Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionF _o(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionr _arr_bwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atr _a andr _b . Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusr _o , Examples of Green's functions are given for the caser _a =0,r _b = and derived for the cases of finiter _a andr _b . The diffusion coefficient is assumed of the form = _o(p)r ^b . The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.     

Comparison between some Hα and X-ray flares

In the present paper, H-evolutive curves of chromospheric events are compared with flux evolutive curves of X-ray events observed at the same time in different spectral regions. A correspondence between the emissions E(I _H/I _chr)'s at higher and higher H-intensity levels, and the X-ray fluxes F()'s in harder and harder -ranges is shown. Further, the present observations seem to indicate the existence of a single triggering mechanism during the flash-phase of a flare. It is also shown that these results may be in agreement with Brown's model for chromospheric flares.     

Energetic properties of interplanetary plasma at the earth's orbit following the August 4, 1972 flare

Solar wind and interplanetary magnetic field data were obtained by the PROGNOZ 1 and PROGNOZ 2 satellites during the period following the August 4, 1972 (0621 UT) solar flare. A thermalized plasma was recorded one hour after the shock followed two hours later by the plasma piston with a bulk velocity higher than 1700 km s^-1. The comparison between the PROGNOZ and PIONEER 9 solar wind data shows an attenuation of the plasma properties with the deflection from the flare's meridian.     

The polarization of the inner solar corona at the eclipse of 10 July 1972

Photographs of the corona in the continuum spectrum (580–700 nm) have been obtained with a doublet camera (F=4m) through rotating sector polarizers with the vibrational directions oriented radially and tangentially to the solar limb. Isophotes of the total emission and its polarized component, as well as diagrams giving the degree of polarization for the (K+F)-corona and the electron corona proper (P _K), have been plotted up to the distance of 1R from the limb. In some inner regions the polarizationP _K exceeds the highest value possible for Thomson scattering under the given conditions. The reality of this anomally is dubious; systematic photometrical errors may account for it. Three-dimensional forms of 15 different coronal rays have been ascertained by comparing the course of polarization along the rays to the family of Baumach curves. The rays are found to deflect substantially from the radial directions out of the plane of the sky. Mean values of the coronal brightness and polarization versus the distance from the Sun have been determined. Contrary to well-known models (Van de Hulst) the mean polarization of the electron corona (P _K) decreases with distance after reaching the maximum (50%) at (1.4–1.6)R from the Sun's centre. This decrease can be explained by deflection of the streamers from radial directions.     

Spectral investigation of the chromosphere

Several hundred H spectrograms from areas close to the solar limb were taken with the 35 cm Coudé refractor at Anacapri. The 41 spectra with the greatest spatial resolution were selected and analysed. At the supergranular boundaries a considerable fraction of the line profiles were found to correspond to Beckers Cloud Model (BCM). Moreover, the BCM parameters of the dark mottles at the limb appear to be approximately equal to those from the center of the disk. On the other hand, we also obtained evidence in disagreement with the general applicability of the BCM to all features of the chromospheric fine structure.We attempted to present the large set of observational data in a fashion that permits their interpretation by alternative theoretical models.Mitteilungen aus dem Fraunhofer Institut Nr. 151.     

The equations of motion of an artificial satellite in nonsingular variables

The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power ofr/r, r being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the Moon or Sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations.     

Magnetic properties of x-ray bright points

Using high resolution KPNO magnetograms and sequences of simultaneous S-054 soft X-ray solar images we have compared the properties of X-ray bright points (XBP) and ephemeral active regions (ER). All XBP appear on the magnetograms as bipolar features, except for very newly emerged or old and decayed XBP. We find that the separation of the magnetic bipoles increases with the age of the XBP, with an average emergence growth rate of 2.2 ± 0.4 km s^–1. The total magnetic flux in a typical XBP living about 8 hr is found to be 2 x 10¹⁹ Mx. A proportionality is found between XBP lifetime and total magnetic flux, equivalent to 10²⁰ Mx per day of lifetime.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

The absorption of energetic electrons by argon gas

The processes by which energetic electrons lose energy in a weakly ionized gas of argon are analysed and calculations are carried out taking into account the discrete nature of the excitation processes. The excitation, ionization and heating efficiences are computed for energies up to 200 eV absorbed in a gas with fractional ionizations varying up to 10^?2.     

Thermal response properties of the Earth's ionospheric plasma

The thermal response of the Earth's ionospheric plasma is calculated for various suddenly applied electron and ion heat sources. The time-dependent coupled electron and ion energy equations are solved by a semi-automatic computational scheme that employs Newton's method for coupled vector systems of non-linear parabolic (second order) partial differential equations in one spatial dimension. First, the electron and composite ion energy equations along a geomagnetic field line are solved with respect to a variety of ionospheric heat sources that include: thermal conduction in the daytime ionosphere; heating by electric fields acting perpendicular to the geomagnetic field line; and heating within a stable auroral red are (SAR-arc). The energy equations are then extended to resolve differential temperature profiles, first for two separate ion species (H⁺, O⁺) and then for four separate ion species (H⁺, He⁺, N⁺, O⁺) in addition to the electron temperature. The electron and individual ion temperatures are calculated for conditions within a night-time SAR-arc excited by heat flowing from the magnetosphere into the ionosphere, and also for typical midlatitude daytime ionospheric conditions. It is shown that in the lower ionosphere all ion species have the same temperature; however, in the topside ionosphere above about 400 km, ion species can display differential temperatures depending upon the balance between thermal conduction, heating by collision with electrons, cooling by collisions with the neutrals, and energy transfer by inter-ion collisions. Both the time evolution and steady-state distribution of such ion temperature differentials are discussed.The results show that below 300km both the electrons and ions respond rapidly (<30s) to variations in direct thermal forcing. Above 600 km the electrons and ions display quite different times to reach steady state, depending on the electron density: when the electron density is low the electrons reach steady state temperatures in 30 s, but typically require 700 s when the density is high; the ions, on the other hand, reach steady state in 700 s when the density is high, and 1500–2500 s when the density is low. Between 300 and 600 km, a variety of thermal structures can exist, depending upon the electron density and the type of thermal forcing; however steady state is generally reached in 200–1000 s.     

The ion-composition of the plasma produced by impacts of fast dust particles

The composition of the impact plasma produced by fast dust particles (v > 1 km/sec) hitting an Au or W target was measured both with a model of the HELIOS micrometeoroid experiment (low electric field at the target) and a high field detector. The plasma composition and the total plasma charge depend strongly on the impact velocity and the electric field strength at the target. Spectra of 9 different projectile-target combinations were analysed. Two types of spectra could be observed, depending on the projectile material. (1) Spectra of metals and hard dielectrics (Mohs' hardness ? 5). Particle constituents of low ionisation energy (e · u ? 7eV, e.g. Na, K, Al) dominate the spectra of these materials at impact velocities below 10 km/sec. At higher speed the relative intensities change and new ions with higher ionisation energies appear. (2) Spectra of soft dielectrics (Mohs' hardness < 3). Below 9 km/sec these materials produced less total charge than did the others. The highest masses were detected at 74 amu. The relative abundance of ions with low ionization energies such as Li, Na, K, etc. is comparatively small. Negative ions were also observed in the impact plasma. Their total number was found to be approximately 3–6% of that of the positive ions at 6 km/sec particle speed.