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.     

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.     

On the thickness and evolution of the dust layer during the formation of the solar system

We discuss certain dynamical processes during the final stage of the sinking of the dust layer. We supposed that turbulance gave rise to a state of slow sinking (quasi-equilibrium) and evaluated the critical thickness at the onset of gravitational instability in the radial direction. We gave a precise numerical relation between 3 length-scales: $\text{〈|Z|〉c : h}{}_1\text{: λ}{}_{\mathrm{T}}\text{= 0.02107 : 0.1592 : 1}$, the first being the mean height of the dust particles at the onset of radial instability, the second being that value of the half-thickness and of the height at which the self-gravity of the dust layer is equal to the solar z-component, and the last being the longest wavelength at the onset of ring instability. We also calculated the time required for the formation of rings and found it to be far shorter than the sinking time.     

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.     

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.     

Habitable zones about main sequence stars

Calculations show that a main sequence star which is less massive than the Sun has a continuously habitable zone about it which is not only closer in than the corresponding zone about the Sun, but is also relatively narrower. Let L(t) represent the luminosity after t billion years of a main sequence star of mass M, and let r_inner and r_outer represent the boundaries of the continuously habitable zone about such a star—that is, the zone in which an Earthlike planet will undergo neither a runaway greenhouse effect in the early stages of its history nor runaway glaciation after it develops an oxidizing atmosphere. Then our computer results indicate that $\text{r}{}_{\mathrm{<mtext>outer</mtext>}}\text{r}{}_{\mathrm{<mtext>inner</mtext>}}$ is roughly proportional to $\text{[}\text{L(3.5)}\text{L(1.0)}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. This ratio is smaller for stars less massive than the Sun (because they evolve more slowly), and the width of the continuously habitable zone about a main sequence star is therefore a strong function of the initial stellar mass. Our calculations show that r_inner = r_outer for $\text{M～0.83M?}$ (i.e., K1 stars), and it therefore appears that there is no continuously habitable zone about most K stars, nor any about M stars.     

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.     

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.     

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

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

.     

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

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

     

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.     

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).     

Ring current simulation in connection with interplanetary space conditions

A ring current model has been obtained which permits calculations ofD_st variations on the Earth's surface during magnetic storms. The changes in D_st are described by the equation

$\text{d}\text{d}\text{t}\text{D}{}_{\mathrm{sto}}\text{= F(EM)?}\text{D}{}_{\mathrm{sto}}\text{tau;}$

where $\text{D}{}_{\mathrm{sto}}\text{= D}{}_{\mathrm{st}}\text{-bp}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{+~tc}$; p = mnv² is solar wind pressure; F(EM) is the function, controlled by the electromagnetic parameters of interplanetary medium, of injection into ring current ; τ is the constant of ring current decay. $\text{C}\text{= C}\text{u}\text{τ?=18}\text{nT}$, where C is the level of the D_st-variation field measurements; ? is the injection function characterizing the quasisteady-state injection of energy into the ring-current region. The constant Ç is determined from the condition that the change of the ring current energy from magnetic storm commencement to end should equal the difference between the injected and dissipated energy throughout the storm. The values of the factors b and τ were found by the method of minimizing the sum of the quadratic deviations of the calculated D_st from the values observed throughout the storm : b = 0.23 nT/(eV cm^?3)^{$\text{1}\text{2}$}, τ = 8.2 h at D_st? ? 55 nT and τ = 5.8 h at -120 ? D_st ? — 55 nT. The injection function F(EM) is of the form F(EM) = d(E_y? A) at the values of the azimuthal component of the solar wind electric field E_y ? A, and F(EM) =0 at A?E_y.d = ? 1.2 × 10^?3 Ts^?1 (mV/m)^?1 and A = ? 0.9 mV m^?1 . Thus, the injection to ring current is possible at the northward B_z component of the IMF.     

The excitation of atomic oxygen to the O(1S) level by energy transfer from N2(A3∑u+) molecules in aurora

The part that the energy transfer reaction $\text{N}{}_2\text{(A}{}^3\text{∑}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{) + O(}{}^3\text{P) → N}{}_2\text{(X}{}^1\text{∑}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{) + O(}{}^1\text{S)}$ plays in the excitation of the auroral green line has been investigated. The contribution is estimated to be 40 per cent in this case, containing pulsating aurora in class IBC 1. Due to greater quenching of the A³∑_u⁺ state, the centroid of the VK emission is displaced 10 km upwards of the green line height, which is centred at 110 km.     

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.     

Low-frequency upstream wave as a probable source of low-latitude Pc 3–4 magnetic pulsations

Daytime Pc 3–4 pulsation activities observed at globally coordinated low-latitude stations [SGC (L = 1.8,λ = 118.0°W), EWA(1.15,158.1°W), ONW(1.3,141.5°E)] are evidently controlled by the cone angle θ_XB of the IMF observed at ISEE 3. Moreover, the Pc 3–4 frequencies ($\text{?}$) at the low latitudes and high latitude (COL; L = 5.6 and λ = 147.9°W) on the ground and that of compressional waves at geosynchronous orbit (GOES 2; L = 6.67 and λ = 106.7°W) are also correlated with the IMFmagnitude(B_IMF).The correlation of $\text{?}$ of the compressional Pc 3–4 waves at GOES 2 against B_IMF is higher than those of the Pc 3–4 pulsations at the globally coordinated ground stations, i.e., γ = 0.70 at GOES 2, and (0.36,0.60,0.66,0.54) at (COL, SGC, EWA, ONW), respectively. The standard deviation ($\text{σ}{}_{\mathrm{n}}\text{= ± Δ?}\text{mHz}$) of the observed frequencies from the form $\text{?}$ (mHz) = 6.0 × B_IMF (nT) is larger at the ground stations than at GOES 2, i.e., $\text{Δ? = ± 6.6}\text{mHz at}$GOES 2, and ±(13.9, 9.1, 10.7, 12.1) mHz at (COL, SGC, EWA, ONW), respectively. The correlations between the IMF magnitude B_IMF and Pc 3–4 frequencies at the low latitudes are higher than that at the high latitude on the ground, which can be interpreted by a “filtering action” of the magnetosphere for daytime Pc 3–4 magnetic pulsations. The scatter plots of pulsation frequency $\text{?}$ against the IMF magnitude B_IMF for the compressional Pc 3–4 waves at GOES 2 are restricted within the forms $\text{? = 4.5 × B}{}_{\mathrm{<mtext>IMF</mtext>}}\text{and}\text{? = 7.5 × B}{}_{\mathrm{<mtext>IMF</mtext>}}$. The frequency distribution is in excellent agreement with the speculation ($\text{<ω}{}_{\mathrm{sc}}\text{Ω}{}_{\mathrm{i}}\text{= 0.3 ～ 0.5}$) of the spacecraft frame frequency of the magnetosonic right-hand waves excited by the anomalous ion cyclotron resonance with reflected ion beams with V₆ = 650 ～ 1150 km s^?1 in the solar wind frame observed by the ISEE satellite in the Earth's foreshock. These observational results suggest that the magnetosonic right-handed waves excited by the reflected ion beams in the Earth's foreshock are convected through the magnetosheath to the magnetopause, transmitted into the magnetosphere without significant changes in spectra, and then couple with various HM waves in the Pc 3–4 frequency range at various locations in the magnetosphere.     

On the photodissociation of water vapour in the mesosphere

The photodissociation of water vapour in the mesosphere depends on the absorption of solar radiation in the region (175–200 nm) of the O₂ Schumann-Runge band system and also at H-Lyman alpha. The photodissociation products are OH + H, OH + H, O + 2H and H₂ + O at Lyman alpha; the percentages for these four channels are 70, 8, 12 and 10%, respectively, but OH + H is the only channel between 175 and 200 nm. Such proportions lead to a production of H atoms corresponding to practically the total photodissociation of H₂O, while the production of H₂ molecules is only 10% of the H₂O photodissociation by Lyman alpha.The photodissociation frequency (s^?1) at Lyman alpha can be expressed by a simple formula

$\text{J}{}_{\mathrm{<mtext>Ly</mtext><mtext>\alpha </mtext>}}\text{H}{}_2\text{O=4.5 ×10}{}^{\mathrm{?6}}\text{1+0.2}\text{F}{}_{10.7}\text{?65}\text{100}\text{exp}\text{[?4.4 ×10}{}^{\mathrm{?19}}\text{N}{}^{0.917}\text{]}$

where F_{10.7 cm} is the solar radioflux at 10.7 cm and N the total number of O₂ molecules (cm^?2), and when the following conventional value is accepted for the Lyman alpha solar irradiance at the top of the Earth's atmosphere ($\text{Δλ = 3.5}\text{A}\text{?}$) q_Lyα,∞ = 3 × 10¹¹ photons cm^?2 s^1?.The photodissociation frequency for the Schumann-Runge band region is also given for mesospheric conditions by a simple formula

$\text{J}{}_{\mathrm{<mtext>SRB</mtext>}}\text{(}\text{H}{}_2\text{O}\text{) = J}{}_{\mathrm{<mtext>SRB</mtext><mtext>,\infty </mtext>}}\text{(}\text{H}{}_2\text{O}\text{) exp [?10}{}^{\mathrm{?7}}\text{N}{}^{0.35}\text{]}$

where J_SRB,∞(H₂O) = 1.2 × 10^?6 and 1.4 × 10^?6 s^?1 for quiet and active sun conditions, respectively.The precision of both formulae is good, with an uncertainty less than 10%, but their accuracy depends on the accuracy of observational and experimental parameters such as the absolute solar irradiances, the variable transmittance of O₂ and the H₂O effective absorption cross sections. The various uncertainties are discussed. As an example, the absolute values deduced from the above formulae could be decreased by about 25-20% if the possible minimum values of the solar irradiances were used.     

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.     

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.