Such high energy-electrons can be used for basic research in physics as well as for producing x rays for applied research in industry and for medical purposes such as cancer therapy. The betatron provides an excellent illustration of the ‘’ reality ’’ of induced electric fields.
Typically, betatrons can produce energies of 100 MeV, in which case the electrons are high relativistic (v= 0.99987c). betatrons can produce enormous currents, in the range of 103 to 105 A.
They are, however, pulsed machines, producing pulses of typical width us or less separated by time intervals in the range of 0.01 – 1s.
The figure shows a cross-section through the inner structure of a betatron. It consists of a large electromagnetic M. The field of which ( indicated by the field lines) can be varied by changing the current in coils C.
The electrons circulate in the evacuated ceramic doughnut-shaped tube marked D. Their orbit is at right angles to the plane of the figure, emerging from the left and entering at the right.
The magnetic field has several functions:
- It guides the electrons in a circular path;
- the changing magnetic field produces an induced electric field that accelerates the electrons in their path;
- it introduces electrons into the orbit and then removes them from the orbit after they have attained their full energy; and
- it provides a restoring force that tends to resist any tendency of the electrons to leave their orbit, either vertically or radially. It is remarkable that the magnetic field is capable of performing all these operations.
- The coils carry an alternating current and produce the magnetic field . for electrons to circulate in the directions as shown in the fig. (counterclockwise as viewed from above), the magnetic field must be pointing upward (taken as positive). Furthermore, the changing field must have positive slope (dB/dl > 0 so that dØB /dt > 0 ) if the electrons are to be accelerated ( rather than decelerated) during the cycle. Thus only the first quarter-cycle of the fig is useful for the operation of the betatron; the electrons are injected at t = 0 and extracted at t = T/4. For the remaining three-quarters of a cycle, the device produces no beam.