In this paper, by analytical estimation and numerical analysis of the ions Mach number domain in an unmagnetized collisionless plasma sheath, the formation condition of a stable sheath has been examined and formulated in the context of kappa distribution formalism. In this study, by theoretical investigation of the normalized variables with respect to well-defined parameters that enclose recent findings of kappa distribution formalism, a generalized Bohm criterion is derived in terms of an extended Mach number, , and a generalized polytropic index, γe, which characterizes different thermodynamic states with a general flexibility from near-thermal equilibrium states to the far-from-thermal equilibrium states. In our formulation, the allowed domains of isothermal and extended Mach number with respect to the connection between the polytropic index and the kappa distribution has been examined. By definition of the extended Mach number, the necessity of supersonic ions at the edge of sheath remains unchanged, but its appearance is different in the terms of the isothermal Mach number. It is shown that the threshold of extended Mach number in far-from-thermal equilibrium states is a sensitive function of the generalized polytropic index and it decreases by closing to the asymptotic limit of anti-equilibrium state (). Moreover, the threshold of isothermal Mach number decreases in the sub-isothermal regions with γe < 1 and so, by closing to the far-from-thermal equilibrium states, the Mach number domain is extended. Specially, it is shown that the thickness of the plasma sheaths reduces for the kappa distributed plasmas with smaller polytropic indices γe. Finally, the possibility for formation of stable plasma sheaths in different thermodynamic sates is discussed, where the validity of the generalized sheath criterion has been confirmed and given by or equivalently .
Ponderomotive forces due to electron modes in unmagnetized plasmas described by kappa distribution functions