Rotational Excitation and Electron Relaxation in Nitrogen

Using the expression given by Gerjuoy and Stein for the cross section for excitation of rotational states in ${\mathrm{N}}_2$ by monoenergetic electrons, an exact expression for the average electron energy loss rate, $〈\frac{d{W}_e}{\mathrm{dt}}〉$, is derived in the case of a Maxwellian velocity distribution. The results are used in the interpretation of cross-modulation experiments performed at microwave frequencies in an afterglow discharge. Computed results are presented for several gas temperatures, $T$, in the range 300-735°K with the electron temperature, $T_e$, being a running variable within 250°K of the gas temperature. It is seen that $〈\frac{d{W}_e}{\mathrm{dt}}〉$ varies linearly with ($T_e-T$), when $T_e$ is less than 10% in excess of $T$; and that the slope, proportional to the inverse electron relaxation time $\tau$, decreases as $T^{-\frac{1}{2}}$. This is also predicted by an approximate, closed form representation of $〈\frac{d{W}_e}{\mathrm{dt}}〉$, which agrees extremely-well with the exact computation. The experimental data on $\tau$, found by microwave cross-modulation techniques, agree well with theory. Using Pack and Phelps' relationship between the electron momentum transfer collision frequency ${\nu }_m$, and $T_e$, it is found that the $G$ factor varies at ${T_e}^{-\frac{3}{2}}$, with $\frac{G}{G_{\mathrm{classical}}}$ ranging from 55.9 at 300°K, to 14.3 at 735°K.