Definitions

# betatron

[bey-tuh-tron or, especially Brit., bee-]
betatron: see particle accelerator.
A betatron is a cyclotron developed by Donald Kerst at the University of Illinois in 1940 to accelerate electrons. The betatron 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.

## How it works

In a betatron, the magnetic field spins the injected electrons and accelerates them at the center where there is a ring-shaped vacuum tube changing the magnetic field and producing an electric field in the vacuum ring.

The stable orbit for the electrons satisfies $theta_0=2pi r_0^2 H_0$ where $theta_0$ is the flux with the orbit at $r_0$ is the radius and $H_0$ is the magnetic field at $r_0$. In other words, the magnetic field at the orbit must be half the average magnetic field over its circular cross section.

## Etymology

The name "betatron" (a reference to the beta particle, a fast electron) was chosen during a departmental contest. Other proposals were rheotron, inductron, and even Ausserordentlichhochgeschwindigkeitelektronenentwickelndenschwerarbeitsbeigollitron, supposedly German for "extraordinarily high-speed electron producing hard work 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).

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

Because the mass of the electron increases at relativistic speeds, the cyclotron becomes less efficient at higher energies, placing an upper limit on its beam energy. These relativistic effects are accommodated in the next generation of accelerators, the Synchrotrons.

## In Popular Culture

• In the Frank Black song "Los Angeles", the betatron is referenced in the line "I met a man; he was a good man, sailing and shoring; he got a betatron, man."