The use of electrostatic, or Langmuir, probes for plasma diagnostics is reviewed. The emphasis is on experimental implementation and current techniques, and particular attention is paid to sources of error in theoretical interpretation as well as to experimental problems that can occur in complex, reactive plasmas.

The use of electrostatic probes for plasma diagnostics—A review

The theory of d.c. and transient probes in stationary and moving plasmas is discussed. The success (or otherwise) of theory in explaining experimental results obtained by many researchers working over a wide range of conditions is noted with the aim of enabling some assessment to be made of the feasibility of carrying out a given probe measurement.

The use of Langmuir probes in the study of high pressure plasmas

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 theory Ii≈5.3e01/4e3/4μi1/4rp1/4vf3/4ne3/4V1/2l,  (mks) where e0 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‐de...

Ion current from a collision-dominated flowing plasma to a cylindrical electrode surrounded by a thin sheath.

A negatively biased flush‐mounted planar probe operated both in a pulsed and dc mode has been used to measure the ionization density in the plasma generated by combustion in a single‐cylinder spark‐ignition engine. The ionization was measured as a function of the air/fuel ratio and was found to exhibit a broad peak (Q?2) whose maximum occurs slightly to the rich side of stoichiometric. The peak ionization was calculated from two slightly different models for ion collection to be ?1019/m3. Values of this magnitude appear to be more reasonable than the very high value of 4×1021/m3 deduced by Rado using a similar experimental setup. Finally, it is proposed that this type of measurement may be useful to monitor engine performance.

The variation of ionization with air/fuel ratio for a spark‐ignition engine

The anode boundary layer in high intensity arcs determines the anode lifetime and processing efficiency in many industrial applications and can be controlled by cold lateral gas flows (LGFs) parallel to the anode. In this paper, properties of the anode boundary layer in a high intensity argon arc with argon and nitrogen LGFs have been studied. Anode heat and current transfer and restrike frequency and restrike length have been measured using a segmented anode and a high speed camera. Electron temperature, electron density and current density have been measured by a Langmuir probe setup. The correlation between these properties and the previously defined arc attachment mode has been described and explained.

http://iopscience.iop.org/article/10.1088/0022-3727/39/13/020/pdf

Experimental investigations of the anode boundary layer in high intensity arcs with cross flow

The transition between diffusive (saturated current) and sheath-convection (current?voltage?) 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 r?gimes. 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.

http://iopscience.iop.org/article/10.1088/0022-3727/6/2/306/pdf

Ion saturation currents to planar Langmuir probes in a collision-dominated flowing plasma

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 be IMG1 where ne is the electron density, μi the ion mobility, e the electronic charge and 0 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.

https://iopscience.iop.org/article/10.1088/0022-3727/2/12/313/pdf

Anomalous currents to a spherical electrostatic probe in a flame plasma

The floating potential (ie the potential assumed by a probe when the net current collected by it is zero) of a spherical electrostatic (Langmuir) probe in a collision-dominated plasma is investigated. The plasma is considered to be either static or flowing at subsonic velocities. The experimentally realistic situation is also considered where the probe is cold compared with the bulk plasma. The two extreme probe temperature conditions are discussed: that in which the electrons remain at their uncooled temperature, characteristic of the bulk plasma; and that in which they cool to the temperature of the neutrals near the probe. It is concluded that only in the case when the electrons cool and the sheath is thin does the floating potential vary appreciably from its value obtained in the absence of thermal gradients and thermoelectric effects. Experimental results are presented which support the concept that, for the opposite of the above condition (ie uncooled electrons, thick sheath), the floating potential is unaffected. In addition, the data have also been analysed in a manner suggested by Lam to yield an accurate value for the electron temperature.

https://iopscience.iop.org/article/10.1088/0022-3727/7/4/309/pdf

The floating potential of a Langmuir probe in a high-pressure plasma

Measurements of the ion current to a circular flat stagnation probe have been performed in a laboratory flame of known ionization density. The measurements were performed over an ionization density range from 1015 to 1018 m−3, probe bias voltages from 5 to 400 V and probe/flame velocities from 3 to 19 m s−1. The measurements show good agreement with the calculated sheath/convection currents: I=(VR)0·8 (neeuinfinity)0·6π(60μ)0·4 (mks) for the case where the sheath is thick compared with the probe, and I=(72R8ne3e3uinfinity3 V2μ0πa−3)0·25 (mks) for the case where the sheath is thin compared with the probe. Here R is the radius of the flat conduction face of the probe, ne the ionization density, e the electronic charge, μ the ion mobility, uinfinity the plasma flow velocity relative to the probe, far from the probe, V the probe bias voltage, 0 the permittivity of free space, and α the radius of the insulator surrounding the conducting face of the probe.

Stagnation probe measurements in flowing plasmas

The method of analysis used in a recent paper by Gick et al (1973) to calculate ion densities in a welding arc from the ion current measured with a cylindrical Langmuir probe is shown to predict densities between one and two orders of magnitude too small. This results in the stated arc temperatures being too low by a few thousand degrees.

R M Clements

Papers

Ion saturation currents to planar Langmuir probes in a collision-dominated flowing plasma

Anomalous currents to a spherical electrostatic probe in a flame plasma

The floating potential of a Langmuir probe in a high-pressure plasma

Stagnation probe measurements in flowing plasmas

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