Table of contents

The absorption coefficients of clouds of elongated (prolate spheroidal) and spherical soot and graphite particles are compared. Much higher absorption coefficients are predicted for the elongated particles, leading to significant increases in emissivity.

A calibrated Langmuir-type probe has been used to measure ionization in argon and argon-oxygen mixtures shock-heated to 2500 to 4000 K in the presence and absence of soot particles. In the absence of oxygen, ionization is due mainly to impurities scrubbed from the tube walls by the gas flow behind the incident shock, and the soot particles cannot become heavily charged. When oxygen is present the charge density is ten to a hundred times greater. This can be explained by the thermal ionization of fragments produced in the course of oxidation of the original soot particles. However, the process does not result in highly charged particles.

With the use of recent values of Townsend's α in dry air, ionization current multiplication in a non-uniform electric field has been computed. Good agreement is obtained between computed values and Johnson's experiments for E_max/p>or=250 (where E_max is the maximum electric field in the gap).

Closed-form expressions are derived for the components of magnetic field due to the currents in single-layer cylindrical coils using a novel scalar potential approach. In addition, an expression is given, in single-integral form, for the potential due to multilayer coils, from which the field components may be readily computed.

An assessment is made of the accuracy of the variational method for calculating neutron reaction rates in plane foils in problems involving velocity-dependent cross sections. This is achieved by using a separable scattering kernel and cross sections which are inversely proportional to velocity, thereby allowing the problem to be solved by analytic methods. We find that the error in the reaction rate, as calculated by the variational method, is at most 7%. This error is an order of magnitude larger than that incurred in one-speed calculations.

Theoretical investigations of noise produced by jet engines should have the following objectives: (i) to understand the noise generation and propagation mechanisms; (ii) to suggest methods of reducing noise levels; (iii) to predict noise levels from various engine configurations.

Because of the complex geometries associated with modern turbofan engines, idealized mathematical and simplified experimental models need to be studied and correlated with full-scale data.

In the first part of this paper, a now classical example of the application of theory to rotor-stator interaction noise is discussed to illustrate how the first two objectives can be obtained essentially from a simple theoretical model. Some of the problems arising from predicting noise levels of interaction tone noise are considered, and a recent test is described that illuminates certain features of these problems.

The second part of the paper describes some of the more recent work associated with the study of combination tone or multiple pure tone noise. This noise is produced in the inlets of turbofan engines whenever the fan blades have supersonic relative tip speeds. Results of large-scale fan tests are used to illustrate the physical characteristics of this noise. A mathematical model is introduced that determines the importance of blade shock-wave spacing in the noise generation process. Finally, a method of estimating the standard deviation of shock-wave spacing is presented and compared with full-scale data.

These, and other similar models, are helping to achieve the three objectives mentioned. They are being incorporated in procedures for predicting noise of advanced engine designs.

When a system is in a state which differs from that of the infinite atmosphere surrounding it, its capacity to do work is measured by the maximum work which the system is capable of producing as it interacts with the infinite sink and eventually reaches the same state as the sink. When the system is subjected to a process there is, in general, a work interaction between the system and the surroundings, together with an exchange of heat with a source or with a sink other than the infinite sink. Here the actual change in available energy is compared with the ideal change in available energy. An efficiency for the process is defined, which will reflect all the losses or irreversibilities in the process. Hitherto, the definition of efficiency for any process from a purely thermodynamic viewpoint has been hampered by using different fundamental relationships in flow and nonflow processes, and for the flow process analysis it has been restricted to adiabatics in which the well-known parameter called `effectiveness' is used as a criterion of efficiency. In the analysis given here the same basic relationships are used independent of the circumstances in which the process takes place. This has been achieved by introducing the concept of `high-grade' energy.

Starting from a simple atomic model giving the potential between electrons and atoms as V(r) = Ze²a^s−1/sr^s with the empirical value s=fraction six-fifths, we combine the diffusion effect due to multiple collisions and the energy retardation in accordance with a modified Thomson-Whiddington law, with the scattering cross section in the Lenard absorption law. On this basis, consistent expressions are obtained for the fraction of transmitted electrons in amorphous solid targets, the backscattering fraction with depth, the fraction of electrons absorbed per unit mass-thickness and the depth-dose function, which are in good agreement with experiments over the energy range 10-1000 keV.

A diffusion model represented by a sphere whose centre is located at the maximum energy dissipation depth, related to the diffusion depth and the range, is found to agree well with experiments.

Output powers of 50 MW have been obtained from an actively Q-switched Nd³⁺: POCl₃: ZrCl₄ liquid laser with input energies of 500 J. Powers of this order of magnitude with such low input energies make the neodymium liquid laser at least as efficient as YAG and glass lasers. The performance of this laser in the 1 J output pulse region is superior to that of YAG and glass lasers. The output characteristics of this laser were studied as a function of the pumping pulse, the cavity mirror reflectivity and the cavity length.

A theoretical study has been made to investigate the dependence of resolution on the coherent properties of the light source in the case of an aberration-free annular aperture operating in partially coherent light. The composite intensity curves have been presented for separations greater than that for Sparrow incoherent light and also for separations in the region of the Rayleigh limit. Even the best resolution shows some variation for these separations.

Data are presented on the angular spread of neutral atoms formed by electron capture and dissociation of H⁺, H₂⁺ and H₃⁺ in H₂, H₂O and C₈F₁₆ targets. Measurements were made at energies of 2·5 to 15 keV and for a range of target densities. The results are presented as the fraction transmitted through an aperture of a given half-angle. It is deduced that the angular spread of atoms from H₂⁺ and H₃⁺ molecular ion beams was predominantly due to the internal excitation energy of the molecular ions and not to simple scattering, even at the lower energies. The angular spread of atoms formed by electron capture by H⁺ in H₂O varied with energy as E^−0·6; this is compared with the cross section for single scattering of H⁺ on oxygen atoms obtained from the classical theory of Firsov, which varies as E⁻¹.

The influence of secondary gas flows on energy transfer distributions is examined for plasma torches operating in the transferred mode. The radial distributions of current and energy flux as a function of secondary gas flow and offset distance were obtained with a split-plate calorimeter. These results indicate that under certain conditions of flow tailoring the energy transfer density from the plasma is increased significantly and the width of the heat-affected zone decreased correspondingly. Arc oscillations have also been determined to elucidate the processes involved in the changes in energy flux which occur as a result of flow tailoring.

In a consumable-electrode arc system the variable portion of the wire electrode between the current pick-up point and the electrode-arc interface (the `electrode stickout') forms an important resistive part of the arc circuit. An approximate relation for the voltage fall along the stickout is calculated in terms of the arc current, the electrode feed speed and the stickout length, on the assumption that the electrode resistivity varies linearly with temperature. Some numerical illustrations are given for stainless steel wire electrodes.

The characteristics of laser-triggered spark gaps, initiated by a switched-out pulse of about 7 ps from a model-locked Nd: glass laser system, are investigated. The formation time delay of breakdown across the gap can be of the order of 1 ns and is found to increase as the gap voltage is reduced. Comparison with spark gaps triggered by Q-spoiled nanosecond laser pulses is made. Finally, a comparison of the agreement between the experimental results and theory suggests that the initiation of gap breakdown is due to the production of only a few free electrons from the electrode surface on which the laser beam is focused.

Experimental results for an axial arc column in the steady flow behind the shock front in a shock tube are presented. Tests were made at currents between 5 A and 150 A for free-stream Mach numbers of 0·4, 0·7, 1·0 and 1·3 in nitrogen gas at a pressure of one atmosphere. A semi-empirical heat transfer theory is proposed and an excellent correlation of the voltage gradient to current data is found.

The transition of a vacuum arc from one steady state to another has been investigated by superposition of a current step. At low rates of change of current there is a decrease in the magnitude of the voltage oscillations and a slight increase in the arcing voltage in agreement with DC observations. At high rates of change of current the arc shows a transient response which includes an increase in the interelectrode voltage which persists for a few tenths of a microsecond. Possible explanations of this behaviour are suggested.

The action integral is used to evaluate the rupturing times and rupturing currents of fuse elements in inductive circuits. With a suitable choice of variables it is shown that all fuses and circuits can be represented by the one equation and there is excellent agreement with measurements made on copper fuses. Particular attention is given to the stored magnetic energy at the time of rupture, since this energy has to be dissipated in the ruptured fuse material. Again, with a suitable choice of variables, a general relation between current cut-off ratio and pre-arcing energy is derived. The existence of a maximum in this relation has been known for many years but the treatment here puts the whole problem on a general quantitative basis. Impulsive performance is considered in conjunction with steady-state performance in a quest for the best fuse element material. Silver appears to be the outstanding material, with the much-used copper some way down in the list of metals. Finally, the impulsive pressure produced in cartridge fuses is considered and good qualitative agreement with measurements obtained in the case of a treatment based on radiation pressure.

Consideration is given to the unsteady motion of a sphere moving from rest under the action of a constant force in elastico-viscous liquids. Expressions are found for the velocity of the sphere; these can be evaluated for all values of the time and material constants involved. Information is provided which may be of use to experimentalists who use the falling-ball technique to determine the limiting zero shear rate viscosity of elastico-viscous liquids. Indications are also given of how this technique may be used to determine the elastic parameters of liquids.

Effects of a magnetic field on the double-probe technique are studied experimentally by means of asymmetric double probes in a low-pressure, high-density plasma. It is found that the magnetic field can considerably affect ion probe currents, even if the ion gyro radius is very much larger than the probe size; for example, by a factor of seventy for transverse current collections. At strong fields the effective collecting area for parallel current collections becomes proportional to something like the periphery of the probe.

The thermal conductivity of spectroscopically pure rhodium has been measured in the temperature range 1180-1573 K. Also, the values of electrical resistivity, spectral emittance and total emissivity in the same temperature range are reported in this paper.

An audio-frequency resonance method has been applied to a set of single-crystal MnF₂ rods to determine the elastic compliances. The derived elastic constants are in good agreement with published data.

Charge carrier mobility has been determined for four characterized polythenes in vacuo, using a surface charge dissipation technique. The mobility has also been examined in two of these polythenes impregnated with iodine. The values of mobility obtained are significantly different for each of the materials, and introduction of iodine into the structure causes a mobility increase of about four orders of magnitude. The experimental results are discussed in terms of a hopping transport mechanism and indicate a significant barrier in transitions between crystalline and amorphous regions. The iodine appears to reduce trapping either by carrier acquisition and transport, or by charge exchange complex formation.

The resistivity, thermoelectric power and magnetoresistance of carbon fibres derived from a polyacrylonitrile-based precursor heat treated to between 1000°C and 2800°C have been examined. The resistivity ratio as a function of heat treatment temperature exhibits a broad minimum roughly at about a heat treatment temperature (HTT) of 1750°C, and both the thermoelectric power and the magnetoresistance undergo a change of sign at that temperature. The importance of the temperature 1750°C, at which fundamental structural changes are believed to take place, is examined in the light of existing band models in the carbon and amorphous semiconductor fields.

In an extension of earlier work, the response of niobium-niobium point-contact Josephson junctions to radiation from hydrogen cyanide and deuterium cyanide lasers has been studied. Constant voltage steps corresponding to the 805, 891 and 964 GHz lines from a HCN laser have been observed as well as steps corresponding to the frequency mixtures of all these lines. In addition, subharmonic and harmonics of `mixed-frequency' steps have also been observed. The first observation of Josephson step structure corresponding to the 1540 and 1578 GHz emissions of a DCN laser is reported.

Indium amalgam has been used for electrical contacts on groups IV, III-V and II-VI semiconductors. The contacts were found to be ohmic to within 0·1% over a wide temperature range.

Mixed crystals of triglycine sulphate and selenate have been grown from water solutions but with modified habits. Their spontaneous polarization far from the Curie point is approximately independent of composition. Their lowest refractive index α varies linearly with composition: from 1·484 for the sulphate to 1·499 for the selenate. The energy gap varies nonlinearly from 5·243 to 5·21 eV for the sulphate and selenate respectively, with a minimum value of 5·195 eV at approximately 30 mol% sulphate.

The theory of Faraday rotation in artificial dielectrics is reformulated, treating the polarizability of embedded elements as a magneto tensor quantity. The rotation measurements are performed at room temperature in a silicon-wax dielectric for its various compositions, using radiation of frequency 24·0 GHz and a magnetic field of up to 1·0 Wb m⁻². The experimental results are compared with the present theory, and also with the theory proposed by Nag and Engineer in 1965. The experimental results are found to show reasonably close agreement with the present theory.

In previously reported calculations of the critical inclusion radius for reverse `spike' domain formation (Carey and Isaac 1964) it was necessary to estimate the magnetostatic energy of the inclusion after the reverse spike had formed. The necessity for this estimate is removed by recent calculations by Carey of the magnetostatic energies of spherical particles with various `free pole' arrangements. Accordingly, the critical inclusion radii for both cobalt and magnetoplumbite have been recalculated, again as a function of magnetic field. It is shown that introduction of the correct expression for the inclusion energy after spike formation leads to the critical inclusion radius being smaller and much less field dependent in both materials.

Hysteresis in a ferromagnetic material is represented by an idealized elliptical magnetization characteristic that neglects harmonics and enables flux density and magnetizing force, when expressed in terms of phasor vectors, to be related by complex permeability. This concept, together with the assumption that all field quantities have a linear relationship and vary sinusoidally in time and space, is then used to obtain steady-state solutions for electromagnetic field problems in materials including both hysteresis and eddy-current effects. Computed values are determined for the flux distribution and losses in semi-infinite and finite-thickness plates.

It is found that when an unguided cylinder falls through a newtonian fluid in a viscometer tube inclined from the vertical the cylinder falls with an increased speed compared with the speed of fall in the vertical position. At an angle of about 15° from the vertical, a cylinder may travel at more than twice its vertical speed. This phenomenon is investigated experimentally, and a theory is derived which shows that the change in fall time is due to the cylinder falling eccentrically in the tube. When the viscometer tube was tilted, a maximum reduction in fall time of 59±2% was produced, which compares well with a theoretical value of 58·4%. The relationship between viscometer tube angle and the eccentricity of the falling cylinder is deduced from the analysis. This relationship is verified experimentally.