Alfven wave refraction by interplanetary inhomogeneities

Pioneer 6 magnetic data reveals that the propagation direction of Alfven waves in the interplanetary medium is strongly oriented along the ambient field. Magnetic fluctuations of frequencies up to 1/30 sec in the spacecraft frame are shown to satisfy a necessary condition for Alfven wave normal. It appears from this analysis that geometrical hydromagnetics may satisfactorily describe deviation of the wave normal from the background field. The rotational discontinuity is likely also to propagate along the field lines

Iron abundance and magnetic permeability of the moon

A larger set of simultaneous data from the Apollo 12 lunar surface magnetometer and the Explorer 35 Ames magnetometer are used to construct a whole-moon hysteresis curve, from which a new value of global lunar permeability is determined to be mu = 1.012 + or - 0.006. The corresponding global induced dipole moment is 2.1 x 10 to the 18th power gauss-cu cm for typical inducing fields of .0001 gauss in the lunar environment. From the permeability measurement, lunar free iron abundance is determined to be 2.5 + or - 2.0 wt. %. Total iron abundance (sum of iron in the ferromagnetic and paramagnetic states) is calculated for two assumed compositional models of the lunar interior: a free iron/orthopyroxene lunar composition and a free iron/olivine composition. The overall lunar total iron abundance is determined to be 9.0 + or - 4.7 wt. %. Other lunar models with a small iron core and with a shallow iron-rich layer are discussed in light of the measured global permeability

Magnetism and the interior of the moon

The application of lunar magnetic field measurements to the study of properties of the lunar crust and deep interior is reviewed. Following a brief description of lunar magnetometers and the lunar magnetic environment, measurements of lunar remanent fields and their interaction with the solar plasma are discussed. The magnetization induction mode is considered with reference to lunar magnetic permeability and iron abundance calculations. Finally, electrical conductivity and temperature calculations from analyses of poloidal induction, for data taken in both the solar wind and in the geomagnetic tail, are reviewed

Lunar electrical conductivity, permeability,and temperature from Apollo magnetometer experiments

Magnetometers were deployed at four Apollo sites on the moon to measure remanent and induced lunar magnetic fields. Measurements from this network of instruments were used to calculate the electrical conductivity, temperature, magnetic permeability, and iron abundance of the lunar interior. Global lunar fields due to eddy currents, induced in the lunar interior by magnetic transients, were analyzed to calculate and electrical conductivity profile for the moon, and those profiles were used to calculate the lunar temperature for an assumed lunar material of olivine. Simultaneous measurements by magnetometers on the lunar surface and in orbit around the moon were use to construct a whole-moon hysteresis curve, from which the global lunar magnetic permeability is determined. Total iron abundance (sum of iron in the ferromagnetic and paramagnetic states) was calculated for two assumed compositional models of the lunar interior. Other lunar models with an iron core and with a shallow iron-rich layer also discussed in light of the measured global lunar permeability. Simultaneous magnetic field and solar plasma pressure measurements show that the remanent fields at the Apollo 12 and 16 sites interact with, and are compressed by, the solar wind. Velocities and thicknesses of the earth's magnetopause and bow shock were also estimated from simultaneous magnetometer measurements

Temperature and electrical conductivity of the lunar interior from magnetic transient measurements in the geomagnetic tail

Magnetometers were deployed at four Apollo sites on the moon to measure remanent and induced lunar magnetic fields. Measurements from this network of instruments were used to calculate the electrical conductivity, temperature, magnetic permeability, and iron abundance of the lunar interior. Global lunar fields due to eddy currents, induced in the lunar interior by magnetic transients in the geomagnetic tail field, were analyzed to calculate an electrical conductivity profile for the moon: the conductivity increases rapidly with depth from 10 to the minus 9 power mhos/meter at the lunar surface to .0001 mhos/meter at 200 km depth, then less rapidly to .02 mhos/meter at 1000 km depth. A temperature profile is calculated from conductivity: temperature rises rapidly with depth to 1100 K at 200 km depth, then less rapidly to 1800 K at 1000 km depth. Velocities and thicknesses of the earth's magnetopause and bow shock are estimated from simultaneous magnetometer measurements. Average speeds are determined to be about 50 km/sec for the magnetopause and 70 km/sec for the bow shock, although there are large variations in the measurements for any particular boundary crossing

Iron abundance in the moon from magnetometer measurements

Apollo 12 and 15 lunar surface magnetometer data with simultaneous lunar orbiting Explorer 35 data are used to plot hysteresis curves for the whole moon. From these curves a whole-moon permeability mu = 1.029 + 0.024 or - 0.019 is calculated. This result implies that the moon is not composed entirely of paramagnetic material, but that ferromagnetic material such as free iron exists in sufficient amounts to dominate the bulk lunar susceptibility. From the magnetic data the ferromagnetic free iron abundance is calculated. Then for assumed compositional models of the moon the additional paramagnetic iron is determined, yielding total lunar iron content. The calculated abundances are as follows: ferromagnetic free iron = 5 + or - 4 wt. percent, and total iron in the moon = 9 + or - 4 wt. percent

Crustal evolution inferred from Apollo magnetic measurements

Magnetic field and solar wind plasma density measurements were analyzed to determine the scale size characteristics of remanent fields at the Apollo 12, 15, and 16 landing sites. Theoretical model calculations of the field-plasma interaction, involving diffusion of the remanent field into the solar plasma, were compared to the data. The information provided by all these experiments shows that remanent fields over most of the lunar surface are characterized by spatial variations as small as a few kilometers. Large regions (50 to 100 km) of the lunar crust were probably uniformly magnetized during early crustal evolution. Bombardment and subsequent gardening of the upper layers of these magnetized regions left randomly oriented, smaller scale (5 to 10 km) magnetic sources close to the surface. The larger scale size fields of magnitude approximately 0.1 gammas are measured by the orbiting subsatellite experiments and the small scale sized remanent fields of magnitude approximately 100 gammas are measured by the surface experiments

Lunar electrical conductivity, permeability and temperature from Apollo magnetometer experiments

Magnetometers were deployed at four Apollo sites on the moon to measure remanent and induced lunar magnetic fields. Measurements from this network of instruments were used to calculate the electrical conductivity, temperature, magnetic permeability, and iron abundance of the lunar interior. The measured lunar remanent fields range from 3 gammas minimum at the Apollo 15 site to 327 gammas maximum at the Apollo 16 site. Simultaneous magnetic field and solar plasma pressure measurements show that the remanent fields at the Apollo 12 and 16 sites interact with, and are compressed by, the solar wind. Remanent fields at Apollo 12 and Apollo 16 are increased 16 gammas and 32 gammas, respectively, by a solar plasma bulk pressure increase of 1.5 X 10 to the -7th power dynes/sq cm. Global lunar fields due to eddy currents, induced in the lunar interior by magnetic transients, were analyzed to calculate an electrical conductivity profile for the moon. From nightside magnetometer data in the solar wind it was found that deeper than 170 km into the moon the conductivity rises from .0003 mhos/m to .10 mhos/m at 100 km depth. Recent analysis of data obtained in the geomagnetic tail, in regions free of complicating plasma effects, yields results consistent with nightside values

Degeneracies in trapped two-component Fermi gases

We report on previously unobserved inter-system degeneracies in two-component equal-mass Fermi gases with interspecies zero-range interactions under isotropic harmonic confinement. Over the past 10 years, two-component Fermi gases consisting of $n_1$ spin-up and $n_2$ spin-down atoms with interspecies zero-range interactions have become a paradigm for modeling condensed matter systems, nuclear matter and neutron matter. We show that the eigen energies of the $(n_1+1,n_2-1)$ system are degenerate with the eigen energies of the $(n_1,n_2)$ system for any s-wave scattering length $a_s$, including infinitely large, positive and negative $a_s$. The existence of the inter-system degeneracies is demonstrated explicitly for few-body systems with $n_1+n_2=4, 5$ and 6. The degeneracies and associated symmetries are explained within a group theoretical framework.Comment: 5 pages with 4 figures + 5 pages of supplemental materia