A study of plasmaspheric density distributions for diffusive equilibrium conditions

We have modelled the plasmaspheric density distribution for a range of solar cycle, seasonal and diurnal conditions with a magnetic flux tube dependent diffusive equilibrium model by using experimentally determined values of ionospheric parameters at 675 km as boundary conditions.Data is presented in terms of plasmaspheric H⁺ and He⁺ density contours, total flux tube content and equatorial plasma density for a range of L-values from 1.15 to 3.0. The variation of equatorial density with L-value shows good agreement with the $\text{1}\text{L}{}^4$ dependence observed experimentally.The results show that the model predicts larger solar cycle and diurnal variation in equatorial plasma density than observed using whistler techniques. However, the whistler method requires a model to deduce the equatorial density and is therefore open to interpretation.Seasonal variations are rather artifical since in this general model we have not attempted to match equatorial densities for flux tubes emanating from the winter and summer hemispheres.     

Numerical studies of the transport of solar protons in interplanetary space

Numerical solutions of the Fokker-Planck equation governing the transport of solar protons are obtained using the Crank-Nicholson technique with the diffusion coefficient represented by K_r=K₀r^b where r is radial distance from the Sun and b can take on positive or negative values. As b ranges from +1 to ?3, the time to the observation of peak flux decreases by a factor of 5 for 1 MeV protons when $\text{V}\text{K}{}_0\text{=}\text{3 AU}{}^{\mathrm{b?1}}$ where V is the solar wind speed. The time to peak flux is found to be very insensitive to assumptions concerning the solar and outer scattering boundary conditions and the presence of exponential time decay in the flux does not depend on the existence of an outer boundary. At $\text{V}\text{K}{}_0\text{? 15 AU}{}^{\mathrm{b?1}}$, 1 MeV particles come from the Sun by an almost entirely convective process and suffer large adiabatic deceleration at b?0 but for b=+1, large Fermi acceleration is possible at all reasonable $\text{V}\text{K}{}_0$ values. Implications of this result for the calculation and measurement of particle diffusion coefficients is discussed. At $\text{b?0}$, the pure diffusion approximation to transport overestimates by a factor 2 or more the time to peak flux but as b becomes more negative, the additional effects of convection and energy loss become less important.     

On the generation of low-frequency waves in the solar wind in the front of the bow shock

The generation of low-frequency waves in the solar wind by the flux of protons accelerated in the magnetosheath is considered. It is shown that pulsations are produced in two partly overlapping frequency ranges. The growth rate of waves is maximal when the angle θ between the direction of the interplanetary magnetic field and the front of the bow shock is not equal $\text{π}\text{2}$. The dependence of the increment of perturbation on the solar wind velocity is analysed. A satisfactory agreement between theory and experimental results on the connection of Pc3–4 properties and parameters of the solar wind is obtained.     

Radiation forces on small particles in the solar system

We present a new and more accurate expression for the radiation pressure and Poynting-Robertson drag forces; it is more complete than previous ones, which considered only perfectly absorbing particles or artificial scattering laws. Using a simple heuristic derivation, the equation of motion for a particle of mass m and geometrical cross section A, moving with velocity v through a radiation field of energy flux density S, is found to be (to terms of order $\text{v}\text{c}$)

$\text{m}\text{v}\text{?}\text{= (}\text{SA}\text{c}\text{)Q}{}_{\mathrm{<mtext>pr</mtext>}}\text{[(1 ?}\text{r}\text{?}\text{c}\text{)}\text{S}\text{?}\text{?}\text{v}\text{c}\text{]}$

, where ? is a unit vector in the direction of the incident radiation, $\text{r}\text{?}$ is the particle's radial velocity, and c is the speed of light; the radiation pressure efficiency factor Q_pr ≡ Q_abs + Q_sca(1 ? 〈cos α〉), where Q_abs and Q_sca are the efficiency factors for absorption and scattering, and 〈cos α〉 accounts for the asymmetry of the scattered radiation. This result is confirmed by a new formal derivation applying special relativistic transformations for the incoming and outgoing energy and momentum as seen in the particle and solar frames of reference. Q_pr is evaluated from Mie theory for small spherical particles with measured optical properties, irradiated by the actual solar spectrum. Of the eight materials studied, only for iron, magnetite , and graphite grains does the radiation pressure force exceed gravity and then just for sizes around 0.1 μm; very small particles are not easily blown out of the solar system nor are they rapidly dragged into the Sun by the Poynting-Robertson effect. The solar wind counterpart of the Poynting-Robertson drag may be effective, however, for these particles. The orbital consequences of these radiation forces-including ejection from the solar system by relatively small radiation pressures-and of the Poynting-Robertson drag are considered both for heliocentric and planetocentric orbiting particles. We discuss the coupling between the dynamics of particles and their sizes (which diminish due to sputtering and sublimation). A qualitative derivation is given for the differential Doppler effect, which occurs because the light received by an orbiting particle is slightly red-shifted by the solar rotation velocity when coming from the eastern hemisphere of the Sun but blue-shifted when from the western hemisphere; the ratio of this force to the Poynting-Robertson force is $\text{(}\text{R}{}_{\mathrm{\odot }}\text{r}\text{)}{}^2\text{[(}\text{w}{}_{\mathrm{\odot }}\text{n}\text{) ? 1]}$, where R_⊙ and w_⊙ are the solar radius and spin rate, and n is the particle's mean motion. The Yarkovsky effect, caused by the asymmetry in the reradiated thermal emission of a rotating body, is also developed relying on new physical arguments. Throughout the paper, representative calculations use the physical and orbital properties of interplanetary dust, as known from various recent measurements.     

Observational Evidence for a Double-Helix Structure in CMEs and Magnetic Clouds

We compare recent observations of a solar eruptive prominence as seen in extreme-UV light on 30 March 2010 by the Solar Dynamics Observatory (SDO) with the multi-tube model for interplanetary magnetic clouds (Osherovich, Fainberg, Stone, Geophys. Res. Lett. 26, 2597, 1999). Our model is based on an exact analytical solution of the plasma equilibrium with magnetic force balanced by a gradient of scalar gas pressure. Topologically, this solution describes two magnetic helices with opposite magnetic polarity embedded in a cylindrical magnetic flux tube that creates magnetic flux inequality between the two helices by enhancing one helix and suppressing the other. The magnetic field in this model is continuous everywhere and has a finite magnetic energy per unit length of the tube. These configurations have been introduced as MHD bounded states (Osherovich, Soln. Dannye 5, 70, 1975). Apparently, the SDO observations depict two non-equal magnetically interacting helices described by this analytical model. We consider magnetic and thermodynamic signatures of multiple magnetic flux ropes inside the same magnetic cloud, using in situ observations. The ratio of magnetic energy density to bulk speed solar wind energy density has been defined as a solar wind quasi-invariant (QI). We analyze the structure of the QI profile to probe the topology of the internal structure of magnetic clouds. From the superposition of 12 magnetically isolated clouds observed by Ulysses, we have found that the corresponding QI is consistent with our double helix model.     

Relative flow of H+ and O+ ions in the topside ionosphere at mid-latitudes

Theoretical results on the daily variation of O⁺ and H⁺ field-aligned velocities in the topside ionosphere are presented. The results are for an L = 3 magnetic field tube under sunspot minimum conditions at equinox. They come from calculations of time-dependent O⁺ and H⁺ continuity and momentum balance in a magnetic field tube which extends from the lower F2 region to the equatorial plane (Murphy et al., 1976).There are occasions when ion counterstreaming occurs, with the O⁺ velocity upward and H⁺ velocity downward. The conditions causing this counterstreaming are described: the H⁺ layer is descending whilst O⁺ is supplied from below either to increase the O⁺ concentration at fixed heights or to replace O⁺ ions lost by charge exchange with neutral H. It is suggested that the results of observations at Arecibo by Vickrey et al. (1976) of O⁺ and H⁺ concentrations and counterstreaming velocities are significantly affected by $\text{E}\text{×}\text{B}$ drift.     

Electric fields in diffuse aurora

The ionospheric electric field has been measured in the E region above the Churchill auroral research range under quiet and under disturbed conditions. Results were obtained $\text{1}\text{1}\text{2}$ and $\text{2}\text{1}\text{2}$ hr before local midnight over an altitude range of 115–165 km. The instruments and analysis differ from those used by other workers. An unusually advantageous vehicle motion resulted in dipole measurements along the magnetic field being modulated by the vehicle motion. Under quiet conditions and in the presence of a diffuse, east-west 2 kR auroral arc, the predominant vector component of the electric field was also quiet and between 35 and 40 $\text{mV}\text{m}$ perpendicular to the magnetic field, southward. Parallel to the magnetic field, the vector component increased from ?17 mV/m at 130 km, reversed direction at 160 km during the latter third of the flight and fluctuated around + 6 mV/m between 155 and 135 km on the descent. Under disturbed conditions during the recovery phase of a large magnetic storm, the electric field was also more disturbed; however, there was no significant electric field along B. Analysis of effects caused when parts of the measurement system are connected by a common magnetic field line, and when one of the probes lies in the wake of the vehicle, shows that measurement perturbations produced by those effects are dominated by the magnetic field line connections and that wake effects are relatively unimportant.     

The influence of a flow field on the stability of the force-free magnetic field

In order to analyse the convective instability of the force-free magnetic field, an exact solution of the MHD equation for the magnetic field (1) together with the flow field (2) of constant speed V₀ making an angle θ with the magnetic field, was chosen as the unperturbed state. The stability of the fields between two parallel conducting walls of seperation d was studied by a linear perturbation method, which led to the eigenvalue problem (12), X being given by (13). It was shown by an approximate variational method that instability will set in by the flow field if V₀ is greater than 1/ $\text{3}$ times Alfven velocity V_A. For , the stability of the force-free field (1) is not influenced by the flow field, which may still be significant in other respects. Perturbations transverse to the magnetic field were found to be the most unstable modes.     

Rotational discontinuities in an anisotropic plasma—II

The theoretical work on rotational discontinuities in an anisotropic plasma is extended and the results are presented in a form more convenient for comparison with observations in the solar wind. Diagrams are presented to help observers identify rotational discontinuities using the values of ρ, B and β on either side. Under average solar wind conditions at 1 AU it is found that B and ρ change by at most a factor of ～1·7, and in a β ? 0·4 plasma ρ changes by at most a factor of 1·1 and B is virtually constant. The changes in physical parameters across a typical rotational discontinuity are illustrated, and the special cases of downstream isotropy and of $\text{p⊥}\text{Bρ}\text{=}\text{constant}$ are considered in detail.     

An analysis of the solar-activity effects in the upper atmosphere

A study of the upper-atmosphere variations induced by solar activity was made by using 29,574 densities derived from the drag of 10 satellites in the interval 1958–1971. In a comparison of the respective merits of the Ca II-plage index and the 10.7 cm solar flux to represent the erratic (‘27 day’) component of the variation, the latter is shown to give invariably better results. The ratio $\text{ΔT}\text{δF}$ of the temperature variations to the variations of the decimetric flux is shown to vary considerably with solar activity, but little with height or with local solar time. The time lag of the atmospheric variations behind those of the decimetric flux varies from a minimum of 0.9 day at noon to 1.6 days at midnight.     

Secular resonance,solar spin down,and the orbit of Mercury

A mechanism capable of accounting for the large mean eccentricity (0.175) and inclination (7°.2) of Mercury is discussed. Provided the gravitational field of the rapidly rotating primordial Sun had a sufficiently large second degree harmonic (i.e., J₂ ? order 10^?3), subsequent solar spin down would drive the orbit of Mercury through two secular resonances with Venus, one involving the precession of the line of apsides, the other one involving the regression of the nodal line. Resonance passage generates contributions to the eccentricity and inclination that are proportional to the square root of the characteristic solar spin down time. We find that an initial solar rotation l period of $\text{P ? 5}\text{1}\text{2}\text{hr}$ guarantees passage through resonance and that a spin down time of $\text{τ = Ω|dΩ/dt|}{}^{\mathrm{?1}}$ of order 10⁶ years could have produced the observed eccentricity and inclination. Such a primordial rotation rate is comparable to the measured rotations of very young stars and the spin down time appears consistent with the time scale derived for magnetic braking of the Sun's rotation by an intense solar wind during a T-Tauri stage of solar evolution.     

Properties of energetic electrons of magnetospheric origin in the magnetosheath and in the solar wind—correlation with geomagnetic activity

Bursts of energetic electrons (from >40keV up to 2MeV) as distinct from the magnetopause electron layer observed by Domingo et al. (1977) have been observed in the magnetosheath and in the solar wind by HEOS-2 at high-latitudes. Although these electrons are occasionally found close to the bow shock and simultaneously with low frequency (magnetosonic) upstream waves our observations strongly indicate that these electrons are of exterior cusp origin. Indeed, the flux intensity is highest in the exterior cusp region and decreases as the spacecraft moves away from it both tailward or upward. The energy spectrum becomes harder with increasing radial distance from the exterior cusp. The measured anisotropy indicates that the particles are propagating away from the exterior cusp. The magnetic field points to the exterior cusp region when these electrons are observed, being, for solar wind observations, centred at longitude 0° or 180° rather than along the spiral and in the magnetosheath, being usually different from the 90° or 270° orientation typical of that region. We exclude, therefore, that acceleration in the bow shock is the source of these particles because $\text{B}$ is not tangent to the shock when bursts are observed. We have also found a one to one correlation between geomagnetic storms' recovery phases and intense, continuous observations of >40 keV electrons in the magnetosheath, while, on the other hand, during geomagnetically quiet (Dst) periods bursts are observed only if AE is much larger than average.     

Coma expansion and photometry of comet Bowell (1980b)

Optical and infrared observations of comet Bowell are presented. The optical observations indicate that the solid grain coma is expanding at only 0.9 ± 0.2 m sec^?1. This is two orders of magnitude slower than the local gas sound speed and may suggest that gas drag is not responsible for stripping the grains from the nucleus. The hypothesis of “electrostatic snap-off” is tentatively advanced to account for the ejection of the grains. Alternatively, the grains may have an unusual size distribution. The extrapolated motion of the grains suggests that the bulk of the coma was formed when the comet was at a heliocentric distance $\text{R ? 10}\text{AU}$. Any water ice in the nucleus would be too cold to give rise to the observed grain coma by equilibrium sublimation at this R. Further evidence against the production of the grain coma by equilibrium sublimation of the nucleus is provided by broadband (J) photometric observations. Almost all of the observed photometric variations of comet Bowell can be ascribed to geometric effects. Simple models indicate that the total grain cross section has been nearly constant since the time of the earliest observations. The present observations, which suggest that water ice sublimation does not control either the optical morphology or the near infrared photometric behavior of comet Bowell, are contrasted with reported high OH production rates. It is concluded that the grain coma may be largely a relic of activity occurring on the nucleus at $\text{R ? 10}\text{AU}$ while the OH may indicate sublimation from the nucleus near perihelion and from coma grains near $\text{R ? 4.6}\text{AU}$.     

Structure of the satellitary accretion disk of Saturn

A detailed computation on the equilibrium structure of an accretion disk around Saturn from which the regular satellites presumably originated is reported. Such a disk is the predecessor of the self-dissipating disk that is formed when the mass infall stops (Cassen and Moosman, 1981, Icarus48, 353–376). When determining the disk structure local energy balance was assumed. Convention was taken into account by introducing local energy dissipation and, in an approximate manner, sonic convection. Changes in the disk structure were investigated by varying the free parameters, i.e., the external flux from both the protosun and the protoplanet, the abundance of dust and the strength of turbulence. It has been verified that the external energy flux does not play an important role in the evolution of the disk structure. Models characterized by either longer times (?3 10³ year) or a noticeable depletion of condensable elements (10^?2 times less than the solar value) have a total mass of the order of 0.34?0.1 times the mass of the regular satellites increased by the mass of the light elements. Low turbulence models (Reynolds critical number $\text{Re}{}^1\text{= 150}$) are characterized approximately by a total mass twice as large the mass of the regular satellites. All the studied models present a temperature distribution that allows the condensation of iron, silicate, and, in the outer regions, ice grains. All models but the one with 10^?2 of the solar value of condensable elements are characterized by a wide convective region that contains the formation zone of the regular satellites.     

Venus: Cloud optical depth and surface albedo from Venera 8

We have used the measurements of the solar flux obtained by the Venera 8 spacecraft inside the atmosphere of Venus and the values of the Venus spherical albedo to deduce the characteristics of the clouds and of the ground. The method used is the exponential kernel approximation and the results have been tested by exact computations with the spherical harmonics method.A cloud layer with an optical thickness $\text{τ}{}_1\text{? 144}$, an albedo for single scattering $\text{ω}{}_0\text{= 0.9998}$ in the rear infrared, above a Rayleigh layer between 0 and 32 km and a ground of reflectivity ? = 0.4, gives a good agreement with the experimental results. A model with two cloud layers is also discussed.     

The locating of hydromagnetic whistler sources and determination of their generating proton spectra

Results are given of the calculations of the group delay time propagating τ(ω, φ₀) of hydromagnetic whistlers, using outer ionospheric models closely resembling actual conditions. The τ(ω, φ₀) dependencies were compared with the experimental data of τ_exp(ω, φ₀) obtained from sonagrams. The sonagrams were recorded in the frequency range $\text{? ? (0.5?2.5) Hz}$ at observation points located at geomagnetic latitudes φ₀ = (53?66)° and in the vicinity of the geomagnetic poles. This investigation has led us to new and important conclusions.The wave packets (W.P.) forming hydromagnetic whistlers (H.W.) are mainly generated in the plasma regions at L = 3.5?4.0. This is not consistent with ideas already expressed in the literature that their generation region is $\text{L ? 3?10}$. The overwhelming majority of the τ_exp values differ considerably from the times at which wave packets would, in theory, propagate along the magnetic field lines corresponding to those of the geomagnetic latitudes φ₀ of the observation points. The second important fact is that the W.P. frequency ω is less than $\text{Ω}{}_{\mathrm{H}}$ everywhere along its propagation trajectory, including the apogee of the magnetic force line ($\text{Ω}{}_{\mathrm{H}}$ is the proton gyrofrequency). Proton flux spectra $\text{E ? (30?120)}$ keV, responsible for H.W. generation, were determined. Comparison of the Explorer-45 and OGO-3 measurements published in the literature, with our data, showed that the proton flux density energy responsible for the H.W. excitation $\text{N}{}_{\mathrm{p}}\text{(}\text{MV}{}_6{}^2\text{2}\text{) ? (5 × 10}{}^{\mathrm{?3}}\text{?10}{}^{\mathrm{?1}}\text{)}\text{H}{}_{\mathrm{a}}{}^2\text{8π}$ where H_a is the magnetic field force in the generation region of these W.P. The electron concentration is $\text{N}{}_{\mathrm{a}}\text{? (10}{}^2\text{?10}{}^3\text{) cm}{}^{\mathrm{?3}}$. The values given in the literature are $\text{N}{}_{\mathrm{a}}\text{? (10}{}^{\mathrm{?10}}\text{?10}{}^3\text{) cm}{}^{\mathrm{?3}}$. The e data considered also leads to the conclusion that the generating mechanism of the W.P. studied probably always co-exists with the mechanism of their amplification.     

Thinning of the near-earth (10∼15 RE) plasma sheet preceding the substorm expansion phase

The timing of the plasma-sheet thinning relative to the onset of the expansion phase of substorms is examined by the analysis of the OGO 5 electron (79 ± 23 keV) and proton (100～150 keV) data with the aid of simultaneous magnetic field observations. It is found that the timing of the thinning is significantly dependent on the distance. At $\text{x}{}^2\text{+ y}{}^2\text{? 15 R}{}_{\mathrm{E}}$ the thinning often starts before the onset, while at $\text{x}{}^2\text{+ y}{}^2\text{? 15 R}{}_{\mathrm{E}}$ it tends to occur after the onset, where x and y refer to solar magnetospheric coordinates. The thinning that precedes the expansion-phase onset has been found to reduce the thickness to ～1 R_E, and further thinning may occur in a spatially limited region. Hence it is conceivable that the formation of the neutral line characterizing the substorm expansion phase is the consequence of the thinning of the plasma sheet in the near-Earth region.