A warm-plasma, hydrodynamic, radio-frequency model of the ion sheath region adjacent to a conductor in a plasma is developed. The sheath has a stepped density profile consisting of several contiguous regions of uniform plasma density. A consistent set of boundary conditions developed from hydrodynamic theory is imposed on the fields at the density steps, and the absorptive boundary condition is used at the conductor-plasma interface. When applied to calculate the radio-frequency admittance of a spherical probe, the single-step version of this theoretical model (1) agrees closely with the admittance calculated using hydrodynamic theory and a continuous density profile and (2) agrees at low frequencies with the admittance calculated using kinetic theory. As a consequence, the single-step or multistep sheath models of this type should be useful in theoretical analyses of a wide range of radio-frequency interactions involving a conductor in contact with a plasma.
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