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A betatron is a type of cyclic particle accelerator. It is essentially a transformer with a torus-shaped vacuum tube as its secondary coil. An alternating current in the primary coils accelerates electrons in the vacuum around a circular path. The betatron was the first machine capable of producing electron beams at energies higher than could be achieved with a simple electron gun.
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The betatron was developed in 1935 by Max Steenbeck in Germany to accelerate electrons, but the concepts ultimately originate from Rolf Widerøe, whose development of an induction accelerator failed due to the lack of transverse focusing. Subsequent development occurred in the United States through Donald Kerst in the 1940s.
Operation principle
In a betatron, the changing magnetic field from the primary coil accelerates electrons injected into the vacuum torus, causing them to circle round the torus in the same manner as current is induced in the secondary coil of a transformer (Faraday's Law).
The stable orbit for the electrons satisfies
where
In other words, the magnetic field at the orbit must be half the average magnetic field over its circular cross section:
This condition is often called Widerøe's condition.
Etymology
The name "betatron" (a reference to the beta particle, a fast electron) was chosen during a departmental contest. Other proposals were "rheotron", "induction accelerator", "induction electron accelerator", and even "Außerordentlichehochgeschwindigkeitselektronenentwickelndesschwerarbeitsbeigollitron", a suggestion by a German associate, for "Hard working by golly machine for generating extraordinarily high velocity electrons" or perhaps "Extraordinarily high velocity electron generator, high energy by golly-tron."
Applications
Betatrons were historically employed in particle physics experiments to provide high-energy beams of electrons—up to about 300 MeV. If the electron beam is directed at a metal plate, the betatron can be used as a source of energetic x-rays or gamma rays; these x-rays may be used in industrial and medical applications (historically in radiation oncology). A small version of a betatron was also used to provide a source of hard X-rays (via deceleration of the electron beam in a target) for prompt initiation of some experimental nuclear weapons by means of photon-induced fission and photon-neutron reactions in the bomb core.
The Radiation Center, the first private medical center to treat cancer patients with a betatron, was opened by Dr. O. Arthur Stiennon in a suburb of Madison, Wisconsin in the late 1950s.
Limitations
The maximum energy that a betatron can impart is limited by the strength of the magnetic field due to the saturation of iron and by practical size of the magnet core. The next generation of accelerators, the synchrotrons, overcame these limitations.