Relaxation of the electron energy distribution function in the afterglow of a ${\mathrm{N}}_2$ microwave discharge including space-charge field effects

The relaxation of the electron energy distribution function (EEDF) in the post-discharge of an $\omega /\left(2\mathrm{}\pi \right)=2.45\mathrm{}\mathrm{GHz}$ microwave discharge in ${\mathrm{N}}_2$ has been investigated by solving the time-dependent Boltzmann equation, including a term taking into account electron losses by diffusion under the presence of a space-charge field. It is shown that although the high-energy tail of the EEDF is rapidly depleted in times of ${10}^{-7}\mathrm{s}$ $(p=2\mathrm{}$ and 10 Torr), the electron density $n_e\mathrm{}\left(t\right),$ the electron transport parameters, and the rate coefficients for some processes induced by electron impact, with energy thresholds typically smaller than ∼2–3 eV, such as, e.g., stepwise excitation of ${\mathrm{N}}_2\left(B{}^3{\Pi }_g\right)$ and ${\mathrm{N}}_2\left(C{}^3{\Pi }_u\right)$ states from ${\mathrm{N}}_2\left(A{}^3{\Sigma }_u^{+}\right)$ metastables and excitation of ${\mathrm{N}}_2(X{}^1{\Sigma }_g^{+},v)$ levels, are only slowly modified in the time interval $t\sim {10}^{-7}-3\times {10}^{-4}\mathrm{s}$ due to the large characteristic times for ambipolar diffusion. As a result of modifications in $n_e\mathrm{}\left(t\right),$ the change from ambipolar to free diffusion regimes occurs abruptly at $t\sim 3\times {10}^{-4}$ and $\sim {10}^{-3}\mathrm{s}$ for $p=2\mathrm{}$ and 10 Torr, respectively.