The plasma-sheath matching problem has attracted new interest during the last few years. It is complicated by the singular structure of the asymptotic (λ D /L → 0) plasma and sheath solutions and by a coupling with the eigenvalue problem originating from the plasma balance of bounded plasmas. Due to these difficulties the existence of a matched asymptotic expression uniformly valid from the plasma core to the wall is widely questioned. The issue is clarified both analytically and numerically by the explicit construction of a matched asymptotic expression and comparison with exact solutions for the hydrodynamic plane Tonks-Langmuir problem. The approximations obtained by consistent matching show excellent agreement with numerical potential curves. The singularities of the asymptotic components are reflected by small discontinuities in the derivatives that vanish in the limit λ D /L → 0.

In this paper the general problem of linking fluid and kinetic plasma parameters, with special attention devoted to the plasma boundaries where, due to strong deviations from thermodynamic equilibrium, there are intrinsic difficulties regarding the closure of the hydrodynamic equations, is considered. This problem is demonstrated by means of two examples for which the solutions of the kinetic equations are known. These examples are the collision-free Tonks-Langmuir model [Phys. Rev. 34, 876 (1929)] and Riemann’s presheath model [Phys. Fluids 24, 2163 (1981)] dominated by charge-exchange collisions. It is found that in the vicinity of the sheath edge the “polytropic” coefficient γ(x) shows an unexpected behavior that contradicts the commonly used hydrodynamic approaches assuming γ=const. In spite of all differences, the two models investigated exhibit quite similar behavior of the hydrodynamic quantities and of the polytropic coefficient in the presheath and sheath regions. This rises to hopes that the results presented in this paper can be generalized to models characterizing other physical scenarios of plasma production and confinement. In particular, the basic findings presented here will, in suitably adopted form, be of importance, e.g., in properly formulating boundary conditions for fluid codes simulating bounded plasmas.

The plasma-wall transition (PWT) layer in a magnetic field parallel to the wall is investigated with a two-fluid approach, where the continuity and momentum equations for electrons and ions are used to describe the semi-bounded plasma, whereas the background gas of neutral particles is assumed to be uniformly distributed. The equations include ionization, recombination and charge exchange processes. The magnetic field is parallel to the confining wall, which is assumed to have a potential different from the one in the bulk plasma. A linear analysis of the PWT layer reveals two distinct length scales, namely the short Debye screening length scale and the much longer collisional length modified by the magnetic field. It is found that the ionization and recombination processes are important to connect the PWT layer to the bulk plasma, which is characterized by a balance between ionization and recombination. The PWT layer is here treated as a unit, without a priori splitting into sheath and presheath sublayers. The nonlinear set of equations is solved numerically to obtain the profiles of the electrostatic potential, the densities, and the velocity components. Near the wall, where the electron velocity is large, the Lorentz force and collisions lead to an electron density distribution significantly different from the Boltzmann one.