In the asymptotic limit λD/λ→0 (where λD is the electron Debye length and λ represents the ion mean free path) the boundary layer of a collision dominated plasma is split up in a collision free planar sheath (scale λD) and a quasi-neutral presheath (scale λ). The “sheath edge” separating the presheath and the sheath is defined by the Bohm criterion. To clear up controversial statements on the validity of the plasma sheath concept and on the role of the Bohm criterion for finite values of λD/λ, a simple fluid model of the ions is used to account for collisions and for space charges in the boundary layer. It is shown that the asymptotic solution on an “intermediate scale” (scale length λ1/5λD4/5) is suitable to match the presheath and sheath solutions smoothly and to construct a convenient approximation for small but finite λD/λ. The intermediate scale, again, is closely related to the Bohm criterion. Various attempts to derive a “generalized” Bohm criterion accounting for collisions are inconsistent.

The influence of collisions on the plasma sheath transition

In the limit of a small Debye length (λD→0), the plasma boundary layer in front of a negative absorbing wall is split up into a collision‐free planar space charge sheath and a quasineutral presheath, where the ions are accelerated to ion sound speed (Bohm criterion) Usually the presheath mechanism depends decisively on collisional friction of the ions, on ionization, or on geometric ion current concentration If the ion dynamics in the presheath is dominated by a magnetic field (nearly) parallel to the wall, an additional effect must be considered to provide an ion transport to the wall The special cases (a) of an ion transport by field lines intersecting the wall at a finite angle and (b) of an ion transport by collisions result in somewhat contradictory conclusions To get a coherent picture, a hydrodynamic model of the presheath is investigated accounting for an oblique magnetic field and for collisions The limiting cases (a) and (b) are discussed, and it is shown that (in plane geometry) the presheath ion acceleration depends always on elementary processes The main effect of a strong magnetic field is to ‘‘compress’’ the collisional presheath into a thin layer with a characteristic extension of the ion gyroradius ρi

Theory of the collisional presheath in an oblique magnetic field

The influence of collisional damping and the radial electron density profile on the characteristics of the wave propagation as well as on the radial distribution of the electric field of electromagnetic surface waves is studied. The discussion is mostly addressed to the situation of surface wave plasmas in the RF frequency range in a strongly collisional case. Some aspects of the influence of the collisional damping on the wave propagation, particularly in view of diagnostic applications, are discussed. The range of validity of the 'thin cylinder approximation' in the collisional case is compared with predictions of the collisionless theory. Furthermore the possibility of the occurrence of a resonant field enhancement as the position of a local plasma resonance under microwave conditions is pointed out.

http://iopscience.iop.org/article/10.1088/0022-3727/25/11/003/pdf

Dispersion characteristics and radial field distribution of surface waves in the collisional regime

Electrodes of pure and doped tungsten for high intensity discharge lamps are investigated in a special model lamp. Our intention is to obtain experimental data to verify models describing the near-electrode region. For the DC case, we have two totally independent methods to determine the cathode fall separately from the anode fall. The first method is based on the spatially resolved measurement of the cathode surface temperature and a treatment of the cathodic power balance. The second method uses Langmuir-probe measurements to determine the plasma potential at known distances from the cathode. The comparison of both methods shows good agreement which justifies the assumptions and simplifications introduced. Parameter studies yield a strong dependency of the cathode fall on the cathode diameter and the material. The cathode length and the fill gas pressure seem to have only minor influence. Comparing the results of our experiment with outcomes of models by several authors, the values for the cathode fall show good agreement, too. However, concerning the total power loss of the cathode, differences between experiment and theory were found.

https://iopscience.iop.org/article/10.1088/0022-3727/35/14/304/pdf

Determination of HID electrode falls in a model lamp III: Results and comparison with theory

Sheath formation is studied for slightly ionized plasmas, i.e. for many typical low-pressure discharges. A sheath adjacent to an insulating wall is a space charge region where the electron flux to the wall is reduced to the corresponding ion flux. Numerical and analytical results show that no lower bound of the ion drift speed vi exists to form a sheath under collisional conditions. The product of the ambipolar ion speed vB and the square root of the ratio of the number density of the ions to that of the electrons occurs as a characteristic ion drift speed vc for the sheath formation. In the interval 0 vc both the electric field and the collisions support the sheath formation. The effect of the electric field alone can form the sheath. When the electron density is relatively small under collision-dominated conditions the space charge density can become relatively large in the neighbourhood of the point where vi = vB, and then the difference between vc and vB is significant. It is also possible that such a point does not exist. At low collisionality, in the centre of the plasma and close to the wall vi vc can be satisfied. When the collisionality is high vi vB occurs close to the wall. The sheath formation can be dominated by collisions in a larger range of parameters than recognized to date. The application of the Bohm criterion is inappropriate when the collisionality is high and the electron density is relative low. Multi-component plasmas are discussed briefly. The concept of a sheath edge is examined critically.

https://iopscience.iop.org/article/10.1088/0963-0252/9/4/313/pdf

Sheath formation in low-pressure discharges

The boundary layer problem of a weakly ionized collision-dominated plasma in front of a negative absorbing wall is considered. The electrons are assumed to be Boltzmann distributed; the ions are governed by symmetric charge exchange. The Debye length is small compared with the mean free path. A former kinetic analysis of the Knudsen layer is matched with an adapted macroscopic theory of the plasma body accounting for ionization, nonplanar geometry and filed-dependent ion mobility. The consistent analysis of plasma and boundary layer is illustrated with the examples of a cylindrical plasma column, a spherical probe in an infinitely extended plasma without ion generation, and a semi-infinite plasma with Saha ionization equilibrium distorted by wall losses.

K U Riemann

Papers

Consistent analysis of a weakly ionized plasma and its boundary layer