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We present a coupled plasma and collisionless sheath model for the simulation of high-density plasma processing reactors. Due to inefficiencies in numerical schemes and the resulting computational burden, a coupled multidimensional plasma and sheath simulation has not been possible for gas mixtures and high-density reactors of practical interest. In this work, we demonstrate that with a fully implicit algorithm and a refined computational mesh, a self-consistent simulation of a reactor including both the plasma and sheath is feasible. We discuss the details of the model equations, the importance of ion inertia, and the resulting sheath profiles for argon and chlorine plasmas. We find that at low operating pressures (10-30 mtorr), the charge separation occurs only within a 0.5-mm layer near the surface in a 300 mm inductively coupled plasma etch reactor. A unified simulation eliminates the use of offline or loosely coupled and oversimplified sheath models which generally leads to uncertainties in ion flux and sheath electrical properties.