14. Explain the principle and action of betatron and
obtain expresion of total energy gained by an
electron. Explain the factors that limits maximum
energy attainable with a betatron
Answers
Answer:
Engineering Physics by Dr. Amita Maurya, Peoples University, Bhopal. > Unit-III >
Betatron
A Betatron was developed by D W Kerst to accelerate the electrons to high energies.
Principle
The principle of the Betatron is same as that of the transformer. In transformer, if an alternating current is passed through the primary coil an alternating magnetic field will appear in the coil. This field produces an induced e.m.f. in the secondary coil. Similarly the changing magnetic flux induces an e.m.f. tangentially along a circular path for the electron which accelerates the electrons to high energies. The electrons is kept accelerating in circular path of constant radius with the help of increasing magnetic field.
Construction
The Betatron is consists of an evacuated doughnut chamber in which electrons are produced by indirectly heated cathode. The doughnut tube is placed between two strong electromagnet such that, when the a.c current is passed in the electromagnets the flux increases in the centre of doughnut (single coil).
Working
When the electron appears at K (cathode) in doughnut tube and the electromagnets are energized the magnetic field increases, the increasing magnetic field has two effects
(i) Induced e.m.f. is produced in electron orbit by changing magnetic flux that gives an additional energy to electron. According to Faraday’s law
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(ii) A radial force (magnetic force) is produced by action of magnetic field whose direction is perpendicular to the electron velocity which keeps the electron moving in circular path. The force is balanced by
centripetal force, i.e.,
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The particle acceleration occurs only with increasing flux (the duration when the flux increases from zero to a maximum value) i.e., the first quarter of the a.c. cycle (T/4 sec), after this the flux starts decreasing which result in decreasing velocity therefore the electron is kept in the tube only for T/4 sec. As the electrons get faster they need a larger magnetic field to keep moving at a constant radius, which is provided
by the increasing field.