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.     

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.     

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.     

A simulation study of the formation of a bipolar magnetic structure

Some recent solar observations show that a bipolar magnetic flux in an active region tends to disappear in situ, in less than one solar rotation, without evidence of spreading. This feature is difficult to explain if it is assumed that magnetic buoyancy is the dominant force in controlling dynamics of a magnetic flux tube, since the assumption implies no other force to submerge the tube. These observations may be explained by assuming that a convective motion is the major cause for the formation of a $\text{Ω}$-shaped geometry of the magnetic flux tube, but that the flux tube thus arisen is submerged by the counteracting Lorentz force as the convective motion decays. A two-dimensional MHD simulation method is used to demonstrate this possibility.     

Plasma temperatures from alouette 1 electron density profiles

Values of plasma temperature and vertical temperature gradient were obtained by fitting theoretical models to 60,000 observed electron density profiles, at heights of 400–1000 km. Results show the diurnal and seasonal changes in temperature from 75°S to 85°N near solar minimum. At night the temperature and temperature gradient are both low inside the plasmapause and high outside. Day-time temperatures increase almost linearly with latitude, from 1500 K at the magnetic equator to a maximum of 3500 K at the plasmapause. There is also a sharp peak at 77° latitude, beneath the magnetospheric cleft. Mean vertical temperature gradients are $\text{ca. 0.5}\text{K}\text{km}$ at night, and 1–4 K/km during the day. The downwards flow of heat, during the day, increases from about zero at 10° latitude to a maximum of $\text{4 × 10}{}^9\text{eV}\text{cm}{}^2\text{sec}$ at the plasmapause. Night-time flows are 5–20 times less, inside the plasmasphere. Increases in magnetic activity cause a temperature increase at 400 km, of about 70 K per unit increase in K_p at all latitudes greater than 65°. The temperature peaks at the plasmapause and the magnetospheric cleft show little increase with magnetic activity, but move equatorwards by ca. 2° in latitude per unit K_p.     

Changes in the ionospheric profile and the faraday factor M with Kp

Using incoherent scatter data from Millstone Hill, we investigated the variations in the shape of the daytime, mid-latitude ionospheric electron density profile associated with changes in geomagnetic activity. The analysis performed was to deduce the dependence upon the 3-hr geomagnetic index Kp of h(N_m), h(0·7 N_m) above and below N_m, the plasma scale height H_T in the range 500–1000 km, and the ratio $\text{N(1000)}\text{N(h}{}_{\mathrm{m}}\text{)}$. The electron density data used spanned the solar maximum years 1968–1971. Daytime data from the period 1000 to 1600 LT were averaged separately for summer, winter and spring-fall. It is shown that the mean value $\text{M}$ of the factor M = B cos θ sec χ used by Titheridge (1972) to relate the Faraday rotation $\text{Ω}$ from a geostationary satellite to the total electron content N_N up to 2000 km is practically the same (to within 1–2 per cent) as the $\text{M}$ value used to relate the N_T and $\text{Ω}$ values both computed up to 1000 km. Taking advantage of this identity, we have used the linear relationship obtained between the ionospheric parameters and Kp to deduce the height at which $\text{M}$ should be evaluated as a function of Kp.     

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.     

On the DC ratio in the atmosphere of Uranus

A method for deriving mixing ratios in the outer planets, mostly independent of scattering processes, is applied to Uranus. It is shown that scattering processes play a major role in the line formation in the atmospheres of Uranus and Neptune; consequently, abundance ratios derived from a reflecting-layer model can be questionable. Using our method, we derive for Uranus $\text{D}\text{C}\text{< 6 × 10}{}^{\mathrm{?3}}$, which is significantly smaller than our result on Jupiter. The simplest explanation implies a C/H enrichment by at least a factor of 6 relative to the solar value.     

Long term modulation of cosmic rays and inferable electromagnetic state in solar modulating region

It is demonstrated that the long term variation in cosmic ray intensity I(t) can be described by an integral equation,

$\text{I(t)=I}{}_{\mathrm{\infty }}\text{?}\text{∫}\text{0}\text{∞}\text{f(τ)S(t?τ)}\text{d}\text{τ}$

, which is derived from a generalization of Simpson's coasting solar wind model. A source function S(t?τ) is given by some appropriate solar activity index at a time t?τ(τ ? 0) and the characteristic functionf(τ)(?0 forτ ? 0) expresses the time dependence of the efficiency of the intensity depression due to solar disturbances represented by S(t ?τ) when the disturbances generated at the solar surface propagate through the modulating region with the solar wind. It is demonstrated further that the equation can be derived from the general diffusion-convection theory on some assumptions, and as a result, the source and characteristic functions can be related to diffusion coefficient and its transition in space. Assuming the sunspot number R (or two activity indices including R) as the source function, the characteristic function f(τ) [or f(τ)'s] is obtained with data of the cosmic ray intensity extended over several decades. Based on the theory, one can obtain from f(τ) the following physical quantities in space, such as the transition and life time of solar disturbances, the boundary of the modulating region, and the radial and time dependences of the diffusion coefficient, radial density gradient and modulated intensity of cosmic rays. Results deduced from the present analysis are consistent with those obtained directly or indirectly by space observations.     

Directional diffusion coefficients of solar protons inside and outside the bow shock

The directional diffusion coefficients of low-energy (? 0.3 MeV) solar protons inside and outside the bow shock are examined during the solar flare event of 24 January 1969. The data are derived from simultaneous observations obtained by Explorer 33 inside the magnetosheath and by Explorer 35 in the interplanetary medium. Although the gross properties of the spin-averaged intensities on a diffusion-type plot appear to be the same in both media, the directional intensities show significant variations. It is shown that directional intensities of low-energy protons can be described reasonably well by anisotropic diffusion with an associated diffusion coefficient. Directional diffusion coefficients are found to differ by a factor as much as three among different directions in space, and from the spin-averaged diffusion coefficient. This suggests that anisotropic diffusion does indeed take place and that so called ‘isotropic’ diffusion coefficients derived in the past from spin-averaged intensities may actually be directional diffusion coefficients in cases where substantial anisotropies (> 50 per cent) exist. The typical postulated ratio of field aligned to cross-field diffusion coefficients is $\text{κ⊥}\text{κ∥}\text{< 0.1}$. The present data would indicate a ratio of ?0.3. This value of the anisotropy is to be taken only as an upper limit of the ratio because of the limitations introduced by the wide field of view of the detectors (~90°) and the lack of directional measurements over the entire sphere. Comparison between directional diffusion coefficients in the interplanetary medium and magnetosheath derived from identical directions in space implies changes in the parameters of the interplanetary magnetic field as it interacts with the bow shock.     

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.     

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 calculated and observed diurnal variation of the ionosphere over Millstone Hill on 23–24 March 1970

A numerical model of current F-region theory is use to calculate the diurnal variation of the mid-latitude ionospheric F-region over Millstone Hill on 23–24 March 1970, during quiet geomagnetic conditions. From the solar EUV flux, the model calculates at each altitude and time step primary photoelectron spectra and ionization rates of various ion species. The photoelectron transport equation is solved for the secondary ionization rates, photoelectron spectra, and various airglow excitation rates. Five ion continuity equations that include the effects of transport by diffusion, magnetospheric-ionospheric plasma transport, electric fields, and neutral winds are solved for the ion composition and electron density. The electron and ion temperatures are also calculated using the heating rates determined from chemical reactions, photoelectron collisions, and magnetospheric-ionospheric energy transport. The calculations are performed for a diurnal cycle considering a stationary field tube co-rotating with the Earth; only the vertical plasma drift caused by electric fields perpendicular to the geomagnetic field line is allowed but not the horizontal drift. The boundary conditions used in the model are determined from the incoherent scatter radar measurements of T_e, T_i and O⁺ flux at 800km over Millstone Hill (Evans, 1971a). The component of the neutral thermospheric winds along the geomagnetic field has an important influence on the overall ionospheric structure. It is determined from a separate dynamic model of the neutral thermosphere, using incoherent scatter radar measurements.The calculated diurnal variation of the ionospheric structure agrees well with the values measured by the incoherent scatter radar when certain restrictions are placed on the solar EUV flux and model neutral atmospheric compositions. Namely, the solar EUV fluxes of Hinteregger (1970) are doubled and an atomic oxygen concentration of at least $\text{10}{}^{11}\text{cm}{}^3$ at 120 km is required for the neutral model atmosphere. Calculations also show that the topside thermal structure of the ionosphere is primarily maintained by a flow of heat from the magnetosphere and the night-time F2-region is maintained in part by neutral winds, diffusion, electric fields, and plasma flow from the magnetosphere. The problem of maintaining the calculated night-time ionosphere at the observed values is also discussed.     

A dynamical effect in the ionospheric f1 layer

Incoherent scatter observations of the ionospheric F₁ layer above Saint-Santin (44.6°N) are analyzed after correction of a systematic error at 165 and 180 km altitude. The daytime valley observed around 200 km during summer for low solar activity conditions is explained in terms of a downward ionization drift which reaches ?30 m s^?1 around 180 km. Experimental determinations of the ion drift confirm the theoretical characteristics required for the summer daytime valley as well as for the winter behaviour without a valley. The computations require an effective dissociative recombination rate of $\text{2.3 × 10}{}^{\mathrm{?7}}\text{(}\text{300/}\text{T}{}_{\mathrm{e}}\text{)}{}^{0.7}\text{(}\text{cm}{}^3\text{s}{}^{\mathrm{?1}}\text{)}$ and ionizing fluxes compatible with solar activity conditions at the time when the valley is observed.     

Deuterium in the early solar system

An attempt is made to construct a self-consistent picture of the deuterium abundance in the early Solar System based on the assumption of chemical equilibrium in the solar nebula. A recent determination of the $\text{D}\text{H}$ ratio for the atmosphere of Jupiter is consistent with a previous estimate of the $\text{D}\text{H}$ ratio for the proto-Sun. The high (> 1.5 × 10^?4) $\text{D}\text{H}$ ratios determined from analyses of carbonaceous meteorites imply an equilibrium temperature < 270°K, in marked disagreement with the equilibrium temperature determined for the same material by oxygen isotope cosmothermometry.     

Spatial structure of solar wind at a time of minimum solar activity

Interplanetary scintillation measurements of the solar wind speed in 1976 show the expected trend that higher speeds are found at higher heliographic latitudes or larger angular distances from the interplanetary current sheet deduced from coronal observations. A careful examination of variations in the speed where the current sheet departs from the equator reveals that the wind speed is not symmetrically distributed about the equator, and the minimum speed occurs at the current sheet. The variation of the speed u with the angular distance from the current sheet, λ, during 1976 is

$\text{u(λ) = 800}\text{sin}{}^{\mathrm{?2\lambda }}\text{+ 350}\text{km/s}\text{,|λ| ?35° = 600}\text{km/s}\text{, |λ| > 35°}$

.     

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 $\text{R ? 4.6}\text{AU}$.     

An interpretation of Akasofu's substorm parameter

It is proposed that Akasofu's substorm parameter $\text{P = l}{}^2\text{VB}{}^2\text{sin}{}^4\text{(}\text{θ}\text{2}\text{)}$ be interpreted as the electromagnetic power flux which enters the magnetosphere from the solar wind.     

Quantitative dependence of the polar cap electric field on the IMF Bz-component and solar wind velocity

Ten years data set is used to separate the influence of IMF B_z-component and solar wind speed on the dawn-dusk component of magnetic variations in the summer polar cap. The reference level was chosen from most quiet periods of winter solstices (small polar cap and auroral zone conductivity) to exclude the inner source component. The linear regression analysis was then used to calculate the PC variation response to B_z under different ranges of solar wind speed. As a result, taking into account the value of polar cap conductivity and effects of induced currents, the response of dawn-dusk electric field component to B_z and V was obtained and the potential difference across the polar cap was estimated to be $\text{Δ?(}\text{kV}\text{) ≈ 6(}\text{V}\text{300}\text{)}{}^2\text{? 9B}{}_{\mathrm{z}}\text{(γ)}$ for B_z ? + 1γ. The results give a proof for simultaneous operation in the magnetosphere of two electric field generation mechanisms, related to the boundary layer processes and magnetic field reconnection. The above-mentioned functional form was shown to correlate effectively with AE index (R = 0.73).