Micropulsations and orthogonal curvilinear coordinates

The theory of torsional hydromagnetic oscillations of the magnetosphere is usually cast in terms of orthogonal curvilinear coordinates. For a general magnetic field B with potential Ω it is shown that no coordinates exist in which a suitable solution may be found unless the Alfvén velocity V_A, together with B and Ω satisfy certain functional relationships. In the case V_A = constant, for example we must have

$\text{(}\text{B}\text{· ?)B =}\text{function of}\text{B}\text{and}\text{Ω}\text{only}$

. The relationships presented are in fact satisfied by all the magnetic fields considered to date.     

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.     

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.     

Hydromagnetic waves in structured magnetic fields

Although the inhomogeneous nature of solar magnetic fields is now well established, most theoretical analyses of hydromagnetic wave propagation assume infinite homogeneous fields. Here we reformulate the hydromagnetic wave problem for magnetic fields which vary in one direction perpendicular to the field. The permitted modes of small amplitude hydromagnetic oscillations are considered, first in the case of a single interface between semi-infinite magnetic and non-magnetic compressible regions, and secondly for a magnetic flux sheath of given thickness imbedded in a nonmagnetic region. It is shown that, for small values of R (the ratio of the Alfvén to the sound speed), an acoustic or p-mode wave front passes through the flux sheath with only minor deformation. However, for large R, the transmitted acoustic wave is attenuated and, depending upon the thickness of the flux sheath and the angle of incidence, a hydromagnetic wave may be effectively trapped and guided along the flux sheath. It is also shown that, for the symmetric vibration of the flux sheath in the absence of incident acoustic waves, only slow mode type waves are permitted. Thus, in compressible regions for which R > 1 the Alfvénic-type fast mode is not a permitted mode of free vibration of a flux sheath.     

Coma expansion and photometry of comet Bowell (1980b)

Optical and infrared observations of comet Bowell are presented. The optical observations indicate that the solid grain coma is expanding at only 0.9 ± 0.2 m sec^?1. This is two orders of magnitude slower than the local gas sound speed and may suggest that gas drag is not responsible for stripping the grains from the nucleus. The hypothesis of “electrostatic snap-off” is tentatively advanced to account for the ejection of the grains. Alternatively, the grains may have an unusual size distribution. The extrapolated motion of the grains suggests that the bulk of the coma was formed when the comet was at a heliocentric distance $\text{R ? 10}\text{AU}$. Any water ice in the nucleus would be too cold to give rise to the observed grain coma by equilibrium sublimation at this R. Further evidence against the production of the grain coma by equilibrium sublimation of the nucleus is provided by broadband (J) photometric observations. Almost all of the observed photometric variations of comet Bowell can be ascribed to geometric effects. Simple models indicate that the total grain cross section has been nearly constant since the time of the earliest observations. The present observations, which suggest that water ice sublimation does not control either the optical morphology or the near infrared photometric behavior of comet Bowell, are contrasted with reported high OH production rates. It is concluded that the grain coma may be largely a relic of activity occurring on the nucleus at $\text{R ? 10}\text{AU}$ while the OH may indicate sublimation from the nucleus near perihelion and from coma grains near $\text{R ? 4.6}\text{AU}$.     

Field-aligned currents between 400 and 3000 km in auroral and polar latitudes

The polar orbiting magnetically stabilized satellite AZUR measured transverse magnetic variations in auroral and polar latitudes by means of a two component flux-gate magnetometer. Simultaneous measurements of $\text{λ2972}\text{A}\text{?}$ and $\text{λ3914}\text{A}\text{?}$ auroral emissions are related to low-energy zero-pitch-angle electron fluxes, which cause the transverse magnetic disturbances. Power spectra of the magnetic field variations are consistent with those of geomagnetic micropulsations.The sources of the field-aligned currents can be located in the Alfvén layer and in the magnetotail.     

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.     

Hydromagnetic waves driven by velocity shear instability in the magnetospheric boundary layer

The bulk flow of the solar wind plasma in the flank-side of the magnetospheric boundary layer, where the magnetic field lines are closed, has a component transverse to the ambient field. There is quite a strong velocity shear. The theoretical model ignores inhomogeneities in the ambient field and the mass density which occur at the magnetopause on about the same length scale as that of the velocity shear.Consideration is restricted to hydromagnetic waves which have a k-vector nearly normal to the B_o-V_o plane, i.e., approximately the magnetopause surface (k_x >k_z ～ k_y′k_xL_B > 1 and L_B = 0.1 ～ 1.0 R_E where L_B is a characteristic length of the boundary layer). It is found that a long-period (T ? 40 sec) hydromagnetic wave [the Alfvén-like wave ($\text{Ω}{}_{\mathrm{<mtext>A</mtext>}}$)] driven by velocity shear instability can be excited in the shear plasma. It is also found that the group velocity of the HM-wave is directed almost along the magnetic field line and that the magnetic variance in the shear plasma tends to be parallel to the B_o-V_o plane. The velocity shear instability in the magnetospheric boundary layer is judged to be a likely source of long-period magnetic pulsations.     

VLF-emissions associated with ring current electrons: Off-equatorial observations

The combination of a small inclination of the orbit (～4°) with the tilt angle (～11°) of the Earth's magnetic dipole axis enabled the S³-A satellite (Explorer 45) to make simultaneous observations of magnetospheric VLF-emissions and the associated enhancement of ring current electrons not only at the magnetic equator but also up to 15° geomagnetic latitudes. Microdensitometer scanning of the wideband data of these emissions reveals that the band of missing emission in the off-equatorial whistler mode emissions (chorus) appears at $\text{f}{}_{\mathrm{<mtext>Ho</mtext>}}\text{2}$ and that the intensities of the off-equatorial emission above $\text{f}{}_{\mathrm{<mtext>Ho</mtext>}}\text{2}$ are very weak in contrast to those of the near equatorial emissions, where $\text{f}{}_{\mathrm{<mtext>Ho</mtext>}}\text{2}$ is the equatorial electron gyrofrequency corresponding to the local gyrofrequency f_H at the satellite. Ray-tracing of whistler mode waves produced by the enhanced ring-current electrons at the geomagnetic equator just outside of the plasmapause has shown that some of these waves are reflected from high latitudes back to the Equator inside the source region. This process had been previously speculated to explain the formation of the bimodal intensity distribution with a gap at half the gyrofrequency (the two-band chorus) in the equatorial emission data. The intensities of those reflected waves, however, are shown to be insufficient to explain the observed emissions below $\text{f}{}_{\mathrm{<mtext>Ho</mtext>}}\text{2}$ at the Equator. These results indicate that the superposition of two types of emissions produced by the same processes but from different locations is not the main mechanism for the formation of the two-band chorus and that the dominant sources of these choruses are located around ± 5° geomagnetic latitude.     

Wave propagation in a magnetically structured atmosphere

The solar atmosphere, from the photosphere to the corona, is structured by the presence of magnetic fields. We consider the nature of such inhomogeneity and emphasis that the usual picture of hydromagnetic wave propagation in a uniform medium may be misleading if applied to a structured field. We investigate the occurrence of magnetoacoustic surface waves at a single magnetic interface and consider in detail the case where one side of the interface is field-free. For such an interface, a slow surface wave can always propagate. In addition, a fast surface wave may propagate if the field-free medium is warmer than the magnetic atmosphere.     

Io's interaction with the magnetosphere

Jupiter's innermost Galilean satellite Io is regarded as a fairly good conductor ($\text{σ > 10}{}^{\mathrm{?5}}\text{Ω}{}^{\mathrm{?1}}\text{m}{}^{\mathrm{?1}}$). The trapping of magnetic field lines by Io and their deformation is described. A neutral point forms in the vicinity of the satellite. The magnetic field annihilation in the neutral point is enhanced by the emission of low frequency hmd waves. The power carried away by these waves may be as high 10¹⁵ W. The characteristic frequency of the wave and its variation while Io orbits around Jupiter is determined.     

On the generation of low-frequency waves in the solar wind in the front of the bow shock

The generation of low-frequency waves in the solar wind by the flux of protons accelerated in the magnetosheath is considered. It is shown that pulsations are produced in two partly overlapping frequency ranges. The growth rate of waves is maximal when the angle θ between the direction of the interplanetary magnetic field and the front of the bow shock is not equal $\text{π}\text{2}$. The dependence of the increment of perturbation on the solar wind velocity is analysed. A satisfactory agreement between theory and experimental results on the connection of Pc3–4 properties and parameters of the solar wind is obtained.     

The influence of a flow field on the stability of the force-free magnetic field

In order to analyse the convective instability of the force-free magnetic field, an exact solution of the MHD equation for the magnetic field (1) together with the flow field (2) of constant speed V₀ making an angle θ with the magnetic field, was chosen as the unperturbed state. The stability of the fields between two parallel conducting walls of seperation d was studied by a linear perturbation method, which led to the eigenvalue problem (12), X being given by (13). It was shown by an approximate variational method that instability will set in by the flow field if V₀ is greater than 1/ $\text{3}$ times Alfven velocity V_A. For , the stability of the force-free field (1) is not influenced by the flow field, which may still be significant in other respects. Perturbations transverse to the magnetic field were found to be the most unstable modes.     

Plasma-sheet dynamics and magnetospheric substorms

We present a conceptual model of the formation of the plasma sheet and of its dynamical behavior in association with magnetospheric substorms. We assume that plasma mantle particles $\text{E}\text{～}\text{×}\text{B}\text{～}$ drift toward the current sheet in the center of the tail where they are accelerated by magnetic-field annihilation to form the plasma sheet. Because of the velocity-dependent access of mantle particles to the current sheet, we argue that the convection electric field and the corresponding rate of field annihilation decrease with increasing radial distance. As a consequence, there exists no steady-state configuration for the plasma sheet, which must instead shrink continuously in thickness until the near-earth portion of the current sheet is disrupted by the formation of a magnetic neutral line. The current-sheet disruption launches a large-amplitude hydromagnetic wave which is largely reflected from the ionosphere. The reflected wave sets the neutral line in motion away from the earth; the neutral line comes to rest at a distance (which we estimate to be a few hundred earth radii) where the incoming mantle particles enter the current sheet at the local Alfvén velocity. At this “Alfvén point” reconnection ceases and the thinning of the plasma sheet begins again. Within this model, the magnetospheric substorm (which is associated with the current-sheet disruption) is a cyclical phenomenon whose frequency is proportional to the rate of convection in the magnetospheric tail.     

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.     

Non-linear motion of a weak inhomogeneity in a magneto-active plasma

The equations of motion of a magnetic field aligned column of ionization embedded in an unbounded weakly ionized plasma immersed in an external electric field E are solved to second order terms in the strength of the initial perturbation, which is assumed to be weak. It is shown that when the Hall currents induced by the internal electrostatic field are taken into account, the centre of mass of the column will, in general, move along a curved path before acquiring the familiar $\text{E ×}\text{B}\text{B}{}^2$ drift velocity.     

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.     

Rädler effect in a collisionless plasma and field-aligned currents in the magnetotail

The mean electromotive force perpendicular to the mean current (Rädler effect) by random hydromagnetic waves in a collisionless plasma is derived. The results are applied to the field-aligned currents in the Earth's magnetotail. It is shown that the Rädler-effect electric field is large enough to give the observed value of the field-aligned currents and can be identified as a possible source for the field-aligned currents.     

Magnetic pulsation behaviour in the magnetosphere inferred from whistler mode signals

During a long series of recordings of the Doppler shift of signals from NLK, Seattle, which have propagated in ducts in the whistler mode, a number of occasions have been noted where the duct has been acted on by the electric field of micropulsation events in the Pc4–5 range. Large oscillations are produced in the Doppler shift of the received VLF signal.It is shown that the field line has an antinode of motion in the equatorial plane, and that the Doppler shift is responding almost entirely to the radial component of the duct motion. The latter enables a comparison to be made between the magnetic disturbance in the magnetosphere and that seen on the ground. Some support is given to the prediction of Hughes (1974) and Inoue (1973) that the magnetospheric disturbance vector when seen on the ground is rotated 90° by the currents induced in the ionosphere. Models of the oscillating field line enable an estimate to be made of the azimuthal component of the electric field in the equatorial plane. This is typically $\text{1}\text{mV}\text{m}$. The model also predicts the north-south magnetic field strength of the transverse standing wave at the base of the magnetosphere, and this value may be compared with that seen on the ground. Values of the order 1–2 times the ground H-component or 5–10 times the ground D-component were found.