No abstract

Experimental results for the ion current to a cylindrical electrode in a flowing continuum plasma are compared with the currents calculated from a convection-dependent thin-sheath theory obtained by extending the theory of Lam to cover convection rather than diffusion-generated currents. The relation derived with this theoryIi≈5.3ε01/4e3/4μi1/4rp1/4vf3/4ne3/4V1/2l,  (mks)where ε0 is the permittivity of free space, e is the electronic charge, μi is the ion mobility, rp is the probe radius, vf is the plasma/probe velocity, ne is the ionization density, V is the probe bias, and l is the probe length, is found, on the average, to predict the experimental currents to within ±30% over ranges of 0.1–5 mm in probe radius, 5×102−4×103 cm/sec in probe/plasma velocity, 5×1016−2×1018/m3 ionization density, and 10–100 V in probe bias. Further support for a convection-dependent thin-sheath model is provided by two experimental observations: (1) The current is observed to vary as V1/2 as predicted by the convection-dependent theory rather than to saturate as would be expected of a diffusion-generated current. (2) Separate measurements reveal a marked asymmetry in the current distribution around the probe surface as expected in a thin-sheath situation.

No abstract

By following the same line of reasoning which the authors used in a previous paper, concerned with cylindrical probes, the ion current Ii to a spherical probe (radius rp, bias voltage V) immersed in a collision-dominated flowing plasma of subsonic velocity vf has been calculated to beIMG1where ne is the electron density, μi the ion mobility, e the electronic charge and ϵ0 the permittivity of free space. This theory is only valid for conditions where the plasma sheath diameter r0>>rp.A propane-air flame with a moving probe was used to investigate the above relationship. Reasonable agreement (considering the approximations made in deriving the theoretical relationship) was obtained between measured and theoretical ion currents.

4553for an argon discharge. The fluctuations are found to contribute significantly to the damping. VI. SUMMARYExperimental observations of Tonks-Dattner resonances in active, neon, argon and xenon discharges reveal fewer and broader resonances than reported for mercury vapor. For neon, the frequencies of the observed resonances lie considerably above the predictions of the PNG theory. In this case, the operating pressure was such that the ion mean free path was considerably less than the discharge tube radius and the measured electron temperatures were below the predictions of the free fall theory. For argon and xenon, the pressures were low enough so that the corresponding ion mean free path was sufficiently long to more nearly satisfy the requirements of the PNG theory and much less discrepancy between experiment and theory was noted, particularly for xenon.The broad resonances observed appear to result mainly from the concomitant occurrence of large axial density variations due to the presence of self-excited moving striations. The contributions of these variations and electron-neutral collisions to the broadening is approximately the same and greatly exceed the corresponding contributions from Coulomb collisions and Landau damping. ACKNOWLEDGMENTSWe wish to thank Professor A. W. Cooper for many helpful discussions. We are also indebted to Mr. H. M. Herreman who was of great assistance in the design of the vacuum systems and who provided many useful suggestions in the course of the experiments. Our thanks are also due to Mr. J. van Gastel for his skillful construction of the glassware and Mr. Peter Wisler for his careful construction of the machined items.Simple theoretical considerations have yielded an approximate formula for the ion current per unit length 1; to a cylindrical probe (radius rp , bias voltage V) immersed in a collision-dominated moving plasma (subsonic velocity=v" electron density=n., ion nlobilitY=/Li).[log (Ii/2n.ev,rp) J2/3 ' where e is the electronic charge. This relation has been checked with a propane/air flame and a moving probe; it is found to be correct within ±50% over several decades of probe voltage, probe-flame velocity and flame ionization. A more favorable choice of!Li in the above expression improves the agreement between theory and experiment to ±30%. Measurements of sheath thickness obtained from the mutual mterference of two adjacent probes support the basic tenets of the theoretical model. It is concluded that, in many instances of probe measurements in flames and other collision-dominated plasmas, the velocity-dependent approach adopted in this paper will be necessary since very large errors can arise if the usual static continuum plasma formulas are used. (Errors of up to a factor of 100 have been reported.)

The transition between diffusive (saturated current) and sheath-convection (currentαvoltage½) behaviour of the current to a negative probe in a high-pressure, flowing plasma has been studied theoretically. By using two physical models, where both effects are considered to be significant, one effect being dominant in one case and the other being dominant in the other case, an approximate relation is derived for the probe current in the transition between these two régimes. This transition is found to cover a variation of two orders of magnitude in ionization density if the required 10% accuracy is to be achieved. It is also found that thermoelectric and nonequilibrium effects due to cooling in the thermal boundary layer do not themselves materially affect the diffusion current.

No abstract

The use of Langmuir or electric probes in collisionless plasmas which are of interest in sputter coating is briefly reviewed. The analysis of the probe current–voltage characteristic, especially that from double floating probes, to yield the plasma parameters, the electron temperature, and the ionization density, is considered in some detail. This paper is intended to be of use to the experimentalist who wishes to use Langmuir probes as a diagnostic tool but does not really want to become an expert in all aspects of probe theory and operation.