An accelerator is used for accelerating charged particles, so that they acquire energy large enough to carry out the nuclear reactions. Historically, linear accelerator was developed to accelerate charged particles are to be accelerated to a very high energy. It is because, the cylindrical tubes of increasing lengths having to be used, as a charged particles gains more and more energy.
Cyclotron was designed by Lawrence and Livingstone in 1931 in order to overcome the drawbacks of the linear accelerator. It is suitable for accelerating heavy charged particles such as protons , alpha particles and positive ions. In a cyclotron , the positive ions cross again and again the same alternating ( radio frequency ) electric field and thereby gain the energy . It is achieved by making them to move along spiral circular paths under the action of a strong magnetic field. It is also known as magnetic resonance accelerator.
It is based on the principle that a positive ion can acquire sufficiently large energy with a comparatively small alternating potential difference by making it to cross the same electric field time and again by making use of a strong magnetic field.
It consists of two D-shaped hollow semicircular metal chambers D1 and D2 , called dees . The two dees are placed horizontally with a small gap separating them. The dees are connected to the source of high frequency electric field. The dees are enclosed in a metal box containing a gas at a low pressure of order 1/1000 mm mercy .
The whole apparatus is placed between two poles of a strong electromagnet N-S given in the attached figure. The magnetic field acts perpendicular to the plane of the dees.
The positive ions are produced in the gap between the two dees by the ionisation of the gas. To produce proton, hydrogen gas is used; while for producing alpha- particles helium gas is used.
Consider that a positive ion is produced at the center of the gap at the time, when the dee D1 is at positive potential and the dee D2 is at a negative potential . The positive ion will move from dee D1to dee D2 . As the magnetic field acts normally to the motion of the positive ion , the positive ion experiences force. The force on the positive ion due to magnetic field provides the centripetal force to the positive ion and it is deflected along a circular path . If B is strength of the magnetic field and m,v and q are respectively the mass , velocity and charge of the positive ion , then
Bqv. = mv²/r
Here , r is the radius of the semi- circular path along which the positive ion will move inside the deeD2.
Thus ,. r = mv/Bq
After moving along the semi- circular path inside the dee D2 , the positive ion reaches the gap between the two dees . At this stage, the polarity of the dees just reverse due to alternating electric field I .e dee D1 becomes negative and dee D2 becomes positive. The positive ion again gains energy, as it is attached by the dee D1. After moving along the semi- circular path inside the dee D1 , the positive ion again reaches the gap and it again gains the energy. This process repeats itself time and again. It is because , the positive ion spends the same time inside a dee irrespective of its velocity or the radius of the circular path It can be proved as below
The time spent inside a dee to cover semi- circular path
t= length of semi-circular path/velocity
So from the equations we obtain the following relation
t .= πm/ Bq .
As required , the time which a positive ion of mass m and charge q spends inside a dee is indeed independent of its velocity and radius of the semi-circular path. It may again be pointed out that decrease in time spent inside a dee due to increasing velocity of positive ions is exactly compensated by the increase in length of the semi-circular path. Due to this condition, the positive ion always crosses the alternating electric field across the gap between the two dees in correct phase.
Under the action of the given magnetic field (B fixed) , the given positive ion ( e/m fixed ) will cover the semi-circular path in a fixed time only , if t is equal to T/2 , where T is the time period of the electric field.
T/2 = πm/ Bq
T = 2πm/Bq
The cyclotron angular frequency ,W = 2π/T= Bq /m
Also,. Cyclotron frequency , v = 1/T = Bq/2πm .
It is also known as magnetic resonance frequency (non- relativistic).
CYCLOTRON ,ITS PRINCIPLE , CONSTRUCTION AND THEORY