The townsend coefficient and runaway of electrons in electronegative gas

We have studied the character of variation of the number of electrons formed in an electronegative gas (SF$_6$) under the action of an external electric field. At any value of the electric field strength E, the number of generated electrons exponentially increases with the distance from the cathode, while the average velocity and energy of electrons attain constant values. At small values of the reduced field strength, $E/p<94$ V/(cm$\cdot$Torr) ($p$ is the gas pressure), the regime of electron attachment prevails that is characterized by negative values of the exponent (negative Townsend coefficients). For $E/p>94$ V/(cm$\cdot$Torr), the electron multiplication proceeds in the usual Townsend regime with positive exponents. In the intermediate region of $E/p=40\div 160$ V/(cm$\cdot$Torr), the electron multiplication coefficient exhibits a linear dependence on $E/p$. Numerical calculations based on a simple model show that the Townsend multiplication regime takes place even in very strong fields where the drag caused by ionization can be ignored. A universal function describing the electron runaway in SF$_6$ is obtained.