Ionization through a sequence of collisions

Abstract

Abstract An electron in a sufficiently high electric field can create an ionization event in a gas at atmospheric pressure. Unfortunately, the energy gained from the electric field in a mean free path is an order of magnitude too small to ionize a molecule. Thus, it is customary to think of the electron as moving a free path distance much greater than the mean free path to gain the energy needed to ionize the molecule in a single collision event. This paper considers a different possibility leading to ionization, namely, that the electron gains sufficient energy to ionize a molecule through a sequence of hard-sphere collisions. The equations of motion of an electron in an electric field are examined, and the effects of forward and backscatter collisions are incorporated into the electron's energy gain equation. The equation's dependence on the electric field and gas pressure are also explicitly defined. It is shown that, through a succession of several collisions, it is possible for an electron to gain sufficient energy to ionize a molecule. Using the energy gain equation and the displacement equation in the field direction, the energy and position of an electron can be followed during a sequence of collisions. To demonstrate, two graphs are presented, one showing the energy gain and the other showing the position of an electron as a function of the number of collisions. The graphs were easily generated from a spreadsheet using a random number generator to randomize the forward and backscatter collision events.