The relationship of the boundary layer of the magnetosphere to IPRP events

A model is proposed in which a mixture of hot solar wind and cold atmospheric plasma flowing in the dayside equatorial boundary layer towards the dawn-dusk plane generates hydromagnetic waves near the frequency $\text{ω = ω}{}_{\mathrm{Bi}}\text{¦1 ? T}{}_{\mathrm{\parallel }}\text{¦T}{}_{\mathrm{\perp }}\text{¦}$ where ω_Bi is the ion gyrofrequency and T_∥, T_⊥ are the temperatures of the solar wind plasma, parallel and perpendicular respectively to the magnetic field B. The model accounts for the properties of IPRP events, i.e. intervals of geomagnetic pulsations of periods rising on average from about 2 s to about 7 s over an interval of about 5 min. The diagnostic potential of this phenomenon for study of the boundary layer is indicated.     

Rotational discontinuities in an anisotropic plasma—II

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

A stability analysis of the spiral sector transition region in the interplanetary magnetic field

We use a four-layer model in a stability analysis of the ME type spiral sector transition in the interplanetary magnetic field. Our results show that (1) three kinds of large-scale waves may be excited in the region and for all three, there exists a low-frequency cut-off. (2) In all three, the rate of growth of instability increases with k; in Model A only, the rate of growth has a maximum and a minimum. (3) As the angle between k and the solar wind velocity vector $\text{V}{}_{\mathrm{q}}$ increases, the cut-off frequency increases, and the excitation of waves gets more and more difficult, until it becomes impossible when k is perpendicular to $\text{V}{}_{\mathrm{q}}$. (4) when the angle between k and $\text{V}{}_{\mathrm{q}}$ is 75°, waves with a wavelength of 5 × 10⁴ km and a phase velocity of 340 km/s may be excited; this agrees with the observations by Voyager 1 at the Earth's magnetopause. Hence we deduce that waves in the spiral sector transition region may be a source that triggers off the Kelvin-Helmholtz instability of the magnetopause.     

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.     

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.     

Long-period magnetic pulsations generated in the magnetospheric boundary layers

Long-period hydromagnetic waves can be excited by the velocity shear instability in the magnetospheric boundary layers, where the penetrated bulk flow of the solar wind comprises a fairly strong velocity shear. Model spaces of the boundary layers are considered to estimate amplification rates on the HM waves in the low-latitude flank-side and in the dayside high-latitude and mantle-side boundary layers, where the ambient magnetic field is assumed to be perpendicular and parallel to the bulk flow of the solar wind, respectively. Wave characteristics of the HM waves are also investigated for the k-vector almost normal to the magnetopause.The localized HM waves in the Pc 3–4, Pc 4–5 and Pc 6 frequency ranges, of which group velocities are mostly parallel to the plane in the ambient magnetic field and the bulk flow directions, i.e., parallel to the magnetopause, are sufficiently amplified in the dayside low- and high-latitude, in the low-latitude flank-side, and in the mantle-side boundary layers, respectively. A left-handed toroidal (transverse) and a right-handed poloidal (compressional) mode of long-period $\text{(T ? 120}\text{s}\text{)Ω}{}_{\mathrm{A}}$-wave are generated in the dawn- and the duskflank boundary layers, respectively, where the k-vector of Alfvénic signals was assumed to be almost in the Archemedean spiral direction. The localized compressional HM waves in the Pc 3–4 range indicate both lefthanded and right-handed polarizations in the dayside boundary layer, which are functions of the k-vector of the waves and the sense of the velocity shear. The variance directions of perturbation fields of the HM waves in the magnetospheric boundary layers tend to be nearly parallel to the magnetopause. These localized HM waves can propagate into the high-latitude ionosphere. We conclude that the localized HM waves driven by the velocity shear instability in the magnetospheric boundary layers are the most probable source of the daytime Pc 3–5 magnetic pulsations in the outer magnetosphere.     

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.     

On viscous attenuation of Alfvenic fluctuations in the solar wind

It is shown that the viscous attenuation of Alfvenic fluctuations is anisotropic and is proportional to the fluctuation component parallel to the mean magnetic field. If the ratio between the parallel and perpendicular components is a constant, then the viscous attenuation experienced by waves with wavelengths larger than the collisional free-path will be concentrated within 20 $\text{R?}$. Between 0.3 AU and l AU, no Alfvenic fluctuations of any frequency is appreciably damped by viscosity determined by Coulomb collision. The mechanism of viscous attenuation caonot explain the observed radial development of the spectrum. If, near the Sun, the Alfvenic fluctuations do have a parallel component, then the viscous damping will have an important accelerating effect on the solar wind in fast diverging stream tubes. If the parallel component is negligible, then the Alfvenic fluctuation will not be attenuated by any classical viscosity.     

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.     

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.     

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).     

Interplanetary energy flux associated with magnetospheric substorms

It is shown that the interplanetary quantity ε(t), obtained by Perreault and Akasofu (1978), for intense geomagnetic storms, also correlates well with individual magnetospheric substonns. This quantity is given by $\text{ε(t) = VB}{}^2\text{sin}{}^4\text{(}\text{θ}\text{2}\text{)l}{}_{\mathrm{o}}{}^2$, where V and B denote the solar wind speed and the magnitude of the interplanetary magnetic field (IMF), respectively, and θ denotes the polar angle of the IMF; l_o is a constant ? 7 Earth radii. The AE index is used in this correlation study. The correlation is good enough to predict both the occurrence and intensity of magnetospheric substonns observed in the auroral zone, by monitoring the quantity ε(t) upstream of the solar wind.     

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

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

.     

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

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

Production and condensation of organic gases in the atmosphere of Titan

The rates and altitudes for the dissociation of atmospheric constituents of Titan are calculated for solar UV, solar wind protons, interplanetary electrons, Saturn magnetospheric particles, and cosmic rays. The resulting integrated synthesis rates of organic products range from 10²–10³ g cm^?2 over 4.5 × 10⁹ years for high-energy particle sources to 1.3 × 10⁴ g cm^?2 for UV at $\text{λ < 1550}\text{A}\text{?}$, and to 5.0 × 10⁵ g cm^?2 if $\text{λ > 1550}\text{A}\text{?}$ (acting primarily on C₂H₂, C₂H₄, and C₄H₂) is included. The production rate curves show no localized maxima corresponding to observed altitudes of Titan's hazes and clouds. For simple to moderately complex organic gases in the Titanian atmosphere, condensation occurs below the top of the main cloud deck at 2825 km. Such condensates comprise the principal cloud mass, with molecules of greater complexity condensing at higher altitudes. The scattering optical depths of the condensates of molecules produced in the Titanian mesosphere are as great as ～ 10²/(particulate radius, μm) if column densities of condensed and gas phases are comparable. Visible condensation hazes of more complex organic compounds may occur at altitudes up to ～ 3060 km provided only that the abundance of organic products declines with molecular mass no faster than laboratory experiments indicate. Typical organics condensing at 2900 km have molecular masses = 100–150 Da. At current rates of production the integrated depth of precipitated organic liquids, ices, and tholins produced over 4.5 × 10⁹ years ranges from a minimum ～ 100 m to kilometers if UV at $\text{λ > 1550}\text{A}\text{?}$ is important. The organic nitrogen content of this layer is expected to be ～ 10^?1?10^?3 by mass.     

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.     

Orientation and shape of the Earth's bow shock in three dimensions

Nearly 2500 shock crossings from HEOS-1, HEOS-2 and 5 IMP spacecraft, covering most of the northern and part of the southern bow shock surface for X values X > ? 20 R_E, have been used to carry out a detailed study of the three-dimensional shape and location of the bow shock. The influence of the different solar wind conditions has been reduced by normalising the observed crossings to an average solar wind dynamical pressure (N₀ = 9.4 cm^?3, V₀ = 450 kms^?1). It has been shown that the shock surface is symmetric with respect to the ecliptic plane and intersects the coordinate axes at 11.9 R_E (X), + 27.0 and ? 22.9 R_E (Y), + 23.9 and ? 24.5 R_E (Z) for the average dynamical pressure (N₀ = 9.4 cm^?3, V₀ = 450kms^?1, with $\text{M}{}_{\mathrm{A}}\text{= 9.3}$, $\text{M}{}_{\mathrm{MS}}\text{= 6.1)}$. The observed aberration of the shock surface is 8.9° ± 1°, i.e. 5.1° larger than the aberration predicted from the Earth's motion. This asymmetry around the solar wind apparent direction is described by equation (6) for different Mach numbers M_A and confirms the predictions of Walters [J. geophys. Res. 71, 1319 (1964)] and Michel [J. geophys. Res. 70, 1 (1965)].The magnetosheath thickness is 3.3 R_E along the X-axis, 11.4 R_E (+ Y), 8.7 R_E (? Y), 9.9 R_E (+Z) and 10.9 R_E along the negative Z axis.     

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.     

Atmospheric waves (≈ 10 min–30 days) in the mesosphere and thermosphere at saskatoon (52°N, 107°W), October 1978–September 1979

Partial reflection radiowave wind observations have been made continuously at Saskatoon for 1 year (September 1978–August 1979). The winds have been obtained in real-time from a twin micro-processor system, that produces profiles (32 heights from 49 to 142km) at 5-min intervals: daytime/night-time profiles normally involve values from $\text{60}\text{70}$ to 120 km.These data have been analyzed to give the daily mean wind and the amplitudes and phases of planetary, tidal (24, 12 h) and internal gravity (I.G.) waves (0.20 ? τ ? 6h). There are oscillations in the mean daily wind, with periods of 2–30 days: the disturbance from 60 to 100 km caused by the stratwarm of February and March is documented. The characteristics of the semi-diurnal tide undergo significant changes in vertical wavelength and time of maxima between summer months (May–August) and winter months (November–February): during summer the S²₂ mode (λ_z ? 150km) seems to dominate, and in other months a mixture of modes (λ_z ? 50km) exist. The diurnal tide is less regular, but during winter and spring λ_z ? 30–60 km, and for other months is very large, suggesting the S_?1¹ mode. Energy densities and scale heights (h₀) are given, and the relative magnitudes of these for the various waves are discussed with respect to height and season: there is a general trend for the growth of the wave amplitude with height (shown by h₀) to increase in the order planetary, tidal and I.G. waves (h₀, ～3–15 km): largest values are in winter and spring. Wave energies are largest in winter, decrease during spring and increase throughout late summer and fall.     

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.