R M Clements

ANOMALOUS CURRENTS TO A SPHERICAL ELECTROSTATIC PROBE IN A FLAME 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.

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

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.

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

Transition from diffusion-convection to sheath-convection of a cold Langmuir probe in a moving compressible plasma

The behaviour of the ion current to a negatively biased probe in a high-pressure, flowing plasma for the situation where the current cannot be considered to be solely dominated by either diffusion or convection is discussed. The transition has been investigated before; here, however, the cooling induced reduction in the local ion mobility and the distortion of the hydrodynamic flow pattern close to the probe are also taken into account. These problems arise inherently because in virtually every practical situation the probe is much colder than the plasma. Recent experimental results obtained in an MHD generator duct yield results which broadly lie between the former (no cooling) and present (very substantial cooling) theories.

Stagnation probe measurements in flowing plasmas

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.

Flush probe studies of plasma flow over a flat plate: theory

The transient electrical properties of a planar probe which is immersed in a flowing continuum plasma and in which the flow velocity is parallel to the probe surface are studied theoretically. When the probe is pulsed negatively, the resultant ion current overshoots its final equilibrium value. The time constant for recovery from this overshoot is shown to yield the information about the plasma flow over the probe. When the plasma sheath edge is inside the hydrodynamic boundary layer it is able to directly probe the velocity structure of the hydrodynamic boundary layer. The theory used to describe the probes electrical properties differs from other thick sheath theories in that both gas compressibility and ion/electron recombination effects are considered.

Comments on `The use of electrostatic probes to measure the temperature profiles of welding arcs'

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.

Blast wave computations using the flux-corrected transport algorithm

Computations of supersonic flows produced by time-dependent energy sources of a general form are presented. The problem is formulated using the equations of motion in Eulerian form and is solved with a numerical algorithm based on the flux-corrected transport method. Illustrations of the method are given both for an experimentally measured power input from a plasma igniter and a time-varying analytic power input. The model is shown to be of use in the design of igniters. It is found that the position of the luminous plasma front is a more sensitive measurable parameter than the shock front position.

Pulsed spherical probe measurements of plasma conductivity in a flowing continuum plasma

Measurements have been made of the electron conductivity in an atmospheric pressure flowing plasma using a pulsed spherical probe. The method involves measuring the peak electron current flowing to the probe in response to a positive pulsed change in the probe potential. It is shown that for many circumstances the pulse technique effectively eliminates the very large potentials which are usually generated at plasma electrode interfaces during plasma resistance measurements.

The AC motion of the sheath edge in a flowing high-pressure plasma

Measurements have been made of the sheath edge motion in response to a small AC perturbation of the negative potential of a planar probe immersed in an unseeded atmospheric pressure flame plasma. These measurements, which were conducted over a frequency range 100-2500 Hz, compare favourably with an analytical solution for the sheath motion. The analysis predicts a low-frequency sheath motion which is dependent on the initial ion velocity at the sheath edge; the effect of a non-zero electric field at the sheath edge on the sheath motion is also discussed.