Numerical solutions to the stable, space-charge-limited emission of secondary electrons from plasma-wall interaction are found based on one-dimensional plasma moment equations that assume cold ions, Maxwellian electrons and cold secondary electrons. The numerical method finds a range of plasma parameters that permit stable emission of secondary electrons in the absence of normal electric fields to the wall. These solutions were not obtained with previous method that solves only for the marginally stable plasma sheath. Range of the ion Mach number at the sheath edge, the floating wall potential relative to the plasmas, and secondary electron emission coefficients corresponding to the vanishing normal electric fields are found for hydrogen, argon and xenon plasmas. The results show that a relatively small range of secondary electron emission coefficient exists to allow stable sheaths structures along with larger ranges of ion injection speed at the sheath edge and floating potential of the emitting wall. (C) 2011 Elsevier B. V. All rights reserved.