known as “particle accelerator” to accelerate charged particle to a very high speed. It uses “crossed” magnetic and electric fields at right angles to achieve the objective. The chief role of magnetic field is to make the process of acceleration confined to a small and manageable region. As far as the change in speed is concerned, it is affected only by the electric field. Recall that magnetic field can not change magnitude of velocity i.e. speed.

But we should be careful in extrapolating above facts to obvious conclusions. As a matter of fact, we shall find that magnetic field actually affects the speed attained by the charged particle indirectly by controlling number of revolutions in the cyclotron. On the other hand, the speed acquired by the charged particle is independent of applied voltage. We shall explore all these aspects in detail in this module.

## Acceleration due to electric field

Electric force accelerates particle only to change its speed if motion of the charged particle is in the direction of electric field. A potential difference V accelerates particle to achieve a speed as given by :

$\frac{1}{2}m{v}^{2}=eV$

$⇒v=\sqrt{\left(\frac{2eV}{m}\right)}$

There is, however, difficulty in generating potential difference greater than ${10}^{6}$ V. For this limiting value, the speed attained by a proton would be :

$⇒v=\sqrt{\left(2X1.6X{10}^{-19}X{10}^{6}/1.66X{10}^{-27}\right)}$ $⇒v=\sqrt{\left(1.928X{10}^{14}\right)}=1.39X{10}^{7}\phantom{\rule{1em}{0ex}}m/s$

This is just 4.63 % of the speed of light and is not good enough. This speed of the particle is thus required to be subjected to repeated application of electric force. This is done linearly by electric force in what is known as “linear accelerator”. Else, we use magnetic field to bend the path of motion and present the charged particle repeatedly to electric field for acceleration as in cyclotron. We should know that there is relative size and cost comparison and advantages between linear accelerator and cyclotron. Sometimes though, the two types of accelerators are used in conjunction where cyclotron functions as the initial accelerator for the system of particle accelerators.

## The particles accelerated by cyclotron

The accelerators are used for accelerating charged elementary particles or charged ions. It can not accelerate a neutral particle. Besides, the cyclotron as described generally, is not used for accelerating light mass particles like electron or positron. The reason is that electron having negligible mass accelerates rather too quickly for repeated acceleration within the given size of cyclotron. Instead, the light mass charged particles are accelerated by a device known as “betatron” which uses torus shaped vacuum tube as secondary coil. The tube is a hollow cylinder shaped in a circle. The varying magnetic field, produced by secondary coil, sets up electric field which, in turn, accelerates electron through the tube. On the other hand, the magnetic field due to primary coil, spins the electron and keeps it in the center of the path.

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