Cyclotron Class 12 | How to study physics | part-4

It consists of two D shaped metal boxes (about 21″ in diameter) with their straight sides facing each other. There is a very small gap between these Dee’s faces across which a high potential difference (of the order of 105 volts) is applied by a high frequency (10-15 megacycles per second) oscillator. Thus an alternating electric field is established between Dee’s during the one-half cycle, one dee is positive and the other is negative while during the next half-cycle, the other is positive and one is negative. A source of the particle (heavy hydrogen for producing deuterons) is placed between the faces. The whole apparatus is placed between the pole pieces NS of a very strong magnet.

 

https://www.youtube.com/watch?v=1r6luj3mkIw

Suppose a deuteron is at the center of the gap and D1 is at negative potential compared to D2 then deuterons will be accelerated by the electric field between the dees towards D1. Since magnetic field B is perpendicular to the direction of motion of deuteron, a force will act on the particle given by

F = qv x B (where v and B are vectors) = qvB

Consequently, the particle moves along a circular path whose radius is given by the cyclotron 2 Cyclotron Working Principle

So time period and frequency are independent of the speed of charge and radius of the circular path. If this frequency is equal to the frequency of the oscillator then by the time the particle complete half revolution the polarity of the field will change. Deuteron will again be accelerated across the gap, its velocity will increase so that now it will move in a circular path of the greater radius but its frequency will not be affected and the process of acceleration continues.

The particle is thus accelerated to gain high velocity. Its kinetic energy increases and when the radius of the path reaches up to the value of the radius of the dee (R), a beam is deflected by a negatively charged plate. Therefore with r=R, its maximum kinetic energy will be

Cyclotron Working Principle 

So the necessary condition for accelerating the deuterons is

f=fo

Cyclotron class 12 Working Principle

where f0 is oscillator frequency. This is called the resonance condition.

As the velocity attained is high, we choose heavier particles e.g., protons, deuterons for acceleration in the cyclotron. The reason is that at such high velocities, mass varies with velocity and f will then depend on velocity, upsetting the resonance condition. This variation in mass is more marked in the case of lighter particles. So cyclotron is suitable only for accelerating heavy particle-like protons, deuterons a – particles, etc.

Electrons cannot be accelerated by cyclotrons because the mass of an electron is very small and a small increase in energy of electron makes the electrons move at very high speed. As a result of it the electron goes quickly out of step with the oscillating electric field, it is for these reasons that other accelerating machines such as a synchrotron, betatron (for accelerating electrons) have been developed. Cyclotron cannot be used for accelerating uncharged particles like neutrons.

Variable Energy Cyclotron Centre (VECC) is located in Calcutta, India. The Centre building itself houses a 224 cm cyclotron, was the first of its kind in India, has been operational since 1977-06-16. It provides proton, deuteron, an alpha particle, and heavy-ion beams of various energies to other institutions.