Sidney A. Self

Focusing of spherical Gaussian beams

Simple procedures and formulas for tracing the characteristics of a spherical Gaussian beam through a train of lenses or mirrors are described which are analogous to those used in geometrical optics to trace repeated images through an optical train.

A tuned Langmuir probe for measurements in rf glow discharges

Measurements of charged‐particle concentrations and the electron energy distribution function (EEDF) have been made in Ar and SF6 glow discharges using a tuned Langmuir probe technique. A simple passive circuit connected to the probe when properly tuned increases the impedance between the probe and ground, thereby forcing the probe to follow the instantaneous plasma potential. In this manner, rf‐induced distortion of the probe characteristic is mitigated. At 13.56 MHz the electron collection characteristic of a detuned probe is distorted by rf interference; the ion collection characteristic is unaffected. The EEDF is highly non‐Maxwellian in argon discharges, but quite Maxwellian in SF6 discharges. The mean electron energy increases with decreasing pressure and increasing power in argon discharges, but is independent of pressure and power in SF6 discharges. The measured distribution functions and charged particle concentrations are in good agreement with calculations.

Optical particle sizing for in situ measurements Part 1

A particle sizing counter suitable for in situ measurements in two-phase flows is presented in a two-part sequence. The technique employs near forwardscatter from the focus of a He-Ne laser beam, together with pulse-height analysis of the signals from individual particles. A novel and essential feature of the technique is a numerical inversion scheme to unfold the dependence of the scattered signals on particle trajectory through the measurement volume. This feature allows the capability of truly in situ measurements with a working space of 50 cm between optical elements. The inversion procedure is performed by an on-line computer or microprocessor unit and uses a prior calibration with monodisperse aerosols of known size. As presently configured, the instrument has a demonstrated capability of determining size distributions in the 1-30-microm diam range, at concentrations up to ~10(5) cm(-3) in flows of temperatures up to 1600 K. The measured dependence of response on particle diameter agrees well with calculations from the Mie scattering theory. It is anticipated that the technique can be extended to cover particle diameters in the 0.5-50-microm range with concentrations up to 10(6) cm(-3). Adaptation to measurements of absorbing and irregular particles can be achieved by a straightforward calibration technique. Part 1 describes the trade offs in the optical design and develops the numerical inversion scheme. Part 2 discusses experimental measurements at ambient conditions and combustion temperatures (1600 K). An assessment of the accuracy of the technique is also presented.

STATIC THEORY OF DENSITY AND POTENTIAL DISTRIBUTION IN A BEAM-GENERATED PLASMA

An electron beam passing through a gas ionizes the gas, and the electrons and ions so produced collect in the vicinity of the beam to form a plasma with a number density that can be much greater than the density of the beam. A one‐dimensional static theory for such a system, with a beam either partially or completely filling the space between two parallel planes, gives the plasma density and potential distribution in the space. The theory requires only minor modifications of the Langmuir‐Tonks free‐fall theory of the positive column. A plasma filling the space occupied by the beam is separated by a low potential sheath from a somewhat lower density plasma that extends to the walls where a second higher potential sheath is formed. A comparison between the results of this theory and some density measurements on beam‐generated plasmas reported in the literature gives reasonable agreement.

Particle size-density relation and cenosphere content of coal fly ash

The results are reported of detailed physical characterization of six ashes from coals representative of those burned in US power plants. Centrifugal separation was used to classify the ashes into six density categories in the range 3.2 g cm−3. The size distributions of all density classes were determined in the range 1–200 μm. For most of the density classes, log-normal functions, truncated outside the measurement limits, described the size distributions quite well. For all six ashes, the median diameter initially decreased and then increased with increasing particle density. The influence of particle structure on this large variation (up to sixfold) in size is discussed. Centrifugal separation using a liquid of density 2.2 g cm−3 was used to estimate the mass fraction of cenospheres (i.e. particles with trapped interior ‘bubbles’) in the ashes. This fraction varied from 95 wt%. The cenosphere content was apparently uncorrelated with coal rank but was positively correlated with the total mineral content of the coal. The median diameters of the cenospheric fractions were found to be two to three times those of the non-cenospheric (solid) fractions. The density-size data were used to determine the Fe2O3 distribution in the ashes.

Asymptotic Plasma and Sheath Representations for Low‐Pressure Discharges

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.

Steady‐State Theory of an Intermediate‐Pressure Discharge Column in a Magnetic Field

A steady‐state theory of a discharge column in a magnetic field is presented which covers the intermediate pressure range where the ion mean free path is neither much greater than, nor much less than, the discharge radius. With increasing pressure and magnetic field, its predictions tend to those obtainable from ambipolar diffusion theory. With decreasing pressure they approximate those of low‐pressure discharge theory based on the use of the third‐moment equation for the ions. The analysis in this paper is based on continuity and momentum‐transfer equations for the electrons and ions, but in contrast to linear ambipolar diffusion theory, the nonlinear ion inertia term is retained. In the plasma approximation, retention of this term gives rise to a plasma‐sheath boundary, where the density is nonzero and the potential finite, located where the ambipolar drift velocity reaches the isothermal sound speed [k(Te+Ti)/mi]1/2. Numerical solutions are presented for the profiles of density, velocity, and potential...

Growth Rates and Stability Limits for Beam‐Plasma Interaction

A treatment is given of the one‐dimensional problem of beam‐plasma interaction, including the effects of plasma and beam thermal velocities and momentum transfer collisions in the plasma. The conditions under which the Landau damping due to the plasma is negligible are first investigated. Neglecting this damping, a weak‐beam approximation to the dispersion relation is derived, and conditions for its validity are established. Expressions are derived for the maximum temporal and spatial growth rates in the limits of cold and hot beams, and few and many collisions. The growth rates given by the weak‐beam approximation are compared with those calculated from the full dispersion relation. The transition from a cold to a hot beam is discussed in terms of the topology of the roots of the dispersion relation, and also in terms of the location of the phase velocities of the most unstable waves relative to the bump in the distribution.

Two-wavelength laser transmissometer for measurements of the mean size and concentration of coal ash droplets in combustion flows

A two-wavelength transmissometer employing a He-Cd laser (lambda(1) = 0.325 microm) and a He-Ne laser (lambda(2) 3.39 microm) has been developed for measuring the Sauter mean diameter of mineral ash droplets in high-temperature high-velocity coal-fired combustion flows. From transmission measurements at the two wavelengths, it is shown that mean diameters in the 0.3-3.5-,microm range may be inferred with a weak sensitivity to particle refractive index and size distribution shape. The volume concentration or loading of the aerosol may then be determined from the measured transmission at either wavelength. The instrument has been used to measure the mean size and loading of ash droplets in a pulverized coal-fire channel flow at temperatures to ~2900 K and velocities of up to 400 m-sec(-1) for combustion MHD power generation applications.

Comparison of wire—plate and plate—plate electrostatic precipitators in turbulent flow

Abstract The transport of pre-charged particles in a wire—plate precipitator in turbulent flow is investigated by numerical solution of the convective diffusion equation. For ease of computation the high voltage wire electrodes are replaced by strip electrodes giving essentially the same potential distribution. It is shown that for equivalent values of the Deutsch and Peclet numbers, the efficiency of the wire—plate system agrees closely with that of a plate—plate system, provided the comparison is made on the basis of equal values of the space-averaged field at the collector. The study does not include corona charging as normally encountered.