Table of contents

It is shown that the thermonuclear reaction rate between two gases in thermal equilibrium and of densities n₁ and n₂ nuclei per unit volume can be written as n₁n₂<σν> where <σν> is a suitable average of the product of the reaction cross section and relative velocity, and for any reaction is a function of temperature alone. These functions are given for a number of exoergic reactions between light nuclei.

Calculations of the power balance in thermonuclear reactors operating under various idealized conditions are given. Two classes of reactor are considered: first, self-sustaining systems in which the charged reaction products are trapped and, secondly, pulsed systems in which all the reaction products escape so that energy must be supplied continuously during the pulse. It is found that not only must the temperature be sufficiently high, but also the reaction must be sustained long enough for a definite fraction of the fuel to be burnt.

Standard formulae for the electrical resistance and for the radiating properties of a fully ionized gas have been combined with pinch-effect relations to obtain the stationary state radial distribution functions and current-voltage characteristics of a radiation-cooled discharge, using a simplified model in which a stationary, axially symmetrical discharge is generated in a long straight tube. The validity of the diffusion conditions implied in the initial equations, the transport properties of the plasma, and the cyclotron radiation arising from thermal motion in the self-magnetic field, are considered. The calculations are applied to the requirements of a power-producing thermonuclear reactor.

The chief results are that in a stationary state a pinched discharge will exist with radiation cooling, that the magnitudes of the voltages, tube diameters and initial gas pressure are within reasonable engineering limits, and that a maximum current of one to two million amperes will be encountered. This maximum is a characteristic current of an ionized gas and, slowly varying numerical factors apart, depends directly only on the fundamental constants e, m, h and c.

While it is possible to present grounds for supposing these results to be independent of some of the assumptions, the work gives no guidance on the extent to which they will be invalidated by the instabilities of the current channel.

A simple theory of the collapse of a high current discharge plasma is described. The theory applies to discharges of the type studied by Cousins and Ware, in which shock waves are generated by the self-magnetic `pinch' forces.

Some hydromagnetic instabilities of a cylindrical ideally conducting fluid, which is confined by the pinch effect of an axial current, are considered. Kruskal and Schwarzschild have previously studied the instabilities of a fluid carrying a surface current. We consider a volume current distributed according to a power law, and some general stability criteria and values of maximum possible growth rates are obtained. The volume current is more stable than the surface current, and in particular an infinite instability at short wavelength is replaced by one of finite growth rate. Finally, viscosity is introduced into the plasma carrying a surface current; disturbances at very short wavelength are damped, and a first approximation is obtained to a wavelength of maximum instability.

Observations of gaseous discharges in both straight and toroidal discharge tubes have shown that a constricted current channel becomes unstable at a particular value of current. Discharges have been studied up to currents of 1500 A and high-speed photographs are reproduced which indicate the helical form of these unstable current channels.

Comprehensive measurements on the reversible and total magnetothermal effect, the reversible susceptibility and the magnetization curves of annealed nickel and cobalt have been made. It is shown that, for reversible changes in magnetization, there is no significant change in the value of the `rotational' coefficient bdouble prime for nickel in high fields, and that reversible changes in intrinsic magnetization and rotations of the magnetization vectors must predominate. For cobalt, with a higher coercivity, these effects also predominate even in relatively low fields. There is no evidence of the reduction in the numerical value of b'' in high fields, which has been deduced from the results of earlier work, and it is suggested that if any additional effects are present in high fields they must be irreversible. There is good agreement with the results of Tebble, Wood and Florentin and of Bates and his co-workers.

The rate of coagulation of an aerosol was calculated by Smoluchowski on the assumption that every collision resulted in the coalescence of two particles. The coagulation rate when there is a potential barrier round the aerosol particles is now calculated and two examples are considered.

Ultrasonic absorption measurements have been made in liquid methylene chloride between 7.5 and 210 Mc/s. These confirm recent work in the vapour by Sette, Busala and Hubbard (1955), from which it was concluded that the relaxation of the vibrational specific heat takes place in two parts. In the frequency range studied here there is a single relaxation of specific heat equal in magnitude to the vibrational specific heat less the contribution of the lowest frequency mode of vibration. The relaxation frequency is 170 Mc/s at 25°C.

Studies of the domain structures in the surface layers of crystals of iron and silicon-iron having (111) and (h0l) type faces, have permitted calculations to be made of the optimum domain sizes in iron crystals as dependent on the crystallographic orientations of their faces and on their sizes.

The effect of thin uniform bubble screens on sound propagation in water has been investigated over a frequency range of 15-100 kc/s for bubbles with diameters between 0.016 and 0.050 cm. The density of the bubble screen was varied from 1 bubble in 10 cm² to 4 bubbles per cm². The results obtained confirm to a considerable accuracy the theory originally proposed by Foldy and also provide values of the damping constants of gas bubbles which are consistent with those obtained from measurements on isolated bubbles.

The theory of the Clusius and Dickel hot wire thermal diffusion column as developed by Furry and Jones has been extended to take into account the temperature dependence of the gas coefficients for a gas whose molecules consist of hard rigid spheres. Tables for the shape factors h, k_c and k_d have been constructed by the method of numerical integration. It is found that the column constants H, K_c and K_d depend strongly on the law of molecular interaction for the gas. The expressions obtained for the constant H are found to agree closely with the experimental data of Nier on helium.

It is shown that the static friction between a specimen of bituminous material and a cast iron disc is due to adhesion between specimen and disc, and that the friction is reduced when the normal load is removed because of elastic interaction between the surfaces.

Application of approximations relating to spheres to the scattering of light by polydisperse dust clouds is discussed theoretically. If the relative refractive index of the particles is low, the shapes of the particles are not extreme, the particles are not orientated, and only the scattering forward through angles less than 30° is considered, the scattering seems likely to resemble that by clouds of spheres of the same sizes. Forward scattering and extinction by carefully fractionated silica dusts suspended in liquid were measured using an extinction method, and for particles larger than 2 microns showed good agreement with Mecke's approximation. For smaller particles absolute extinction measurements were not made, but relative values indicated the presence of aggregates. The aggregates seemed to diffract like opaque discs, and the unaggregated particles seemed to scatter like Rayleigh-Gans spheres.

The influence of temperature on the wear rate of a particular combination of metals, 60/40 brass on tool steel, has been investigated over the range 20°C to 600°C. Two regimes of wear were found. At low temperatures, extensive intermetallic contact and welding occur, and the wear rate increases with increasing temperature. At high temperatures, however, the wear rate decreases by several orders of magnitude and protective surface films are generated during sliding. The latter reduce both the extent of intermetallic contact and the frequency with which it occurs. A transition between these two regimes of wear also occurs at a critical load, the magnitude of which increases with the temperature. At loads above the transition load, the increase in wear rate with increasing temperature is accounted for by the associated decrease in hardness of the 60/40 brass, and the relationship W=KL/P_m is obeyed, where W is the wear rate, L is the load and P_m is the flow pressure. At loads below the transition load, however, there is no definite relationship between the wear rate, load and flow pressure. It is suggested that in this regime of wear, the main effect of temperature arises from its influence on the reaction rate between the sliding metals and the surrounding atmosphere.

A calculation is made of the splitting of the energy levels of Eu³⁺ ions in their ground state which arises from the interactions of the nuclear magnetic moment with external and internal magnetic fields and of the nuclear quadrupole moment with the crystalline electric field. The feasibility of determining these nuclear properties by nuclear magnetic resonance is discussed. The method is applicable to all paramagnetic substances with singlet ground states.

The Bloch-Wilson theory for the Hall effect of a mixed conductor in an arbitrary magnetic field is discussed. A method of computation based upon the use of an electronic computer for fitting the theoretical expression to experimental data is described.

To test the theory the method was applied to InSb. Good agreement was obtained between the observed behaviour of two p-type single crystals and the theoretical expression. The fitting of the theory to the experimental results enables the concentration of holes and electrons and their mobilities to be determined over a range of temperature. This leads to values of the intrinsic carrier concentration which are in good agreement with those found by other workers. It is also shown that in these specimens the mobility ratio falls as the temperature is reduced and that this behaviour can be expected from the effects of lattice and impurity scattering on the holes and electrons.

The possible modes of propagation of compressional waves in solid cylindrical rods are described by the solutions of the `frequency equation'. It has been found possible to solve this equation at frequencies near 10 Mc/s by a graphical method which is readily applicable. Using this method the variation of phase velocity ν<sub>p</sub> with frequency has been evaluated for the most important modes of propagation, namely those having phase velocities near to that in an unbounded medium, ν<sub>1</sub>. It is shown that in the vicinity of ν<sub>p</sub>=ν<sub>1</sub> the variation of phase velocity with frequency is characterized by a series of `plateau' regions over which ν_p is approximately constant, these regions being separated by `steps' through which ν_p changes rapidly with frequency.

Consideration of the displacement amplitudes shows that the mode with ν_p nearest to ν₁ has, in general, a pressure variation across the radius which is most likely to be excited experimentally under conditions described in a previous paper by the authors.

Corrections to 1956 Proc. Phys. Soc. B 69 1056