A relation in families of periodic solutions

We show the existence of a general relation between the parameters of periodic solutions in dynamical systems with ignorable coordinates. In particular, for time-independent systems with an axis of symmetry, the relation takes the form T/A=–/E, whereT is the period,A is the angular momentum, is the angle through which the system has rotated after one period, andE is the energy.     

Tridiurnal variations in cosmic-ray intensity

The tridiurnal wave in cosmic-ray intensity expected from a free space anisotropy is theoretically calculated for different cosmic-ray stations which are characterized by different shapes of asymptotic cones of acceptance. The amplitude A and the time of maximum Tmax are given for latitude dependence of the form cosⁿ λ and rigidity dependence of the form $\text{R}{}^{\mathrm{\beta }}\text{exp (?(R?}\text{1}\text{R}{}_0\text{))}$, where λ and R are the latitude and rigidity respectively and n, β, R₀ are constants. The values of A and Tmax, are calculated for different values of n, β and R₀ for each station. The dependence of A and Tmax on the anisotropy parameters is studied for the proper selection of cosmic-ray stations whose data may be used in determining these parameters.Available experimental data were used to find the observed amplitudes of the tridiurnal variations at five stations using power spectrum analysis with hanning applied on the averaged trains. Minimum variance analysis of the theoretical and experimental amplitudes showed that β has a value between 1 and 2, R₀ greater than 100 GV and n smaller than 3.     

VLF emissions and substorm activity

The resonant interaction between the whistler mode waves and the energetic electrons near the plasmapause boundary has been studied in the presence of field aligned currents which seem to exist during substorm activity. It is shown that the electrons which carry the current along the direction of the magnetic field enhance the whistler mode growth considerably if the streaming velocity is small compared to the phase velocity of the wave. It is likely that this is one of the mechanisms explaining the intense VLF emissions observed near the plasmapause during substorm activity.     

Shear-induced instability and arch filament eruption: A magnetohydrodynamic (MHD) numerical simulation

We investigate, via a two-dimensional (nonplanar) MHD simulation, a situation wherein a bipolar magnetic field embedded in a stratified solar atmosphere (i.e., arch-filament-like structure) undergoes symmetrical shear motion at the footpoints. It was found that the vertical plasma flow velocities grow exponentially leading to a new type of global MHD-instability that could be characterized as a Dynamic Shearing Instability, with a growth rate of about 8{ovV} _A a, where {ovV} _A is the average Alfvén speed and a ^–1 is the characteristic length scale. The growth rate grows almost linearly until it reaches the same order of magnitude as the Alfvén speed. Then a nonlinear MHD instability occurs beyond this point. This simulation indicates the following physical consequences: the central loops are pinched by opposing Lorentz forces, and the outer closed loops stretch upward with the vertically-rising mass flow. This instability may apply to arch filament eruptions (AFE) and coronal mass ejections (CMEs).To illustrate the nonlinear dynamical shearing instability, a numerical example is given for three different values of the plasma beta that span several orders of magnitude. The numerical results were analyzed using a linearized asymptotic approach in which an analytical approximate solution for velocity growth is presented. Finally, this theoretical model is applied to describe the arch filament eruption as well as CMEs.     

Deep drilling at the Siljan Ring impact structure: oxygen-isotope geochemistry of granite

The Siljan Ring is a 362-Ma-old impact structure formed in 1700-Ma-old I-type granites. A 6.8-km-deep borehole provides a vertical profile through granites and isolated horizontal diabase sills. Fluid-inclusion thermometry, and oxygen-isotope compositions of vein quartz, granite, diabase, impact melt, and pseudotachylite, reveal a complex history of fluid activity in the Siljan Ring, much of which can be related to the meteorite impact. In granites from the deep borehole, ¹⁸O values of matrix quartz increase with depth from near 8.0 at the surface to 9.5 at 5760 m depth. In contrast, feldspar ¹⁸O values decrease with depth from near 10 at the surface to 7.1 at 5760 m, forming a pattern opposite to the one defined by quartz isotopic compositions. Values of ¹⁸O for surface granites outside the impact structure are distinct from those in near-surface samples from the deep borehole. In the deep borehole, feldspar coloration varies from brick-red at the surface to white at 5760 m, and the abundances of crack-healing calcite and other secondary minerals decrease over the same interval. Superimposed on the overall decrease in alteration intensity with depth are localized fracture zones at 4662, 5415, and 6044 m depth that contain altered granites, and which provided pathways for deep penetration of surface water. The antithetic variation of quartz and feldspar ¹⁸O values, which can be correlated with mineralogical evidence of alteration, provides evidence for interaction between rocks and impact-heated fluids (100–300° C) in the upper 2 km of the pluton. Penetration of water to depths below 2 km was restricted by a general decrease in impact-fracturing with depth, and by a 60-m-thick diabase sill at 1500 m depth that may have been an aquitard. At depths below 4 km in the pluton, where water/rock ratios were low, oxygen isotopic compositions preserve evidence for limited high-temperature (>500° C) exchange between alkali feldspar and fluids. The high-temperature exchange may have been a post-impact event involving impact-heated fluids, or a post-magmatic event.     

Spectrum of cosmic fireballs

A progress report on cosmic fireballs is presented. The main new results are: (a) the phenomenon should be almost universal, and most explosive -ray sources should show the characteristic fireball spectrum; (b) even if the radiation density is insufficient, pair production in electron-proton or electron-electron scattering might start the fireball; (c) some computed fireball spectra are shown. They all have in common a 1/E low-energy behaviour, a 100 keV flattening, and a 0.5 MeV cut-off.Paper presented at the Symposium on Cosmic Gamma-Ray Bursts, held at Toulouse, France, 26–29 November, 1979.     

Radius of convergence of Lie series for some elliptic elements

For equatorial orbits about an oblate body, we show that the Lie series for the elliptic elementse,f,l and diverge when the oblateness exceeds a critical multiple of the transformed eccentricity constant. The use of similar truncated series expansions for such elliptic elements by Brouwer accounts for the first-order errors at low eccentricity in his derived coordinates for an artificial satellite.     

A survey of coronal holes and their solar wind associations throughout sunspot cycle 20

To gain insight into the relationships between solar activity, the occurrence and variability of coronal holes, and the association of such holes with solar wind features such as high-velocity streams, a study of the period 1963–1974 was made. This period corresponds approximately with sunspot cycle 20. The primary data used for this work consisted of X-ray and XUV solar images obtained from rockets. The investigation revealed that:

1. The polar coronal holes prominent at solar minimum, decreased in area as solar activity increased and were small or absent at maximum phase. This evolution exhibited the same phase difference between the two hemispheres that was observed in other indicators of activity.
2. During maximum, coronal holes occurred poleward of the sunspot belts and in the equatorial region between them. The observed equatorial holes were small and persisted for one or two solar rotations only; some high latitude holes had lifetimes exceeding two solar rotations.
3. During 1963–74 whenever XUV or X-ray images were available, nearly all recurrent solar wind streams of speed ?500 km s^?1 were found associated with coronal holes at less than 40° latitude; however some coronal holes appeared to have no associated wind streams at the Earth.

     

The strength of the Sun's polar fields

The magnetic field strength within the polar caps of the Sun is an important parameter for both the solar activity cycle and for our understanding of the interplanetary magnetic field. Measurements of the line-of-sight component of the magnetic field generally yield 0.1 to 0.2 mT near times of sunspot minimum. In this paper we report measurements of the polar fields made at the Stanford Solar Observatory using the Fe i line 525.02 nm. We find that the average flux density poleward of 55° latitude is about 0.6 mT peaking to more than 1 mT at the pole and decreasing to 0.2 mT at the polar cap boundary. The total open flux through either polar cap thus becomes about 3 × 10¹⁴ Wb. We also show that observed magnetic field strengths vary as the line-of-sight component of nearly radial fields.