Table of contents

The instantaneous population densities for the excited levels of hydrogen-like ions in an optically thin plasma, which is not necessarily in equilibrium, have been calculated for a range of electron temperature of 4000Z² °K to 256 000Z² °K and electron density of 10⁸Z⁷ cm^-3 to 10¹⁸Z⁷ cm^-3, where Z is the charge of the bare nucleus. The population densities depend linearly on the ground level population densities and tables are presented of two coefficients representing this relation for some of the lower excited levels.

The calculations include the processes of excitation, de-excitation, ionization by electron collision, spontaneous radiative decay, three-body recombination and radiative recombination. Processes involving the absorption of photons are neglected and it is assumed that the free electrons have a Maxwellian distribution.

The validity of the calculations in the extremes of the ranges is discussed.

The calculations illustrate the transition from high densities where all the excited levels have nearly a Saha-Boltzmann population to low densities where the radiative capture-cascade model is valid.

From the population density of the excited levels, the power lost by line radiation by hydrogen-like ions, radiative recombination of electrons onto the bare nuclei and bremsstrahlung of the free electrons in the field of the bare nucler is calculated.

Since energy is lost by radiation, the total energy dissipated during the ionization of one hydrogen-like ion may be much greater than the simple ionization energy of the ion. This has been calculated for electron temperatures between 16 000Z² °K and 256 000Z² °K.

The reliability of the procedure introduced by Gryzinski in 1959 for the calculation of the cross sections of atoms and molecules towards impact ionization is assessed with the aid of the available experimental data. It is found that fair success is achieved in many cases, but that in some cases the cross sections are seriously underestimated.

Coulson and Neilson have observed in 1961 that there exists a relation, which is almost exactly linear, between the error in the energy of the ground state of helium and the mean value of 1/r₁₂, when these quantities are evaluated using certain approximate wave functions. In this paper some mathematical explanation of this relation is presented. The reasoning is based primarily on the virial theorem, and to some extent on perturbation theory.

The scattering properties of the equatorial electrojet at a frequency of 21 Mc/s has been investigated. The results obtained suggest these irregularities first occur when the electrojet current density is about 6.4 × 10^-6 A m^-2. The corresponding drift velocity of the electrons is less than the mean thermal velocity of the ions. This situation does not favour the spontaneous formation of plasma waves, which is the mechanism suggested by Cohen and Bowles to account for the irregularities in the electrojet.

The rapid and deep fading of the received signal suggest there are only a few scattering centres present which are moving at velocities of about 300 m sec^-1. It is suggested that these scattering centres might be plasma waves with cylindrical wave fronts originating in the region of the electrojet which have been disturbed by the passage of meteors.

The motion of a charged particle through a low-density electron plasma placed in an external magnetic field has been investigated by using transport equations. The motion of the particle in the direction of the applied magnetic field is considered in some detail; the particles moving at right angles to the magnetic field are considered very briefly. The charge density developed in the medium as a result of interaction of the medium with the moving particle through a long-range Coulomb force is evaluated for the wavelength λ, which is such that R > λ > λ_D, where R is the distance from the moving particle and λ_D the Debye wavelength.

Three types of charge-density waves have been found to be associated with the moving test particle. One is a `plasma electron' wave that exists only for velocities of the test particle that are greater than the average thermal speed of the plasma electron; this wave also shows a Mach cone distribution. The second is an elliptically shaped `extraordinary' electromagnetic wave that exists for all velocities of the test particle, and is coupled to the plasma electron wave. The third is an almost spherical weak wave associated with the ordinary electromagnetic wave. This third wave is not coupled to the other two waves within the range of approximation considered here, and it goes over to an exponentially decreasing charge distribution in the limit of a very small magnetic field.

Electrostatic oscillations in velocity-gradient plasmas are studied with the aid of two simplifying models: (i) the slipping-stream model; and (ii) the adjacent-stream model. The slipping-stream model is dealt with in the present paper, and the adjacent-stream model in the following paper. In the simplest slipping-stream plasma the mean longitudinal velocity u, parallel to the z axis, varies linearly in a transverse direction: du/dx = α = const. Various assumptions are made in the treatment: collisions are neglected; it is assumed that a longitudinal magnetic field is sufficiently intense to suppress transverse oscillatory electron motions; it is assumed that the boundaries are sufficiently conducting for the electric potential to vanish at these boundaries; and finally only electron electrostatic interactions are considered. It is first shown that in the case of a zero-temperature slipping stream, longitudinal electron oscillations are stable, in the sense that there are no modes which are exponentially time-growing, when ω_e²/α² < ¼, where ω_e is the electron plasma frequency. When the longitudinal velocity u is an arbitrary function of the transverse coordinate x, general considerations show that ω_e² < ¼(du/dx)_max² is a sufficient condition for stability, where (du/dx)_max² is the maximum value of the velocity gradient squared in the stream. It is then shown that in the case of a finite temperature the slipping stream has increased stability and larger velocity gradients are necessary to cause instability.

In the adjacent-stream model the mean longitudinal velocity, parallel to the z axis, is u₁ in the range of -a₁ <or= x < 0, and u₂ in the range 0 < x <or= u₂. The assumptions made in the present paper are similar to those used previously in the treatment of the slipping-stream model. When the adjacent streams are of zero temperature it is shown that there are longitudinal electron oscillations which are exponentially time-growing, and the system is therefore always unstable. A general stability criterion is then derived for arbitrary but preferably single-humped distribution functions. However, the determination of the stability conditions for given distribution functions presents some difficulty, and in the particular case of Maxwellian distributions an alternative but approximate method is used. It is shown that there is stability for all velocity differences between the two streams when the transverse dimensions are comparable with, or less than, the Debye length, or when the velocity difference is comparable with, or less in magnitude than, the characteristic thermal speed of the electrons.

In connection with the use of gas Cerenkov detectors for the measurement of the energy of electron beams, it has been found necessary to take into consideration the modification of the radiation due to the end effects in the detector. Using electrons of energy in the range 26-29 MeV, observations have been made of radiation both below and above the Cerenkov threshold, the intensity and angular distribution of which are in good agreement with the transition radiation theory of Frank and Ginsburg and the theory of Cerenkov radiation as formulated by Tamm.

The threshold technique as a method of measuring beam energy is considered in the light of the above investigations.

A mechanism is proposed to account for the second dispersion region which occurs in polar liquids at frequencies higher than the Debye frequency. This mechanism is a vibration of the molecules about temporary equilibrium positions which are determined by the arrangement of the neighbours. It leads to a value of the high frequency limit, _∞, of the Cole-Cole arc for the Debye dispersion given by (_∞ - n²)/(₀ - n²) = 2kT/Iω₀², where ω₀ is the resonant frequency of the vibration, n is the optical refractive index and I is the mean moment of inertia of the molecules about axes normal to the dipole axis, but provided ω₀ >> 1/τ, where τ is the dielectric relaxation time, it does not modify the semicircular form of the arc.

The distribution function of carriers in a high electric and a simultaneous magnetic field is derived taking into consideration the effect of both acoustic and optical phonon scattering. Using this distribution function, expressions for the Hall mobility are obtained. These expressions indicate, and the numerical results calculated with the parameter values of n-type germanium also verify, that if optical phonon scattering occurs in addition to acoustic phonon scattering the value of the Hall mobility is increased. The Hall mobility is also found to increase with magnetic field.

The effects of pressure p, voltage v and interelectrode distance d on the production of active nitrogen by a high-frequency discharge have been examined simultaneously with the study of its physical and spectral characteristics. The results show that afterglow intensity I is a smooth function of p, v and d. The (I, v) curves have intensity maxima I_max, and a plot of I_max against p³ gives a linear relation indicating a three-body mechanism. Activation is poor when the discharge has strong N₂⁺ bands, or has bands of Gaydon's S, or Kaplan's second or fifth positive systems, characteristic of a condensed discharge. Stanley's short-duration afterglow has also been produced.

The method of electron nuclear double resonance (ENDOR) has been used to measure the interaction between a Eu²⁺ ion in CaF₂ and its ligand fluorine nuclei. Expressing the interaction in the form A_sS. I + A_p(3S_zI_z -S. I), with z along the bond axis, the parameters are found to be A_s = -2.23±0.01 Mc/s and A_p = +4.01±0.01 Mc/s. The value of A_s is of the same sign as, but a factor of 4 smaller than, the value predicted theoretically by Freeman and Watson in 1961. Interactions with next nearest neighbour fluorine nuclei are found to be nearly dipolar. An appendix discusses the possible line shift and line broadening of both fluorine and europium ENDOR due to high order effects in the fluorine and europium hyperfine interactions.

The paper presents a variation principle for the exact solution of transport or susceptibility problems. It is equivalent to the exact equation for the density matrix, whereas existing variation principles are based on the Boltzmann equation. Explicit forms are given for typical cases, including the electric conductivity and the electric and magnetic susceptibility.

In general the variation principle makes a functional stationary but has no extremum property. However, for coefficients representing a dissipative effect it can be written as a minimum principle.

In a perturbation approximation it reduces to the known variation principles. The cases of conductivity in an external magnetic field, and of magnetic resonance in a molecular gas, are discussed.

The radial Hartree-Fock equations for all atomic systems up to neon are solved by perturbation methods to first order in powers of the nuclear charge.

The mobility of a charged impurity in a Fermi liquid of neutral particles has been calculated. A simplified form of the distribution function has been used to evaluate the collision integral in Boltzmann's equation. The mobility is found to be proportional to 1/(kT)². A brief discussion of the structure of an ion in ³He and of the applicability of the calculation is given.

An amendment is made to the expression for the polarizability of BH₄^-, CH₄ and NH₄⁺, given recently by the authors (Proc. Phys. Soc., 82, 289), and revised calculated values and comments are given.

An attempt has been made to excite some long-lived nuclear isomers with bremsstrahlung of maximum energy 0.8 MeV. Previously reported activities in lead and selenium were not found. Excitation of the silver isomers is discussed.