As part of a systematic study of approximations commonly made in solutions of the Boltzmann equation for electrons in molecular gases, we have investigated the effects of anisotropic scattering on electron transport coefficients in ${\mathrm{N}}_2$ and have extended our study of the multiterm expansion technique to higher E/n. A critical survey of published data yields a set of differential and integral cross sections for electron energies from 0.003 to ${10}^4$ eV. For electric-field–to–gas-density ratios E/n between 10 and 500 Td (1 Td${=10\mathrm{}}^{\mathrm{-}21}$ V ${\mathrm{m}}^2$), the changes in the commonly measured transport and reaction coefficients resulting from the introduction of anisotropic elastic and inelastic scattering, while keeping the elastic momentum-transfer cross section constant, are less than 1%.

These calculations were made with use of the multiterm spherical-harmonic expansion solution of the Boltzmann equation. For 500<E/n<1500 Td the changes in scattering anisotropy cause changes in transport and reaction coefficients which increase with E/n to about 10%. The errors in drift velocity, mean energy, and the reaction coefficients resulting from the use of the two-term spherical-harmonic expansion rather than a six-term expansion are less than 3% at 1500 Td.

However, the errors in the diffusion coefficients become large (>25%) at our highest E/n. The calculated transport coefficients are in generally good agreement with experiment for E/n less than 300 Td, but the differences increase at higher E/n. The importance of proper interpretation of ionization and excitation experiments at high E/n is illustrated by calculations which model either an exponential growth of density in time or an exponential growth with position. The calculated ionization coefficients are low compared to most experiments for E/n less than 200 Td. At E/n>600 Td the agreement is good for the spatial growth experiments, but the calculated values are below experiment from the temporal growth experiments. The calculated excitation coefficients are generally higher than experiment at low and high E/n but in agreement with experiment at E/n near 150 Td.

• Received 22 October 1984

DOI:https://doi.org/10.1103/PhysRevA.31.2932