A new multi-term solution technique for the electron Boltzmann equation of weakly ionized steady-state plasmas Original Research Article

A new method for solving in higher order accuracy the Boltzmann equation of the electrons in weakly ionized steady-state plasmas is presented. The solution of the kinetic equation is based on the multi-term expansion of the electron velocity distribution function in Legendre polynomials and the iterative solution of the resultant differential equation system for the expansion coefficients. To some extent the efficient method presents a limit of analogous techniques recently developed to solve time- or space-dependent kinetic equations in higher order accuracy. The approach allows us to treat elastic as well as anisotropic scattering in collisions. The presentaton of the numerical technique is followed by some representative well as anisotropic scattering in collisions. The presentation of the numerical technique is followed by some representative examples of its application to a model plasma and real plasmas in mercury and molecular nitrogen. The results obtained are in excellent agreement with those obtained by more complex and time consuming techniques presented in previous papers.