Theory of the positive column of a gas discharge

An attempt is made to provide a theoretical explanation of the effect of the positive column on the voltage-current characteristic of a glow or an arc discharge. Such theories have been developed before, and all are based on balancing the production and loss of charged particles and accounting for the energy supplied to the plasma by the applied electric field. Differences among the theories arise from the approximations and omissions made in selecting processes that affect the particle and energy balances. This work is primarily concerned with the deviation from the ambipolar description of the positive column caused by space charge, electron-ion volume recombination, and temperature inhomogeneities.

The presentation is divided into three parts, the first of which involved the derivation of the final macroscopic equations from kinetic theory. The final equations are obtained by taking the first three moments of the Boltzmann equation for each of the three species in the plasma. Although the method used and the equations obtained are not novel, the derivation is carried out in detail in order to appraise the validity of numerous approximations and to justify the use of data from other sources. The equations are applied to a molecular hydrogen discharge contained between parallel walls. The applied electric field is parallel to the walls, and the dependent variables—electron and ion flux to the walls, electron and ion densities, transverse electric field, and gas temperature—vary only in the direction perpendicular to the walls. The mathematical description is given by a sixth-order nonlinear two-point boundary value problem which contains the applied field as a parameter. The amount of neutral gas and its temperature at the walls are held fixed, and the relation between the applied field and the electron density at the center of the discharge is obtained in the process of solving the problem. This relation corresponds to that between current and voltage and is used to interpret the effect of space charge, recombination, and temperature inhomogeneities on the voltage-current characteristic of the discharge.

The complete solution of the equations is impractical both numerically and analytically, and in Part II the gas temperature is assumed uniform so as to focus on the combined effects of space charge and recombination. The terms representing these effects are treated as perturbations to equations that would otherwise describe the ambipolar situation. However, the term representing space charge is not negligible in a thin boundary layer or sheath near the walls, and consequently the perturbation problem is singular. Separate solutions must be obtained in the sheath and in the main region of the discharge, and the relation between the electron density and the applied field is not determined until these solutions are matched.

In Part III the electron and ion densities are assumed equal, and the complicated space-charge calculation is thereby replaced by the ambipolar description. Recombination and temperature inhomogeneities are both important at high values of the electron density. However, the formulation of the problem permits a comparison of the relative effects, and temperature inhomogeneities are shown to be important at lower values of the electron density than recombination. The equations are solved by a direct numerical integration and by treating the term representing temperature inhomogeneities as a perturbation.

The conclusions reached in the study are primarily concerned with the association of the relation between electron density and axial field with the voltage-current characteristic. It is known that the effect of space charge can account for the subnormal glow discharge and that the normal glow corresponds to a close approach to an ambipolar situation. The effect of temperature inhomogeneities helps explain the decreasing characteristic of the arc, and the effect of recombination is not expected to appear except at very high electron densities.

Discharge and turbidity of the regulated River Tees. Variance spectrum analysis

High suspended sediment loads may be deleterious to adult salmonids and invertebrates in gravel-bedded streams. Further, the accumulation of fine material in the interstices of the gravel may have an adverse impact on the recruitment of the young stages of salmonids. It is important therefore not only to quantify the rates and degrees of silting but also to identify sediment sources and to determine both, the frequency of sediment inputs to the system and the duration of high sediment concentrations. This report explores the application of variance spectrum analysis to the isolation of sediment periodicities. For the particular river chosen for examination the method demonstrated the essentially undisturbed nature of the catchment. The regulated river chosen for examination is the River Tees in Northern England. Variance spectrum analysis was applied to a series of over 4000 paired daily turbidity and discharge readings.

Gas laser discharge noise and its effect on the laser output

A large portion of the noise in the light output of a laser oscillator is associated with the noise in the laser discharge. The effect of the discharge noise on the laser output has been studied. The discharge noise has been explained through an ac equivalent circuit of the laser discharge tube.

The discharge noise corresponds to time-varying spatial fluctuations in the electron density, the inverted population density and the dielectric permittivity of the laser medium from their equilibrium values. These fluctuations cause a shift in the resonant frequencies of the laser cavity. When the fluctuation in the dielectric permittivity of the laser medium is a longitudinally traveling wave (corresponding to the case in which moving striations exist in the positive column of the laser discharge), the laser output is frequency modulated.

The discharge noise has been analyzed by representing the laser discharge by an equivalent circuit. An appropriate ac equivalent circuit of a laser discharge tube has been obtained by considering the frequency spectrum of the current response of the discharge tube to an ac voltage modulation. It consist of a series ρLC circuit, which represents the discharge region, in parallel with a capacitance C', which comes mainly from the stray wiring. The equivalent inductance and capacitance of the discharge region have been calculated from the values of the resonant frequencies measured on discharge currents, gas pressures and lengths of the positive column. The experimental data provide for a set of typical values and dependencies on the discharge parameters for the equivalent inductance and capacitance of a discharge under laser operating conditions. It has been concluded from the experimental data that the equivalent inductance originates mainly from the positive column while the equivalent capacitance is due to the discharge region other than the positive column.

The ac equivalent circuit of the laser discharge has been shown analytically and experimentally to be applicable to analyzing the internal discharge noise. Experimental measurements have been made on the frequency of moving striations in a laser discharge. Its experimental dependence on the discharge current agrees very well with the expected dependence obtained from an analysis of the circuit and the experimental data on the equivalent circuit elements. The agreement confirms the validity of representing a laser discharge tube by its ac equivalent circuit in analyzing the striation phenomenon and other low frequency noises. Data have also been obtained for the variation of the striation frequency with an externally-applied longitudinal magnetic field and the increase in frequency has been attributed to a decrease in the equivalent inductance of the laser discharge.

The brine and gas content of sea ice with attention to low salinities and high temperatures

Based on the well known sea ice phase diagram, equations are derived for determining the brine and gas content of sea Ice for high temperatures (range 0 to -2 °C) and low salinities. The presently widely used equations of Cox and Weeks (1982) are valid only for temperatures below -2°C. Fresh-water ice is used as a boundary condition for the equations. The relative salt concentrations in brine are_assumed to be the same as in normal (or standard) seawater. Two sets of equations are presented: 1) accurate formulae based on UNESCO standard sea water equations, and 2) approximate formulae based on general properties of weak solutions. The approximate formulae are not essentially different from the classical system which basically assumes the freezing point to be a linear function of fractional salt content. The agreement between the two approaches is excellent and the approximate system is good enough for most applications.

Mathematical models for the prediction of temperature distributions resulting from the discharge of heated water into large bodies of water

Mathematical models for heated water outfalls were developed for three flow regions. Near the source, the subsurface discharge into a stratified ambient water issuing from a row of buoyant jets was solved with the jet interference included in the analysis. The analysis of the flow zone close to and at intermediate distances from a surface buoyant jet was developed for the two-dimensional and axisymmetric cases. Far away from the source, a passive dispersion model was solved for a two dimensional situation taking into consideration the effects of shear current and vertical changes in diffusivity. A significant result from the surface buoyant jet analysis is the ability to predict the onset and location of an internal hydraulic jump. Prediction can be made simply from the knowledge of the source Froude number and a dimensionless surface exchange coefficient. Parametric computer programs of the above models are also developed as a part of this study. This report was submitted in fulfillment of Contract No. 14-12-570 under the sponsorship of the Federal Water Quality Administration.

Review of discharge consents. River Irwell catchment report

This is the Review of discharge consents, River Irwell catchment report produced by the North West Water Authority (NWWA) in 1979. The purpose of this Report is to make recommendations for the revision of consents for discharges within the catchment of the River Irwell, downstream and including the River Medlock in Manchester. This revision has the sole objective of recognising the present effluent and river water quality - proposals for long term river water quality objectives are to be put forward in other Reports. The report identifies the existing situation regarding the legal status of effluent discharges from Authority and non-Authority owned installations within the catchment, details the determinant concentration limits included in existing discharge consents (where appropriate) and proposes the limits to be included in the reviewed consents. The reviewed consents will reflect the quality of effluent achievable by good operation of the existing plant based on 1977 effluent quality data but taking into account any improvements, extensions etc. that have been or are about to be carried out and any known further industrial and/or housing development in the works drainage area.

Biological survey: River Teign and tributaries with references to the discharge of ball clay wastes

This is the Biological survey of River Teign and tributaries with references to the discharge of ball clay wastes, document produced by South West Water Authority in 1973. This report focuses on on-site assessment of the benthic macro-invertebrates of the lower River Teign, River Bovey, Ugbrooke Stream and Blatchford Brook was undertaken on 19th and 22nd August 1977 to assess the effects of discharges from ball clay mining premises. Inspection of aquatic fauna in the field is of necessity, less extensive than laboratory identification of sorted samples, so that the resulting data underestimates the water quality. This is more pronounced in the Chandler Score than in the Trent Biotic Index which does not take account of species abundance. Chandler should thus be interpreted by the trends described rather than by absolute values calculated.