Exact steady solutions in a one-dimensional kinetic model of the processes in a low-density plasma layer near a dielectric surface are constructed analytically with allowance for secondary electron emission. It is shown that, for low electron temperatures, the solutions describe a regime in which the electric potential and electron density decrease monotonically toward the dielectric wall (a classical Debye layer). For higher electron temperatures, there are solutions describing regimes such that the electric potential and electron density increase monotonically toward the wall (an inverse Debye layer).
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Морозов et al. (2007) studied this question.