Radially dependent solutions of Boltzmann’s equation in low-temperature plasmas using a modified two-term expansion

A new method for obtaining spatially resolved electron energy distributions is described and applied to cylindrical bore electric discharges. The method is based on a modified two-term spherical harmonic expansion of Boltzmann’s equation in which energy-resolved drift and diffusion are included, as well as Joule heating or cooling by the ambipolar field. It is found that low-energy electrons may be heated by the large ambipolar electric field gradients near the wall while higher-energy electrons may escape the plasma. Therefore, diffusion cooling and Joule heating in the ambipolar field may simultaneously occur, but for different portions of the electron energy distribution.