In the limit of a small Debye length ( lambda D to 0) the analysis of the plasma boundary layer leads to a two-scale problem of a collision free sheath and of a quasi-neutral presheath. Bohm's criterion expresses a necessary condition for the formation of a stationary sheath in front of a negative absorbing wall. The basic features of the plasma-sheath transition and their relation to the Bohm criterion are discussed and illustrated from a simple cold-ion fluid model. A rigorous kinetic analysis of the vicinity of the sheath edge allows one to generalize Bohm's criterion accounting not only for arbitrary ion and electron distributions, but also for general boundary conditions at the wall. It is shown that the generalized sheath condition is (apart from special exceptions) marginally fulfilled and related to a sheath edge field singularity. Due to this singularity, smooth matching of the presheath and sheath solutions requires an additional transition layer. Previous investigations concerning particular problems of the plasma-sheath transition are reviewed in the light of the general relations.

https://iopscience.iop.org/article/10.1088/0022-3727/24/4/001/pdf

The Bohm criterion and sheath formation

The collisionless plasma‐sheath equation is discussed in the limit that the ratio of Debye length to discharge dimension is vanishingly small, for the cases of planar, cylindrical, and spherical symmetric discharges. Separate representations for the plasma and sheath regions are found and numerical results given for the potential profiles, ion currents, energy distributions, and floating wall potentials for two different assumptions regarding the ion generation function in each case.

Asymptotic Plasma and Sheath Representations for Low‐Pressure Discharges

This paper is concerned with the double sheath which is normally present in front of a hot cathode in a low‐pressure dc discharge. The authors present a theory of an idealized form of this sheath, under space‐charge‐limited cathode emission conditions. The discrepancies from this model to be expected in a practical situation are discussed, and comparisons are made with experimental results. To obtain these, an electron beam probing technique was used, and electric field measurements were made directly in the cathode sheath of a low‐pressure mercury‐vapor discharge. Good agreement was obtained between the simplified theory and the experiments.

Structure of the double-sheath in a hot-cathode plasma

The steady state of a nonisothermal cylindrical discharge in a longitudinal magnetic field is described by three moment equations in the plasma approximation for electrons and ions. Volume generation of electron‐ion pairs by single‐stage ionization, the presence of axial current, and collisions with neutrals are considered. The theory yields radial profiles of the charged particle velocities, density, potential, electron and ion temperatures, and demonstrates similarity laws for the positive column. The results are compared with two‐moment theories and with experimental data on helium, argon, and mercury vapor found in the literature for a wide range of pressures.

Theory of a steady-state nonisothermal positive column in a magnetic field

Gaseous ion lasers

Collisionless Plasma Sheath in Cylindrical Geometry

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Collisionless Plasma Sheath in Cylindrical Geometry