0It is a device used to accelerate charged particles like protons, deutrons, αα-particles, etc, to very high energies.
PRINCIPLE :
A charged particle can be accelerated to very high energies by making it pass through a moderate electric field a number of times. This can be done with the help of a perpendicular magnetic field which throws the charged particle into a circular motion, the frequency of which does not depend on the speed of the particle and the radius of the circular orbit.
CONSTRUCTION :
As shown in the figure, a cyclotron consists of the following main parts:
1. It consists of two small, hollow, metallic half-cylinders D1D1 and D2D2 called deesdees as they are in the shape of DD.
2. They are mounted inside a vacuum chamber between the poles of a powerful electromagnet.
3. The dees are connected to the source of high-frequency alternating voltage of few hundred kilovolts.
4. The beam of charged particles to be accelerated is injected into the dees near their center, in a plane perpendicular to the magnetic field.
5. The charged particles are pulled out of the dees by a deflecting plate (which is negatively charged) through a window WW.
6. The whole device is in high vacuum (pressure ∼10−6∼10−6 mm of Hg) so that the air molecules may not collide with the charged particles.
THEORY :
Let a particle of charge qq and mass mm enter a region of magnetic field B→B→ with a velocity v→v→ normal to the field B→B→. The particle follows a circular path, the necessary centripetal force begin provided by the magnetic field. Therefore,
Magnetic force on charge qq = Centripetal force on charge qq
or
qvBsin90o=mv2rqvBsinâ?¡90o=mv2r or r=mvqBr=mvqB
Period of revolution of the charged particle is given by
T=2πrv=2πv.mvqB=2πmqBT=2πrv=2πv.mvqB=2πmqB
MAXIMUM K.E OF THE ACCELERATED IONS :
The ions will attain maximum velocity near the periphery of the dees. If v0v0 is the maximum velocity acquired by the ions and r0r0 is the radius of the dees, then
mv20r0=qv0Bmv02r0=qv0B or v0=qBr0mv0=qBr0m
The maximum kinetic energy of the ions will be
K0=12mv20=12m[qBr0m]2K0=12mv02=12m[qBr0m]2
or
K0=q2B2r202mK0=q2B2r022m.
LIMITATIONS OF CYCLOTRON:
1.According to the Einstein’s special theory of relativity,the mass of a particle increases with the increase in its velocity as
m=m01−v2/c2√m=m01−v2/c2
2. Electrons cannot be accelerated in a cyclotron.A large increase in their energy increases their velocity to a very large extent.This throws the electrons out of step with the oscillating field.
USES OF CYCLOTRON:
