Formation of inverse electron distribution function and absolute negative conductivity in nonlocal plasma of a dc glow discharge

The inversion of the electron energy distribution function (EEDF) at low energies and the absolute negative electron conductivity are predicted and confirmed by numerical modeling of a direct current glow discharge in argon. It is shown that, in contrast to the local approximation used earlier for searching the inverse EEDF, in a real gas-discharge plasma, the formation of the EEDF is significantly affected by the terms with spatial gradients in the Boltzmann kinetic equation. In analogy with the inverse population of excited states in lasers, such a medium will amplify electromagnetic waves.

Figure 1

The profiles of electron density $n_e$, ion density $n_i$, electron temperature $T_e, f_0\left(x,0\right)$, and the maximal value of the EEDF at a given $x, f_0^{max}\left(x\right)$. The vertical dashed lines show the points of electric field reversal.

Figure 2

The profiles of the electric potential $\phi \left(x\right)$, electric field $E_x\left(x\right)$, and ${\left.\left(\partial f_0/\partial w\right)\right|}_{w=0}$ (in arbitrary units) for the same discharge calculation as in Fig. 1. The vertical dashed lines show the points of electric field reversal.

Figure 3

$f_0(x,w)$ for different values of the coordinate $x$ for the same discharge calculation as in Fig. 1.

Figure 4

The coefficients $d\left[w^{1/2}{D}_r\left(w\right)\right]/dw$ for argon and helium and the corresponding functions ${\tilde{\mu }}_{\text{Ar}}\left(w\right)$ and ${\tilde{\mu }}_{\text{He}}\left(w\right)$. The EEDF (dashed curve) is the same as in Figs. 1, 2, 3, for $x=0.7L$. The dashed horizontal lines correspond to the electron mobilities ${\mu }_{Ar}$and ${\mu }_{He}$ in argon and helium, respectively calculated for this EEDF.

Figure 5

The spatial profiles of the electron mobility in argon ${\mu }_{\text{Ar}}$ and its positive ${\mu }_{\text{Ar}}^{+}$ and negative ${\mu }_{\text{Ar}}^{-}$ components calculated for the same EEDF as in Figs. 1, 2, 3, 4. For comparison, the dashed lines show the profiles of ${\mu }_{\text{He}},{\mu }_{\text{He}}^{+}$, and ${\mu }_{\text{He}}^{-}$ calculated for the same EEDF but with a cross section of helium. The vertical dashed lines show the points of electric field reversal.