Townsend avalanche
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A Townsend avalanche is a cascade reaction involving electrons in a region with a sufficiently high electric field. This reaction must also occur in a medium that can be ionized, such as air. It is exploited in devices such as Geiger counters and Proportional counters to detect and measure the energy of an ionizing radiation. Incoming radiation ionizes one of the atoms or molecules in the medium. The positive ion drifts towards the cathode, while the freed electron drifts towards the anode of the particular device. It accelerates in the electric field, gaining sufficient energy such that it frees another electron upon collision with another atom/molecule of the medium. The two free electrons then travel together some distance before another collision occurs. The number of electrons travelling towards the anode is multiplied by a factor of two for each collision, so that after n collisions, there are 2n free electrons.
When the electrons reach the anode, a current is induced, which is amplified further with electronics. This gives a clear signal that allows humans one way to detect and measure some of the characteristics of the incident ionizing radiation.
Devices that make use of the Townsend avalanche usually have a cylindrical geometry in order to achieve the required field strength. If the cylinder has a radius b and the thin wire anode in the center has radius a, then the electric field is
