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The inverse and space-charge limited (SCL) sheaths between a Maxwellian low-temperature plasma source and a dielectric surface that emits secondary electrons are carefully investigated by a 1D3V, steady-state, kinetic sheath model with fully self-consistent wall secondary electron emission conditions, within a broad range of plasma electron temperature Te. The multistep electron emission (MEE) phenomenon caused by the near-wall potential increment is specially considered, and it is found that the total emitted electron velocity distribution function perpendicular to the dielectric wall approximately obeys two-temperature Maxwellian and half-Maxwellian distribution. Under cold plasma ion assumption, results show that when Te>Tec (the first threshold) the sheath goes into entirely inverse sheath regime: (1) the ion energy E at the sheath edge equals 0, i.e., no presheath is necessary to accelerate ion; (2) the wall total electron emission coefficient Γ=1, i.e., no charge is lost at the wall; (3) the wall potential is just about 0∼0.03(Te/e) for all the cases; (4) the sheath depth is thinner than one Debye length. When Te≥TeSCL (the second threshold), another solution of SCL sheath is also found. It clearly indicates that the two sheaths are possible near plasma-facing dielectric wall with strong electron emission, but they do not always emerge in pairs. Further comparative calculations predict that the MEE phenomenon can significantly decrease the wall potential Φw, virtual cathode potential Φvc, and near-wall potential increment ΔΦ (i.e., Φw-Φvc) for SCL sheath, but slightly increase Φw for the inverse sheath. In addition, the differences between the two sheaths are discussed.

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