A theory for marine source arrays

General mathematical expressions for a marine source array’s (1) far‐field pulse spectrum, (2) radiated energy density, and (3) directivity are developed for both a source in an infinite homogeneous medium and a source operating near the ocean surface. These results, intended to assist the analysis and design of marine source arrays, apply to any marine source array when (1) individual elements radiate isotropically, (2) their individual waveforms are specified, and (3) the array geometry is specified. Arbitrary geometry and arbitrary isotropic waveforms are allowed. The theory assumes linear superposition of the individually specified waveforms, and is consistent with the “square law effect” for identical elements. For an array of small elements, expended energy agrees with the array’s radiated energy found using far‐field methods. Also, the energy radiated from an array with large element spacing is equal to the sum of the independently radiated energies. Two closely spaced identical elements radiate four times the energy contained in a single outgoing waveform over all space. The appropriate directivity definition for marine seismic sources is the ratio of the radiated energy density per unit solid angle in a particular direction to the average radiated energy density per unit solid angle. This definition allows directivity to be expressed explicitly in terms of the individual frequency spectra and geometry.

Laser generated plasma as a source for real time studies in X-ray crystal research: Part I: Fundamental remarks about source characteristics and requirements

Because of the large number of X-ray photons which will be emitted per unit solid angle and wavelength interval, laser generated plasmas have good prospects as X-ray sources for time-resolved diffraction experiments in solid state research. Starting from this a modified two-crystal diffractometer will be described, which uses the particular advantages of laser plasmas as X-ray flash sources. Requirements for the source will be determined and discussed.

The scattering of electrons by metal vapours. I.—cadmium

Since the discovery of the diffraction of electrons by gas atoms* a large amount of experimental and theoretical work has been devoted to the study of electron scattering in gases. As a result it is now possible to recognize the main processes occurring in the collisions with the gas atoms and it has been found that it is usually only necessary to calculate the scattering by the undisturbed field of the atom in order to explain the experimental results. As a consequence considerable simplification is introduced in the theory of the phenomena and it follows that the diffraction effects are mainly determined by the ratio of the wave-length of the incident electrons to the distance from the centre of the atom at which the magnitude of the potential energy of the electron in the atomic field is comparable with its kinetic energy. When this ratio is large (very slow electrons) the angular distribution per unit solid angle of the scattered electrons is independent of angle. As the ratio decreases maxima and minima appear and the diffraction effects become more and more complicated until such electron energies are reached that the ratio begins to increase again. For such energies the simple picture fails but Born’s approximation applies and the angular distribution per unit solid angle decreases uniformly with increase of angle. Thus one would expect potassium and argon to give similar angular distributions for electrons with energies considerably greater than the ionization energy of the N electron of potassium but, when the electron energy becomes comparable with this energy, the presence of the outer electron in the alkali metal atom should produce much more complicated angular distributions than are observed for electrons of the same energy scattered by argon. If the above view of the phenomena is correct, it follows that the field of an atom may be approximately determined merely by comparison of the diffraction effects which it produces in scattering electrons with those produced by atoms whose fields are known. All that is necessary is to effect this comparison at a series of different electron energies. A generalization of this method to molecules which have approximately spherically symmetrical fields would also be possible.