Townsend coefficient and runaway of electrons at relativistic velocities

An electron-multiplication regime at large field strengths, in which case an electron can acquire a relativistic kinetic energy over the multiplication length, is considered. It is shown that, even in such superstrong fields, the Townsend electron-multiplication mechanism is valid if the distance between the electrodes is rather large. The Townsend coefficient and the drift velocity in helium are obtained in such fields. The electron-escape curve, which separates the region of efficient electron multiplication from the region where electrons escape from the gap without undergoing multiplication, is obtained.