High-energy electron distribution in an electron-beam-generated argon plasma

Abstract

The time evolution of high-energy electron distribution in an electron-beam-generated argon plasma is calculated. The distribution is derived for energy values above the threshold value of the first excited state (11.56 eV) from a reduced Boltzmann equation with no electron-neutral and electron-electron collisions. This equation can be numerically solved with a continuous source term taking account of all the new plasma electrons produced over the total energy range by primary electrons. As a result, the distribution reaches a steady state within a very short time tau _s and its shape is pressure independent for a given current density, and a given energy of the beam, the evolution time tau _s being inversely proportional to the pressure. Moreover, the energy distributions for given beam energy and pressure are in the same ratio as the primary-electron currents. An analytical approximation for the distribution tail is given as a function of the beam parameters (energy and current) and may be used for an electron-beam-generated Ar plasma as soon as these parameters are known. The branching ratios for energy deposition with electron-beam energy ranging between 10³ and 10⁶ eV is calculated. The relative influence of primary and secondary electrons is also discussed.