Geometrical hydromagnetics

Journal Article · Tue Jan 01 04:00:00 EST 1963 · Journal of Geophysical Research

DOI:https://doi.org/10.1029/JZ068i001p00147· OSTI ID:4744507

Bazer, J.; Hurley, J.

The propagation of small disturbances in an infinitely conducting, perfect, compressible medium is studied from the standpoint of geometrical hydromagnetics. The medium need not be homogeneous. A wavelike time-harmonic disturbance is assumed given on an arbitrary reference surface. Then the various phase fronts, slow, Alfven, and fast, that may be thought to evolve out of this surface are obtained as solutions of first-order partial differential equations. These eikonal-like equations are solved, as in optics, by means of rays, which are shown to satisfy Hamilton's equations and Fermat's principle. The hydromagnetic analog of Huygens' phase front construction is described. Next, the variation of the disturbance strengths along the rays is determined in terms of the disturbance strengths on the reference surface, to complete the geometrical solution. A noteworthy feature of this solution is that its component modes of propagation, slow, Alfven, and fast, are uncoupled as long as the medium is free of diffracting objects and surfaces of discontinuity. As an illustration of the general theory, the complete geometric solution for the propagation of Alfven disturbances in a dipole field is described with the aid of explicit formulas. Fast wave propagation in various types of inhomogeneous magnetic fields is also briefly discussed. Finally, the problem of reflection and refraction of slow, Alfven, and fast disturbances at (possibly curved) surfaces of discontinuity is treated. The hydromagnetic analogs of Snell's laws are derived, and their relation to Huygens' wavelet construction is elucidated. It is shown that the introduction of an appropriate set of direction angles for the unperturbed magnetic field (on each side of the discontinuity) (1) reveals the symmetries of Snell's laws,' (2) leads immediately to a simplification of V. C. A. Ferraro's laws relating to the reflection and refraction of Alfven waves, and (3) makes possible a simple graphical method for determining the angles and speeds at which the various reflected and refracted waves emerge. The isotopic compositions of xenon from troilite and from chondrules from the Bruderheim meteorite were studied. The troilite is depleted in xenon relative to the total meteorite and has a negligibie Xe¹²⁹ anomaly, suggesting a very low iodine content. The chondrules are depleted in xenon of normal composition but show an enrichment of anomalous Xe¹²⁹ by a factor of 2.9. In one gas fraction from these chondrules, the Xe¹²⁹/Xe¹³² ratio reached 9.6, a new high for this quantity. The wide variations in Xe¹²⁹/Xe¹³² within this meteorite are further evidence for in situ decay of I¹²⁹. These data are discussed in the light of the recent suggestion by Wood that chondrules are primitive material which condensed from cooling gases during the formation of the solar nebula. Unusually large anomalies in Xe¹²⁴ and Xe¹²⁶ from the chondrules are tentatively attributed to cosmic irradiation.

• Research Organization: New York Univ., New York
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-008987
• OSTI ID: 4744507
• Journal Information: Journal of Geophysical Research, Journal Name: Journal of Geophysical Research Journal Issue: 1 Vol. 68; ISSN 0148-0227
• Publisher: American Geophysical Union
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

58 GEOSCIENCES
ANGULAR DISTRIBUTION
DIFFERENTIAL EQUATIONS
DIFFRACTION
DIPOLES
DISTURBANCES
ELECTRIC CONDUCTIVITY
EQUATIONS
FERMAT PRINCIPLE
GEOMETRY
HOMOGENEOUS REACTORS
HYDROMAGNETIC WAVES
MAGNETIC FIELDS
MAGNETOHYDRODYNAMICS
MOTION
OSCILLATIONS
PRESSURE
REFLECTION
REFRACTION
SURFACES
VARIATIONS
VELOCITY