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# Investigatory Project on Cyclotron

Investigatory Project on Cyclotron for Class 12th

Aim: To accelerate positively charged particles like proton, deuteron etc.

Principle:

Positive ions are subjected to a magnetic field perpendicular to the direction of the velocity of the ions. The magnetic force Bqv acting on the ions keeps them in a circular path in two evacuated hollow semicircular dees. The radius of the orbit increases as ions are accelerated by an alternating voltage applied between the dees. The governing equation is,

mv2/r = Bqv, where m is the mass of the ion and r the radius of the circular orbit.

Materials and Apparatus:

It consists of two semicircular flat metal (ex. copper) boxes D1 and D2 called `dees' and are constructed with a small gap amid them. A source of ions is positioned near the centre point of the gap amid the `dees'. The `dees' are coupled to the terminals of a radio frequency oscillator, such that the high frequency alternating potential having several MHz resides amid the dees, which work as electrodes. The `dees' are included in insulated metal (such as copper) which is well evacuated. The entire apparatus is located amid the pole pieces of a strong electromagnet that offers a magnetic field perpendicular to the flat plane of the `dees'.

Working and theory

The positive ion to be accelerated is produced by the source s. Suppose at this instant D1 is at negative potential and D2 at positive potential. Therefore the ions will be accelerated towards D1. On entering D1 it is affected by the perpendicular magnetic field and hence it describes a semicircular path of radius r such that,

mv2/r = Bqv

Therefore, r = mv/Bq

Time taken by the ion to describe the semicircular path is given by,

t = πr/v = πm/Bq = a constant

Thus the time is independent of both speed of the ion and radius of the circular path. The frequency of the oscillator is so adjusted that the time taken by the ion to describe a semicircular path is equal to half period of the oscillator. Thus when the ion reaches the gap the polarity of the dees is reversed. i.e., D1 becomes positive and D2 negative. The positive ion is accelerated towards D2. It describes a circular path of larger radius and will arrive at the gap just when the polarity of the dees is reversed. Thus the positive ion goes on accelerating every time it reaches the gap between the dees and finally acquires the required kinetic energy. The accelerated ion can be deflected out of the dee to the target through a window by a deflecting electrode.

Maximum energy of positive ion

If R is the maximum radius of the circular path which is almost equal to the radius of the 'dee' and vmax the maximum velocity of ion, then,

Mvmax2/R = Bqvmax

Therefore, vmax = BqR/m

Maximum kinetic energy = ½mv max2 = ½m x (BqR/m)2 = B2q2R2/2m

Cyclotron frequency

If T is the time period of the oscillator, then,

T = 2t = 2πm/Bq

The cyclotron frequency, f = (Bq/2πm). This is known as magnetic resonance frequency. This is the same as the frequency of the oscillator.

Limitations of cyclotron

1. If the positive ion is accelerated to very high speed comparable to the speed of light, its mass varies according to the relation, m = m0 /([1 - v2]/c2; where m0 is the rest mass of the ion. Hence the equation for frequency changes. So the ion cannot be accelerated beyond a certain limit.

2. Cyclotron is suitable only for accelerating heavy particles. Electrons cannot be accelerated by cyclotron.

3. Uncharged particles also cannot be accelerated by cyclotron.