Alberta Y. Alksne

Hydromagnetic flow around the magnetosphere

Abstract A magnetohydrodynamic model for the interaction of the solar wind and the geomagnetic field is described, the degree to which the governing equations may be approximated by the simpler equations of the classical Chapman-Ferraro theory combined with gasdynamics is examined, and numerical results for a number of representative cases are presented. In the hydromagnetic model, the magnetosphere boundary and distant tail are represented by tangential and contact discontinuities, and the bow wave by a fast hydromagnetic shock wave. The connectivity of interplanetary and geomagnetic fields, and the asymptotic directions of the wake and shock waves at great distances from the Earth are discussed in terms of properties of these discontinuities. Detailed numerical results for the location of the bow wave, and the density, velocity, and temperature of the flow in the region between the bow wave and the magnetosphere are presented for Mach numbers 5, 8 and 12 for γ = 5 3 and 2. The calculated position of the bow wave is shown to be in good accordance with that observed in shadowgraph photographs of supersonic flow past a model magnetosphere in the Ames Supersonic Free-Flight Wind Tunnel. Results are also presented that illustrate the distortion of the interplanetary magnetic field in the region between the bow and the magnetosphere for cases in which the magnetic field in the incident stream is inclined at 45 and 90° to the free-stream direction.

EXTERNAL AERODYNAMICS OF THE MAGNETOSPHERE.

The flow of the solar wind past the earth and its magnetosphere constitutes a problem similar in many ways to the familiar, but complex problem of the external aerodynamics of round-nosed bodies in a supersonic stream. It is the purpose of this paper to provide a resume of some of the basic ideas, both theoretical and experimental, that support this correspondence, and to present a connected account of many of the principal quantitative results that have been obtained through application and extension of methods developed originally for the aerodynamics of re-entry vehicles. In addition, the basic concepts of the theory of the solar wind itself are outlined in some detail in order to illustrate the basic unity of the entire theoretical description of the solar wind and its interaction with the geomagnetic field. Finally, extensive discussions of the internal consistency of the theory and the degree to which the results correspond to conditions observed in space are included for the purpose of providing an understanding of the overall reliability of the theory.

The steady-state magnetic field in the transition region between the magnetosphere and the bow shock.

Abstract The direction and intensity of the magnetic field throughout the transition region have been calculated by use of the equations of magnetohydrodynamics for several orientations of the interplanetary field. The equations were solved by an approximate method appropriate for steady flow when the magnetic energy density is considerably less than the kinetic energy density of the flow. The resulting field lines are three-dimensional curves, having been distorted by the flow around the magnetosphere. Two projections are presented, one on a plane containing the free-stream velocity vector and field vector and the other on a plane perpendicular to the free-stream velocity vector. Lines of constant flux density are shown on both projections.

Effect of neutral sheet currents on the shape and magnetic field of the magnetosphere tail

Abstract This paper describes a modification of the usual first order theory of the shape of the magnetosphere boundary that incorporates in a simple way the principal effects of the electrical currents in the neutral sheet of the extended geomagnetic tail. Numerical results presented for a variety of representative cases show that an additional flaring out of the magnetosphere tail ultimately of the order of a few Earth radii occurs over a distance of several tens of Earth radii, and that there is an associated decrease in the intensity of the magnetic field because of the need to approximately conserve the total magnetic flux in each half of the tail cross-section. Comparisons with data obtained in space with Explorer 18 and 33 satellites and Pioneer 6 and 7 spacecraft show that this modification of the theory leads to a substantial improvement in the agreement between the calculated and observed dimensions of the magnetosphere tail and the strength of the magnetic field contained therein.

Comparison of theoretical predictions of the flow and magnetic fields exterior to the magnetosphere with the observations of pioneer 6

Abstract Data from Pioneer 6, obtained along the portion of its trajectory from the magnetosphere boundary to beyond the Earths bow wave, are compared with theoretical results calculated using the continuum fluid model of the steady-state interaction of the solar wind and the geomagnetic field together with the observational values for the velocity, density, temperature, and the magnetic field in the incident solar wind. It is found that the agreement between the calculated and observed values is, in general, very satisfactory. This conclusion applies to the entire run of values for the velocity, density, and magnetic field intensity as well as to the locations of the virtually discontinuous changes in values at the magnetosphere boundary and the bow wave.

Theoretical proton velocity distributions in the flow around the magnetosphere

Abstract Relations from kinetic theory are combined with results from fluid calculations to determine a microscopic interpretation of the properties of the solar wind as it flows around the magnetosphere. Proton velocity distributions are presented as a function of the particle speed and direction for several points in space for representative values of the solar wind parameters. The results illustrate how the velocity distribution is highly collimated in the incident stream, is completely isotropic at the magnetosphere nose, and the degree to which it changes back to that of a highly collimated stream along the flanks of the magnetosphere. Except for a very small region in the vicinity of the magnetosphere nose, the number of particles that move in the upstream direction is insignificantly small compared with the number that move in the direction of the bulk velocity. The most probable speed of the protons, as viewed in a frame fixed in the Earth, is always in the direction of the local bulk velocity, and tends to be relatively constant throughout the flow in spite of substantial changes in temperature and bulk velocity. The paper concludes with a discussion of the relation of these results to the measurements that would be made by various types of instruments commonly used to observe plasma flows in space.

MAGNETIC AND ELECTRIC FIELDS IN THE MAGNETOSHEATH.

Abstract A method is given by which the steady-state magnetic field at any point in the magnetosheath can be calculated for a uniform interplanetary field of any arbitrary direction and magnitude by linear superposition of the field vectors shown on three graphs. Such superposition is made possible by use, for the magnetosheath flow field, of the steady-state, axisymmetric velocity function obtained from gasdynamic calculations. The resulting equations for the field, B, are thus linear and homogeneous in B . Two additional graphs are given from which the electric field E can be obtained by superposition. One further graph contains the information required to calculate the charge density. Algebraic formulas are given which simplify and systematize the use of the graphs.

Does Io's ionosphere influence Jupiter's radio bursts.

Goldreich and Lynden-Bells theory of Jupiters Io-correlated decametric radiation sets a lower limit to Ios conductivity, high enough to carry the current associated with the radiated power. Dermotts analysis of conductivities of rocks and ice shows no such conductivity at Ios temperature. However, we show that if Io has even a small atmosphere, say of methane as suggested by Binder and Cruikshank, or of argon or nitrogen, it will have an ionosphere with adequate conductivity to meet the above criterion. A requirement for higher conductivity was found by Goldreich and Lynden-Bell on the basis of motion of magnetic lines past Io. This requirement appears to us unnecessary in view of experiments which prove that motion of the lines is not the source of the electromotance.

A Fluid Model for the Interaction of the Solar Wind and the Geomagnetic Field

Data obtained in space, particularly that from IMP-1, have established that many of the gross features of the interaction of the solar wind and the geomagnetic field can be described by the continuum theory of fluid flow. The purpose of this paper is twofold: (a) to indicate briefly how one can arrive at results for the magnetosphere boundary, the bow wave, and the associated flow field from a purely fluid point of view without resort to a mixture of particle and fluid models as usually employed and (b) to present numerical results for the flow parameters in the shock layer between the bow wave and the magnetosphere boundary. The objective is not to get a complicated theory that encompasses all phenomena of importance, but rather the simplest body of analysis that appears able to describe the average bulk properties of the solar wind as it flows steadily through the bow wave and around the forward portion of the magnetosphere. A more complete account of this study is given by Spreiter etal. (1966).