Explain the working of a cyclotron with the help of neat diagram write the
Answers
The cyclotron, devised by Lawrence and Livingston, is a device for accelerating ions to high speed by the repeated application of accelerating potentials.
Principle: The positive ions produced from a source are accelerated. Due to the presence of perpendicular magnetic field the ion will move in a circular path. The phenomenon is continued till the ion reaches at the periphery where an auxiliary negative electrode (deflecting plate) deflects the accelerated ion on the target to be bombarded.
Expression for K.E. attained: If R be the radius of the path and Vmax the velocity of the ion when it leaves the periphery, then
Vmax =qBR/m
The kinetic energy of the ion when it leaves the apparatus is,
When charged particle crosses the gap between dees it gains KE = qV In one revolution, it crosses the gap twice, therefore if it completes n-revolutions before emerging the does, the kinetic energy gained
Working: The principle of action of the apparatus is shown in fig. The positive ions produced from a source S at the centre are accelerated by a dee which is at negative potential at that moment. Due to the presence of perpendicular magnetic field the ion will move in a circular path inside the dees. The magnetic field and the frequency of the applied voltages are so chosen that as the ion comes out of a dee, the dees change their polarity (positive becoming negative and vice-versa) and the ion is further accelerated and moves with higher velocity along a circular path of greater radius. The phenomenon is continued till the ion reaches at the periphery of the dees where an auxiliary negative electrode (deflecting plate) deflects the accelerated ion on the target to be bombarded. The function of electric field is to accelerate the charged particle and so to impart energy to the charged particle. The function of magnetic field is to provide circular path to charged particle and so to provide the location where charged particle is capable of gaining energy from electric field. Expression for Period of Revolution and Frequency: Suppose the positive ion with charge q moves in a dee with a velocity v, then,
where m is the mass and r the radius of the path of ion in the dee and B is the strength of the magnetic field.
The angular velocity w of the ion is given by,
The time taken by the ion in describing a semi circle, i.e., in turning through an angle p is,
Thus the time is independent of the speed of the ion i.e., although the speed of the ion goes on increasing with increase in the radius (from eq. 1) when it moves from one dee to the other, yet it takes the same time in each dee.
From eq. (3) it is clear that for a particular ion, m/q being known, B can be calculated for
