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

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

.     

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.     

Characteristics of localized resonance coupling oscillations of the slow magnetosonic wave in a non-uniform plasma

We analyze linear resonance oscillations in a non-uniform one-fluid finite-β plasma, which is oversimplified to understand easily fundamental characteristics of the resonance oscillations. A linear resonance oscillation of localized slow magnetosonic mode $\text{[ω}{}^2{}_{\mathrm{s}}\text{=}\text{ω}{}^2{}_{\mathrm{A}}\text{(1 +}\text{V}{}^2{}_{\mathrm{A}}\text{V}{}^2{}_{\mathrm{s}}\text{)}\text{]}$, which has the diamagnetic property in a uniform plasma, is newly found to be excited in the radially non-uniform plasma. The localized slow resonance indicates a radially polarized compressional oscillation (δB_∥ ? δB_H ? δB_D). The sense of the Alfvénic polarizations in the H-D plane near the resonant point is a function of both the propagation in the azimuthal direction and the slope of wave amplitude in the radial direction, whereas the sense of the resonant slow magnetosonic polarizations changes in accordance only with the switch in the azimuthal propagation direction. Further multi-satellite studies are necessary to establish the resonant structures of the slow magnetosonic waves in the magnetosphere.     

Comment on the group velocity of surface waves on the plasma sheet boundary

In the recent estimation by Maltsev and Lyatsky (1984) of the group velocity of surface waves on the inner boundary of the plasma sheet, the effect of the curvature of the field lines of the ambient magnetic field of the Earth on the spectrum has been assessed. The authors have not accounted for the fact, however, that the group velocity of the compressional surface magnetohydrodynamic waves itself is nonzero transverse to the magnetic field—a characteristic which has been omitted in the spectrum of Chen and Hasegawa (1974), being used by Maltsev and Lyatsky.This characteristic of compressional surface MHD waves is inherent for the spectrum $\text{ω = (}\text{k}{}_6\text{k}\text{)V}{}_{\mathrm{A}}\text{(k}{}^2{}_6\text{+ 2k}{}^2{}_{\mathrm{\perp }}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, obtained by Nenovski (1978) in the cold plasma limit V_A ? V_S(V_A is Alfvén velocity, and V_S, sound velocity). A comment has been made on the restrictions, proceeding from the approximation, used by Maltsev and Lyatsky. The estimation of the velocities for movements of auroral riometer absorption bays have been reviewed.     

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 O(1S) quantum yield from O2+ dissociative recombination

Recent laboratory studies show that the $\text{O}\text{(}{}^1\text{S}\text{)}$ quantum yield, $\text{f}\text{(}{}^1\text{S}\text{)}$, from O₂⁺ dissociative recombination varies considerably with the degree r of vibrational excitation. However, the suggestion that the high values for $\text{f}\text{(}{}^1\text{S}\text{)}$ deduced from airglow and auroral observations can be explained by invoking vibrational excitation, creates a number of problems. Firstly, the rapid vibrational deactivation of O₂⁺ ions by collisions with O atoms will keep r too low to account for the magnitude of $\text{f}\text{(}{}^1\text{S}\text{)}$; secondly, r varies considerably from one atmospheric source to another but its relative values (which should be reliable) do not co-vary with those of $\text{f}\text{(}{}^1\text{S}\text{)}$; thirdly, because r increases markedly above the peak of the $\text{X5577}\text{A}\text{?}$ dissociative recombination layer, the fits which theorists have obtained to the observed volume emission rate profiles would have to be regarded as fortuitious. It is tentatively suggested that $\text{f}\text{(}{}^1\text{S}\text{)}$ is higher in the airglow and aurora than in the laboratory plasma studied by Zipf (1980) because of the electron temperature dependence of the $\text{O}\text{(}{}^1\text{S}\text{)}$ specific recombination coefficient for O₂⁺(v^' ? 3) ions.The repulsive ${}^1\text{Σ}{}_{\mathrm{<mtext>u</mtext>}}\text{[}{}^1\text{D}\text{+}{}^1\text{s}\text{]}$ state of O₂ does not provide a suitable channel for the dissociative recombination. A possible alternative is the bound ${}^3\text{Π}{}_{\mathrm{<mtext>u</mtext>}}\text{[}{}^5\text{S}\text{+}{}^3\text{s}\text{]}$ state with predissociation to the repulsive ${}^3\text{Π}{}_{\mathrm{<mtext>u</mtext>}}\text{[}{}^3\text{P}\text{+}{}^1\text{s}\text{]}$ state.     

Emission line shapes produced by dissociative excitation of atmospheric gases

Special line shapes are derived fro the λ 1356 Å (${}^5\text{S}{}^0\text{-}{}^3\text{P}$) transition of atomic oxygen from metastable (${}^5\text{S}{}^0\text{-}{}^3\text{P}$) time-of-flight spectra produced by electron impact dissociative excitation of O₂, CO₂, CO, and NO, and they are compared with the broadened λ 1304 A resonance line shapes deduced by Poland and Lawrence (1973) from atomic oxygen absorption studies. The non-thermal line shapes for both airglow emission features are shown to have an effective width comparable to a 60,000 K thermal doppler line shape for an electron impact energy of 100eV. The variation of the effective line width with electron-impact energy from threshold to 300 eV is given. Since the effective line width of the resonance radiation produced by dissociative excitation is very large compared with the doppler absorption widths of the ambient O atoms at normal exospheric temperatures, the anomalously broadened resonance lines will propagate through a planetary atmosphere as though they were optically thin. Thus, electron-impact dissociation of CO and CO₂ will contribute to the observed optically thin component of the λ 1304 Å emission in the upper atmospheres of Venus and Mars. However, the process cannot account for more than 10% of the observed optically thin emission because of the small magnitude of the excitation cross-section and the comparatively high-energy threshold for the process. The possibility that the source of the kinetically energetic $\text{O}\text{(}{}^3\text{S}$) atoms is the dissociative recombination of vibrationally excited CO₂⁺ ions is discussed.     

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.     

The roles of the north-south component of the interplanetary magnetic field on large-scale auroral dynamics observed by the DMSP satellite

An extensive study of DMSP photographs and the simultaneous interplanetary magnetic field data suggests that the quantity defined by

$\text{S=∫}{}^{\mathrm{\tau }}{}_0\text{(Ф}{}_{\mathrm{D}}\text{? Ф}{}_{\mathrm{N}}\text{)dt}$

has a fundamental importance in substorm processes, where Φ_D and Φ_N denote the production rate of merged (or open) field lines along the dayside X-line and of reconnected (or closed) field lines along the nightside X-line, respectively; t = 0 is measured from the time when the B_z component begins to decrease after a prolonged period of a large positive B_z value. It is shown, first of all, that substorms occur so long as S > 0, regardless of the sign of the B_z component and its changes (namely, the southward and northward turnings) and of its time derivative as well. Secondly, the intensity of substorms is proportional to S². By introducing the quantity S, the recent confusion of the problem of the roles of the north-south component of the interplanetary magnetic field on substorm processes can be removed.Since S is equal to the amount of the open magnetic fluxes at a time reckoned from t = 0, it is proportional to (A₁ ? A₀), where A₀ denotes the minimum polar cap area (namely, the area bounded by the minimum auroral oval) and A₁ the polar cap area at an arbitrary time t. Therefore, substorms can occur whenever the auroral oval is larger than its minimum size. Further, an intense substorm tends to occur along a large oval.The quantity S can also be considered as an excess flux, and thus the substorm can be considered as a process by which the magnetosphere tends to remove sporadically the excess energy associated with S.     

Pitch angle dependence of the charge-exchange lifetime of ring current ions

Previous work has parameterized the pitch angle dependence of the charge-exchange lifetime τ of ring current ions in terms of γ, the power of the cosine of the mirror latitude λ_m of the particles, such that $\text{τ(λ}{}_{\mathrm{m}}\text{)}\text{τ(0) ≌}\text{cos}{}^{\mathrm{\gamma }}\text{λ}{}_{\mathrm{m}}$ at given L. Using the atomic hydrogen density model of Johnson and Fish, previous authors have suggested values of γ = 5 or 6. We here evaluate γ as a function of λ_m and L using the more recent Chamberlain density models, and show that γ = 3?4 is more appropriate over most of the pitch angle and L range. Consequently, ion distributions in the ring current decay phase are expected to become rather less anisotropic in pitch angle due to chargeexchange than previously believed. We have also investigated the use of several other simple approximate analytic forms for $\text{τ(λ}{}_{\mathrm{m}}\text{)}\text{τ(0)}$, one of which gives far better agreement with the numerical results than the cos^γ λ_m, variation, and should hence be used in future studies.     

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.     

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.     

A self-consistent evaluation of the rate constants for the production of the OI 6300 Å airglow

The quenching rate k_N2 of $\text{O(}{}^1\text{D)}$ by N₂ and the specific recombination rate α_1D of O₂⁺ leading to $\text{O(}{}^1\text{D)}$ are re-examined in light of available laboratory and satellite data. Use of recent experimental values for the $\text{O(}{}^1\text{D)}$ transition probabilities in a re-analysis of AE-C satellite 6300 Å airglow data results in a value for k_N2 of 2.3 × 10^?11 cm³s^?1 at thermospheric temperatures, in excellent agreement with the laboratory measurements. This implies a value of J_O2 = 1.5 × 10^?6s^?1 for the O₂ photodissociation rate in the Schumann-Runge continuum. The specific recombination coefficient α_1D = 2.1 × 10^?7cm³s^?1 is also in agreement with the laboratory value. Implications for the suggested $\text{N}\text{(}{}^2\text{D) + O}{}_2\text{→ O(}{}^1\text{D) + NO}$ reaction are discussed.     

On fourier-analysis of geomagnetic pulsations pc-1, “two-fold” and “three-fold” pulsations pc-1 and fundamental frequencies of the magnetospheric cavity—I

The paper gives the results of detailed studies of the frequency spectra $\text{S}{}_{\mathrm{s}}\text{(?)}$ of the chain of the wave packets F_s(t) of geomagnetic pulsations PC-1 recorded at the Novolazarevskaya station. The bulk of the energy of F_s(t) is concentrated in the vicinity of the central frequencies $\text{?}{}_{\mathrm{s0}}$ of spectra—the carrier frequencies of the signals. The velocity $\text{V}{}_0\text{≌ 6.10}{}^3\text{km s}{}^{\mathrm{?1}}$ of the flux of protons generating these signals correspond to them. The spectra of the signals have oscillations—“satellites” irregularly distributed in frequency. These satellites, as the authors believe, testify to the presence of the individual groups of protons of low concentration whose velocities vary within 10³–10⁴ km s^?1.Their energy is only of the order of 10^?2–10^?3 of the energy of the main proton flux. Clearly pronounced maxima on double and triple frequencies $\text{? = 2?}{}_{\mathrm{s0}}\text{and}\text{3?}{}_{\mathrm{s0}}$ are detected. They show that the generation of pulsations PC-1 is accompanied by the generation on the overtones of wave packets called in this paper “two-fold” and “three-fold” pulsations PC-1. Intensive symmetrical satellites of a modulation character have been discovered on frequencies $\text{?}{}^{\mathrm{\pm }}{}_{\mathrm{sK}}$. Frequency differences $\text{Δ?}{}_{\mathrm{sK}}{}^{\mathrm{\pm }}\text{=}\text{¦?}{}_{\mathrm{s0}}\text{? ?}{}_{\mathrm{sK}}{}^{\mathrm{\pm }}\text{¦}\text{= (0.011,0.022}\text{and}\text{0.035)}\text{Hz}$ correspond to them. The authors believe that the values of Δ?^±_sK are resonance frequencies of the magnetospheric cavity in which geomagnetic pulsations PC-1 are generated. It is established that the values of Δ?^±_sK coincide closely with the carrier frequencies of geomagnetic pulsations PC-3 and PC-4 generated in the magnetosphere. This leads to the conclusion that the resonance oscillations of the magnetospheric cavity are their source. Thus, the generation of geomagnetic pulsations of different types and resonance oscillations in the magnetosphere are integrated into a unified process. The importance of the results obtained and the necessity to check further their trustworthiness and universality, using experimental data gathered in different conditions, is stressed.     

Geopotential coefficients of order 29, from analysis of the orbit of satellite 1967-104B

The orbit of the satellite 1967-104B has been analysed as it passed through 29:2 resonance with the Earth's gravitational field between January 1977 and September 1978. From the changes in inclination and eccentricity the following lumped 29th-order geopotential harmonic coefficients were obtained: $\text{10}{}^9\text{C}\text{?}{}_{29}{}^{0.2}\text{= 4.1 ± 0.8}$, $\text{10}{}^9\text{S}\text{?}{}_{29}{}^{0.2}\text{= 10.3 ± 2.4}$, $\text{10}{}^9\text{C}\text{?}{}_{29}{}^{1.1}\text{= ? 160 ± 19}$, $\text{10}{}^9\text{S}\text{?}{}_{29}{}^{1.1}\text{= 79 ± 10}$, $\text{10}{}^9\text{C}\text{?}{}_{29}{}^{\mathrm{?1.3}}\text{= 38 ± 14}$, $\text{10}{}^9\text{S}\text{?}{}_{29}{}^{\mathrm{?1.3}}\text{= 19 ± 5}$. These values have been compared with existing comprehensive geopotential models: the best agreement is with the model of Rapp (1981).     

The role of protons of the radiation belts in the generation of Pc 3–5

A new theory of the Alfvén wave generation in inhomogeneous finite β two component plasma is developed ($\text{β =}\text{8πρ}\text{β}{}_0{}^2$, ρ and B₀ are plasma pressure and unperturbed magnetic field, respectively). The analysis was carried out for these waves both for long wave approximation kρ_i ? 1 as well as for $\text{kρ}{}_{\mathrm{i}}\text{? 1}$ (k and ρ_i are wave vector and larmor radius of protons). The influence of the loss-cone on the development of the instability is considered. The theory is applied to explain the generation mechanism of Pc 3–5.     

Editorial

The Galilean satellites Io, Europa, and Ganymede interact through several stable orbital resonances where $\text{λ}{}_1\text{? 2λ}{}_2\text{+}\text{ω}{}_1\text{= 0, λ}{}_1\text{? 2λ}{}_2\text{+}\text{ω}{}_2\text{= 180°, λ}{}_2\text{? 2λ}{}_3\text{+}\text{ω}{}_2\text{= 0}$ and λ₁ ? 3λ₂ + 2λ₃ = 180°, with λ_i being the mean longitude of the ith satellite and $\text{ω}{}_{\mathrm{i}}$ the longitude of the pericenter. The last relation involving all three bodies is known as the Laplace relation. A theory of origin and subsequent evolution of these resonances outlined earlier (C. F. Yoder, 1979b, Nature279, 747–770) is described in detail. From an initially quasi-random distribution of the orbits the resonances are assembled through differential tidal expansion of the orbits. Io is driven out most rapidly and the first two resonance variables above are captured into libration about 0 and 180° respectively with unit probability. The orbits of Io and Europa expand together maintaining the 2:1 orbital commensurability and Europa's mean angular velocity approaches a value which is twice that of Ganymede. The third resonance variable and simultaneously the Laplace angle are captured into libration with probability ～0.9. The tidal dissipation in Io is vital for the rapid damping of the libration amplitudes and for the establishment of a quasi-stationary orbital configuration. Here the eccentricity of Io's orbit is determined by a balance between the effects of tidal dissipation in Io and that in Jupiter, and its measured value leads to the relation $\text{k}{}_1\text{?}{}_1\text{/Q}{}_1\text{≈ 900k}{}_{\mathrm{<mtext>J</mtext>}}\text{/Q}{}_{\mathrm{<mtext>J</mtext>}}$ with the k's being Love numbers, the Q's dissipation factors, and f a factor to account for a molten core in Io. This relation and an upper bound on Q₁ deduced from Io's observed thermal activity establishes the bounds 6 × 10⁴ < Q_J < 2 × 10⁶, where the lower bound follows from the limited expansion of the satellite orbits. The damping time for the Laplace libration and therefore a minimum lifetime of the resonance is 1600 Q_J years. Passage of the system through nearby three-body resonances excites free eccentricities. The remnant free eccentricity of Europa leads to the relation $\text{Q}{}_2\text{/?}{}_2\text{? 2 × 10}{}^{\mathrm{?4}}\text{Q}{}_{\mathrm{<mtext>J</mtext>}}$ for rigidity μ₂ = 5 × 10¹¹ dynes/cm². Probable capture into any of several stable 3:1 two-body resonances implies that the ratio of the orbital mean motions of any adjacent pair of satellites was never this large.A generalized Hamiltonian theory of the resonances in which third-order terms in eccentricity are retained is developed to evaluate the hypothesis that the resonances were of primordial origin. The Laplace relation is unstable for values of Io's eccentricity e₁ > 0.012 showing that the theory which retains only the linear terms in e₁ is not valid for values of e₁ larger than about twice the current value. Processes by which the resonances can be established at the time of satellite formation are undefined, but even if primordial formation is conjectured, the bounds established above for Q_J cannot be relaxed. Electromagnetic torques on Io are also not sufficient to relax the bounds on Q_J. Some ideas on processes for the dissipation of ideal energy in Jupiter yield values of Q_J within the dynamical bounds, but no theory has produced a Q_J small enough to be compatible with the measurements of heat flow from Io given the above relation between Q₁ and Q_J. Tentative observational bounds on the secular acceleration of Io's mean motion are also shown not to be consistent with such low values of Q_J. Io's heat flow may therefore be episodic. Q_J may actually be determined from improved analysis of 300 years of eclipse data.     

New high-speed photometry of EH Lib and a binary interpretation of its period change

Six times of maxima of the ultrashort-period cepheid variable EH Librae were measured in 1980 May to June and in 1981 January, with a three-channel photocounting high-speed photoelectric photometer. These, together with all the photoelectric times of maxima over the past 30 years, are used to re-examine the nature of the change of the period. We found that we can fix the times of maxima by the following formula

$\text{T}{}_{\max }\text{= T}{}_0\text{+P}{}_0\text{E+}\text{1}\text{2}\text{βE}{}^2\text{+A}\text{sin}\text{2π}\text{EP}{}_0\text{E}{}_0$

where T₀ = HJD 2433438.6088 and P₀ = 0.0884132445 d represent the initial maximum epoch and the pulsation period, β = ?2.8 × 10^?8/yr; A = 0.0015 d, P₀ = 6251 d = 17.1 yr are the semi-amplitude and the period of the sine curve, and E is the number of periods elapsed since T₀, and (E₀ = 70700).If we interpret this 17.1 year periodicity as a modulation of the phase of maximum by binary motion, then the semi-amplitude of the orbital radial velocity variation is K = 2πasini/E₀ = 0.45 km/s and the mass function is

$\text{f(m)=}\text{m}{}^3{}_2\text{sin}{}^3\text{i}\text{(m}{}_1\text{m}{}_2\text{)}{}^2\text{=}\text{(a}\text{sin}\text{i)}{}^3\text{E}{}^2{}_0\text{=6 x 10}{}^{\mathrm{?5}}\text{M}{}_{\mathrm{\odot }}$

     

Electric fields and potential patterns in the high-latitude ionosphere for different situations in interplanetary space

The potential ? of the electric field at high latitudes has been obtained by solving numerically the second order differential equation in spherical coordinates:

$\text{?}\text{1}\text{2}\text{(rσ}{}^{\mathrm{H}}\text{?}{}_{\mathrm{\theta }}\text{)}{}_{\mathrm{\theta }}\text{+}\text{1}\text{r}\text{(σ}{}^{\mathrm{H}}\text{?λ)}{}_{\mathrm{\lambda }}\text{+}\text{1}\text{r}\text{(σ}{}^{\mathrm{P}}\text{?}{}_{\mathrm{\lambda }}\text{)}{}_{\mathrm{\theta }}\text{?(σ}{}^{\mathrm{P}}\text{?}{}_{\mathrm{\theta }}\text{)}{}_{\mathrm{\lambda }}\text{=}\text{1}\text{r}\text{(rψ}{}_{\mathrm{\theta }}\text{)}{}_{\mathrm{\theta }}\text{+}\text{1}\text{r}{}^2\text{ψ}{}_{\mathrm{\lambda \lambda }}$

, where θ is colatitude, λ is longitude, σ^H and σ^P are the height-integrated Hall and Perdersen ionospheric conductivities, r = sinθ, and ψ is the current function. The boundary condition is ? = 0 on the geomagnetic parallel θ = 34°. Values of ψ are determined from geomagnetic field variations at the Earth's surface from geomagnetic field variations at the Earth's surface for various conditions in interplanetary space. σ^P and σ^H are taken to vary with season, local time, tilt of the geomagnetic dipole axis (UT), and intensity of corpuscular precipitation (the model proposed by Wallis and Budzinski, 1981). The model distributions of ?^M and E^M = -▽?^m so obtained are compared with observational results. The feasibility has been demonstrated of interpreting the statistical results and individual measurement data in terms of a unified dynamic model of ionospheric electric fields. The model makes allowance for the changes of electromagnetic “weather” in interplanetary space.