Convex profiles from asteroid lightcurves

Integral geometry is used to solve a two-dimensional simplification of the three-dimensional lightcurve inversion problem, and a method is introduced for obtaining a convex profile, $\text{P}$, from asteroid lightcurve data. Whenever four ideal conditions are satisfied, $\text{P}$ is an estimator for the asteroid's “mean cross section,” $\text{C}$, a convex set defined as the average of all cross sections $\text{C}$ cut by planes a distance z above the asteroid's equatorial plane. $\text{C}$ is therefore a two-dimensional average of the asteroid's three-dimensional shape. The ideal conditions are that (A) each curve $\text{C}\text{(z)}$ is convex. (B) the asteroid's scattering law is uniform and geometric, (C) the astrocentric declinations of the Sun and Earth are zero, and (D) the solar phase angle θ ≠ 0. If Condition C is known to hold, the extend to which the lightcurve can be accounted for by a geometrically scattering convex object can be quantified in terms of an appropriate “goodness-of-fit” static. If the solar phase angle is zero, as for radar “lightcurve,” then (i) method yields a profile $\text{P}{}_{\mathrm{<mtext>s</mtext>}}$ the symmetrization $\text{C}{}_{\mathrm{<mtext>s</mtext>}}$ of $\text{C}$; (ii) Condition A need not hold and if it does not, then the inversion yields the symmetrization of the asteroid's mean convex hull; and (iii) Fourier analysis of the lightcurve can reveal violation of Condition B. Doppler-frequency resolution of radar echoes at several rotational phases adds information by constraining the convex hull $\text{H}{}_{\mathrm{<mtext>p</mtext>}}$ of the asteroid's (not necessarily convex) polar silhouette. Estimation of a convex profile from a photoelectric or radar lightcurve is a problem in weighted-least-squares optimization subject to inequality constraints. The solution uses a recursive quadratic programming algorithm to derive a Fourier parameterization for $\text{P}$ from the coefficients in the lightcurve's Fourier expansion. The method has been tested by inverting analytically generated lightcurves for geometrically scattering ellipsoids with semiaxes a ? b ? c, and the inversion yields $\text{P}\text{=}\text{P}{}_{\mathrm{<mtext>s</mtext>}}\text{?}\text{C}\text{=}\text{C}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{H}{}_{\mathrm{<mtext>p</mtext>}}$ when the viewing geometry (Condition C) is close to ideal. For situations when the asteroid's pole direction is unknown, a test is offered of the hyphothesis that a given lightcurve can be due to a geometrically scattering ellipsoid with $\text{a}\text{c}\text{? ?}$, where ? is an priori upper bound on the maximum axis ratio. Convex profiles are presented for 15 Eunomia, 118 Peitho, 246 Asporina, 281 Lucretia. 790 Pretoria, 1685 Toro, and 1978 CA.     

Total current to cylindrical collectors in collisionless plasma flow

A theory is presented for charged-particle collection by a cylindrical conducting object, such as a spacecraft or an electrostatic probe, which is moving transversely through a collisionless plasma, such as those in the upper atmosphere and space. The calculation is approximate, using symmetric potential profiles which are exact for the infinite-cylinder stationary case. Theoretical current predictions are presented for ratios of collector potential to electron thermal energy eφ_c/kT_e from 0 to ?25, for ion-to-electron temperature ratios T_i/T_c = 1 and 0.5, ratio of collector radius to electron Debye length r_c/λ_D from 0 to 100, and ratio of flow speed to ion thermal speed $\text{S}{}_{\mathrm{i}}\text{= U/(2kT}{}_{\mathrm{i}}\text{/m}{}_{\mathrm{i}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ from 0 to 10. Comparisons with existing exact calculations by other authors show that none of these fulfil all of the requirements for nontrivial comparison. Appropriate parameter ranges for future exact calculations are thereby suggested. These are as follows: (a) r_c/λ_D should be large enough that the collector not be in or near orbit-limited conditions; (b) the ratio $\text{S}{}_{\mathrm{i}}{}^2\text{/¦χ}{}_{\mathrm{c,\; i}}\text{¦}$ of ion directed energy to potential energy change in the sheath, should be close to unity or if

$\text{S}{}_{\mathrm{i}}{}^2\text{/¦χ}{}_{\mathrm{c,i}}\text{¦? 1,}\text{then}\text{S}{}_{\mathrm{i}}\text{? 1}$

.     

Comparison of Quasi-specular radar scatter from the moon with surface parameters obtained from images

Quasi-specular radar data used to determine apparent surface roughness σ_χ of geologic surfaces displays a variable wavelength λ dependence ranging between $\text{σ}{}_{\mathrm{\chi }}\text{～ λ}{}^0\text{and}\text{σ}{}_{\mathrm{\chi }}\text{～ λ}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$ for $\text{0.01 ? λ ? 1}\text{m}$. The strongest changes in σ_χ with wavelength are observed in lunar mare, while scatter from lunar highlands is nearly wavelength independent. Commonly used, gently undulating surface models for electromagnetic scatter predict no wavelength dependence. Wavelength dependence occurs whenever a significant fraction of the surface has local radii of curvature comparable to the observing wavelength. This condition can be determined by comparison of the value of the integrated surface curvature spectrum with the radar wavenumber, multiplied by a constant that depends on the geometry. Variations in curvature statistics calculated from photogrammetric reduction of lunar images are consistent with the observed variations in quasi-specular scatter between λ = 13 and 116 cm at the same locations. Variations in the strength of the wavelength dependence are correlated with the sizes of lunar craters that lie near the upper size limit for the local steady-state distribution. This correlation is also consistent with variations in the curvature spectrum calculated from crater size-frequency distributions.     

Mars: Subsurface properties from observed longitudinal variation of the 3.5-mm brightness temperature

Measurements at 3.5 mm of the disk-average brightness temperature of Mars during the 1978 opposition can be represented by

$\text{T}{}_{\mathrm{B}}\text{(Mars, 3 5 mm, Jan/Feb 1978)}\text{=}\textcolor{red}{}$

(The errors cited are from the internal scatter; the estimated absolute calibration uncertainty is 3%.) This longitudinal variation must be taken into account if Mars is to be used as a calibration source at millimeter wavelengths. The total range of the 3.5-mm variation is three to four times larger than both the 2.8-cm and 20-μm variations. This unexpected result can possibly be explained by subsurface scattering from rocks ?1.5-cm radius.     

On the molecular scattering in the terrestrial atmosphere : An empirical formula for its calculation in the homosphere

A recent determination by D. R. Bates of the Rayleigh scattering cross section (σ_RS) for air from 0.2 to 1 μm leads to a simple empirical formula (λ in μm) $\text{σ}{}_{\mathrm{RS}}\text{=}\text{4.02 × 10}{}^{\mathrm{?28}}\text{λ}{}^{\mathrm{4+x}}\text{cm}{}^2$ where $\text{x =}\text{0.389λ + 0.09426}\text{λ ? 0.3228}$ for the spectral region 0.2 μm < λ < 0.55 μm ; the accuracy is within ±0.5%. From the visible at 0.55 μm to the infrared (i.r.) at 1 μm, the same accuracy can be obtained using a constant value, x = 0.04. The formula accounts for the degree of depolarization which varies with the wavelength according to the latest determination by Bates.     

Interactions of plasmas with magnetic field boundaries

The magnetopause, the boundary layer, or current sheath, which separates the magnetosphere from the solar wind, is the particular interaction considered in this paper.The collision free electron skin depth, $\text{ξ}{}_{\mathrm{e}}\text{=}\text{c}\text{ω}{}_{\mathrm{pe}}$, where c is the velocity of light and ω_pe, is the plasma frequency, gives a classical measure of the penetration depth of a collisionless plasma by an electromagnetic field. This penetration depth is small compared with the dimensions of the magnetosphere and hence the boundary layer may be conveniently considered in one dimension.In General all one dimensional solutions lie within an order of magnitude of the value of ξ_e, the only exception being the important one, in which the electric field perpendicular to the current sheath plane is not present, either due to a particular trapped particle distribution or due to a short circuiting end effect. For this exception the thickness is increased by the factor ($\text{m}{}_{\mathrm{i}}\text{i/m}{}_{\mathrm{e}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.The current sheath solutions discussed are equilibrium solutions but not necessarily stable equilibrium solutions.The extension of the models to three dimensions has a larger effect than might at first be expected. The effect may be intuitively understood as a consequence of flux conservation in the sheath. The one dimensional solutions then correspond to the current sheath profiles at the thinnest point of the three dimensional sheath.     

Determination of magnetic field direction in a comet's head

The Stokes parameters of resonance radiation scattered by a Na atom with the angular momentum F aligned by directed unpolarized radiation in a magnetic field H ～ 10^?5?10^?1 Oe are presented. An influence of the orientation of the magnetic field on these parameters are studied; the intensity ratio $\text{I(D}{}_2\text{)}\text{I(D}{}_1\text{)}$ changes within ±5%, and the polarization degree P(D₂) within ±25%. Measurements of $\text{I(D}{}_2\text{)}\text{I(D}{}_1\text{)}$ and P(D₂), if the geometry of scattering is known, may give information on the direction of the magnetic field in the sodium atmospheres of comets, as well as Io's sodium cloud or man-made cosmic clouds.     

An estimator of the underlying size distribution of overlapping impact-craters

The stochastic model of lunar type impact-crater formation which assumes (a) random impacts, (b) circular craters, each obliterating any portions of earlier craters lying within, and (c) a probability P_i(t) that a newly formed crater (primary or secondary) has an area a_i is analyzed to develop a method of estimating P_i from the final overlapping pattern. It is found that if each crater is weighted by the fraction of the rim which is visible and which lies in an observation area A, then the expected value of the weighted sum $\text{Ω}{}_{\mathrm{i}}$ of craters of area a_i is simply proportional to P_i for any degree of coverage under several conditions, including (a) constant P_i for all i, and (b) P_i stepping from a constant early value to zero (for some i's) with otherwise arbitrary bombardment. Furthermore, in the general case, the expected value of the contribution $\text{ΔΩ}{}_{\mathrm{i}}\text{(t}{}_0\text{)}\text{to}\text{Ω}{}_{\mathrm{i}}$ produced during t₀ ± Δt/2 is found to be proportional to P_i(t₀). Thus measurement of $\text{Ω}{}_{\mathrm{i}}$ in the first two cases, or of $\text{ΔΩ}{}_{\mathrm{i}}$ if crater age data is available in the last case, provides an estimate of the desired P_i. Therefore the $\text{Ω}{}_{\mathrm{i}}$ introduce the correct weighting factors that just compensate for the effect of overlap.Expressions for the variances of $\text{Ω}{}_{\mathrm{i}}\text{and}\text{Ω = Σ}{}_{\mathrm{i}}\text{Ω}{}_{\mathrm{i}}$ are derived from which it is shown that under the above conditions, $\text{Ω}{}_{\mathrm{i}}\text{/Ω}\text{or}\text{ΔΩ}{}_{\mathrm{i}}\text{/ΔΩ}$ are consistent estimators of P_i. Formal evaluation of the variances is carried out in the special case of constant P_i and no secondary cratering. A criterion for the degree of coverage is given; in particular it is shown that the expectation of $\text{σ = Σ}{}_{\mathrm{i}}\text{a}{}_{\mathrm{i}}\text{Ω}{}_{\mathrm{i}}$ at saturation is just A.     

Analysis of HI content in galaxies

We have collected data on 241 galaxies from 13 sources and made a statistical analysis after reduction to a uniform system. We found that the Hubble sequence is one of increasing $\text{〈}\text{M}{}_{\mathrm{<mtext>H</mtext>}}\text{M}{}_{\mathrm{<mtext>T</mtext>}}\text{〉}$ and $\text{〈}\text{M}{}_{\mathrm{<mtext>H</mtext>}}\text{L}{}_{\mathrm{<mtext>B</mtext>}}\text{〉}$, these mean values increasing monotonically from .0016 and .024 at E to .084 and .83 at Im, but the dispersion is large.The HI content in barred spiral is greater than that in ordinary spirals, and this is consistent with their statistics of angular momentum and colour.The HI content is related to colour; it is greater in bluer systems. The large dispersion suggests that it also depends on some other factors, but these are smoothed out when averaged over each type, resulting in a linear relation between $\text{〈log(}\text{M}{}_{\mathrm{<mtext>M</mtext>}}\text{M}{}_{\mathrm{<mtext>T</mtext>}}\text{〉}$ and 〈(B ? V^O_T)〉. Unlike the colour-colour diagram, the large dispersion on the $\text{log}\text{(}\text{M}{}_{\mathrm{<mtext>H</mtext>}}\text{L}{}_{\mathrm{<mtext>B</mtext>}}\text{) ? (B ? V}{}^0{}_{\mathrm{<mtext>T</mtext>}}\text{)}$ is not related to peculiar galaxies.     

Small-scale turbulence in the atmosphere of Venus

Previous studies based on radio scintillation measurements of the atmosphere of Venus have identified two regions of small-scale temperature fluctuations located in the vicinity of 45 and 60 km. A global study of the fluctuations near 60 km, which are consistent with wind-shear-generated turbulence, was conducted using the Pioneer Venus measurements. The structure constants of refractive index fluctuations c_n² and temperature fluctuations c_T² increase poleward, peak near 70° latitude, and decrease over the pole; c_n² varies from 2 × 10^?15 to 1.5 × 10^?14m^{$\text{2}\text{3}$} and c_T² from 4 × 10^?3 to 7 × 10^?2°K²m^{$\text{?2}\text{3}$}. These results indicate greater turbulent activity at the higher latitudes. In the region near 45 km the refractive index fluctuations and the corresponding temperature fluctuations are substantially lower. Based on the analysis of one representative occultation measurement, $\text{c}{}_{\mathrm{<mtext>n</mtext>}}{}^2\text{= 2 × 10}{}^{\mathrm{?16}}\text{m}{}^{\mathrm{<mtext>?2</mtext><mtext>3</mtext>}}\text{and}\text{c}{}_{\mathrm{<mtext>T</mtext>}}{}^2\text{= 7.3 × 10}{}^{\mathrm{?4}}\text{°}\text{K}{}^2\text{m}{}^{\mathrm{<mtext>?2</mtext><mtext>3</mtext>}}$ in the 45-km region. The fluctuations in this region also appear to be consistent with wind-shear-generated turbulence. The turbulence level is considerably weaker than that at 60 km; the energy dissipation rate ε is 4.9 × 10^?5m²sec^?3 and the small-scale eddy diffusion coefficient K is 2 × 10³ cm² sec^?1.     

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.     

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.     

Deuteron whistler and trans-equatorial propagation of the ion cyclotron whistler

New ion cyclotron whistlers which have the asymptotic frequency of one half the local proton gyrofrequency, $\text{G}{}_{\mathrm{p}}\text{2}$, and the minimum (or equatorial) proton gyrofrequency, G_pm, along the geomagnetic field line passing through the satellite have been found in the low-latitude topside ionosphere from the spectrum analysis of ISIS VLF electric field data received at Kashima, Japan. Ion cyclotron whistlers with asymptotic frequency of G_pm or $\text{G}{}_{\mathrm{pm}}\text{2}$ are observed only in the region of $\text{B}{}_{\mathrm{m}}\text{>}\text{B}\text{2}$ or rarely $\text{B}{}_{\mathrm{m}}\text{>}\text{B}\text{4}$, where B is the local magnetic field and B_m is the mini magnetic field along the geomagnetic field line passing through the satellite.The particles with one half the proton gyrofrequency may be the deuteron or alpha particle. Theoretical spectrograms of the electron whistlers (R-mode) and the ion cyclotron whistlers (L-mode) propagating along the geomagnetic field lines are computed for the appropriate distributions of the electron density and the ionic composition, and compared with the observed spectrograms.The result shows that the ion cyclotron whistler with the asymptotic frequency of $\text{G}{}_{\mathrm{p}}\text{2}$ is the deuteron whistler, and that the ion cyclotron whistlers with the asymptotic frequency of G_pm or $\text{G}{}_{\mathrm{pm}}\text{2}$ are caused by the trans-equatorial propagation of the proton or deuteron whistler from the other hemisphere.     

Cyclotron side-band emissions from ring-current electrons

VLF-emissions with subharmonic cyclotron frequency from magnetospheric electrons have been detected by the S³-A satellite (Explorer 45) whose orbit is close to the magnetic equatorial plane where the wave-particle interaction is most efficient. These emissions are observed during the main phase of a geomagnetic storm in the nightside of the magnetosphere outside of the plasmasphere around L = 3–5. The emissions consist essentially of two frequency regimes, one below the equatorial electron gyro-frequency, , and the other above . The emissions below are whistler mode and there is a sharp band of “missing emissions” along . The emissions above are electrostatic mode and the frequency ranges up to . It is concluded that these emissions are generated by the enhanced relativity low energy (1–5 keV) ring current electrons, penetrating into the nightside magnetosphere during the main phase of a magneto storm. Although the high energy (50–350 keV) electrons showed remarkable changes of pitch angle distribution, their associations with VLF-emissions are not so significant as those of low energy electrons.     

Non-adiabatic processes in a two-fluid plasma and energization of the plasma sheet plasma

The change of energy of a collisionless, two-fluid plasma consists of the adiabatic gain or loss of energy, which is due to the work done by the electromagnetic forces, and of the non-adiabatic change associated with the presence of the “rest” field $\text{E}{}^1\text{=}\text{E}\text{+ (}\text{1}\text{c}\text{)}\text{V}\text{×}\text{B}$. The non-adiabatic gain or loss of energy per unit ti may be expressed by the relation

$\text{Q=}\text{E}{}_{\mathrm{\parallel }}\text{·}\text{i}{}_{\mathrm{\parallel }}\text{+}\text{c}\text{eNB}{}^2\text{B·}\text{f}\text{?}\text{×f}$

where i is the density of conductive current, N the ion number-density, and f (f?) the sum of inertia and pressure divergence of ions (electrons). Symbols of parallelism refer to the direction of B.A special case of non-adiabatic energization of a slowly convecting plasma sheet plasma is discussed in some detail. Regardless of the value of V, the non-adiabatic energization may significantly exceed any conceivable energization associated with the electric field $\text{?(}\text{1}\text{c}\text{)}\text{V}\text{×}\text{B}$.     

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.     

Love numbers of the giant planets

We calculate the Love numbers k_n for n = 2 to 10, and determine the “gravitational noise” from tides. The new values k₂ for Jupiter, Saturn, and Uranus yield new estimates for the planetary dissipation functions: $\text{Q}{}_{\mathrm{<mtext>J</mtext>}}\text{? 2.5 × 10}{}^4$, $\text{Q}{}_{\mathrm{<mtext>S</mtext>}}\text{? 1.4 × 10}{}^4\text{, Q}{}_{\mathrm{<mtext>U</mtext>}}\text{? 5 × 10}{}^3$.     

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.     

Electron runaway in turbulent astrophysical plasmas

An astrophysical electron acceleration process is described which involves turbulent plasma effects: the acceleration mechanism will operate in ‘collision free’ magnetoactive astrophysical plasmas when ion-acoustic turbulence is generated by an electric field which acts parallel to the ambient magnetic lines of force. The role of ‘anomalous’ (ion-sound) resistivity is crucial in maintaining the parallel electric field. It is shown that, in spite of the turbulence, a small fraction of the electron population can accelerate freely, i.e. runaway, in the high parallel electric potential. The number density n^(B) of the runaway electron component is of order $\text{n}{}^{\mathrm{(B)}}\text{?}\text{n}\text{2}\text{(}\text{c}{}_{\mathrm{s}}\text{U}{}_{\mathrm{\parallel }}{}^{\mathrm{?}}\text{)}{}^2$, where n = background electron number density, c_s = ion-sound speed and U_∥^? = relative drift velocity between the electron and ion populations. The runaway mechanism and the number density n^(B) do not depend critically on the details of the non-linear saturation of the ion-sound instability.     

Application of methane band-model parameters to the visible and near-infrared spectrum of Uranus

Laboratory band-model absorption coefficients of CH₄ are used to calculate the Uranus spectrum from 5400 to 10,400 Å. A good fit of both strong and weak bands for the Uranus spectrum over the entire wavelength interval is achieved for the first time. Three different atmospheric models are employed: a reflecting layer model, a homogeneous scattering layer model, and a clear atmosphere sandwiched between two scattering layers. The spectrum for the reflecting layer model exhibits serious discrepancies but shows that large amounts of CH₄ (5–10 km-am) are necessary to reproduce the Uranus spectrum. Both scattering models give reasonably good fits. The homogeneous model requires a particle scattering albedo $\text{(}\text{g}\text{?}\text{w}{}_{\mathrm{<mtext>p</mtext>}}\text{) ? 0.998}$ and an abundance per scattering mean free path $\text{(}\text{a}\text{?}\text{)}\text{of}\text{a}\text{?}\text{1}\text{km-am}$. The parameters derived from the sandwich layer model are: forsb the upper scattering layer a continuum single scattering albedo ($\text{g}\text{?}\text{w}{}_0$) of 0.995 and a scattering optical depth variable with wavelength consistent with Rayleigh scattering; for the clear layer they are a CH₄ abundance (a) of 2.2 km-am and an effective pressure (p) ? 0.1 atm; for the lower cloud deck a Lambert reflectivity (L) of 0.9 resulted. A severe depletion of CH₄ in the upper scattering layer is required. An enrichment of CH₄/H₂ over the solar ratio by a factor of 4–14 in the lower atmosphere is, however, indicated.