Geomagnetic Flux Tubes Research Articles

Double‐hump H+ velocity distribution in the polar wind

The polar wind is an ambipolar plasma outflow from the terrestrial ionosphere at high latitudes. As the ions drift upward along geomagnetic flux tubes, they move from collision‐dominated (ion barosphere) to collisionless (ion exosphere) regions. A transition layer is embedded between these two regions where the ion characteristics change rapidly. A Monte Carlo simulation was used to study the steady‐state flow of H+ ions through a background of O+ ions. The simulation domain covered the collision‐dominated, transition, and collisionless regions. The model properly accounted for the divergence of magnetic field lines, the gravitational force, the electrostatic field, and H+‐O+ collisions. The H+ velocity distribution, f(H+), was found to be very close to Maxwellian at low altitudes (deep in the barosphere). As the ions drifted to higher altitudes, f(H+) formed an upward tail. In the transition layer, the upward tail evolved into a second peak with a kidney bean shape, and hence, f(H+) developed a double‐humped shape. The second peak grew with altitude and eventually became dominant as the ions reached the exosphere. This behavior is due to the interplay between the electrostatic force and the velocity‐dependent Coulomb collisions. Moreover, the H+ heat flux, q(H+), was found to change rapidly with altitude in the transition layer from a positive maximum to a negative minimum. This remarkable feature of q(H+) is closely related to the coincident formation of the double‐humped structure of f(H+). The double‐hump distribution might destabilize the plasma or, at least, cause enhanced thermal fluctuations. The double‐hump f(H+), and the associated wave turbulence, have several consequences with regard to our understanding of the polar wind and similar space physics problems. The plasma turbulence can significantly alter the behavior of the plasma in and above the transition region and, therefore, should be considered in future polar wind models. The wave turbulence can serve as a signature for the formation of the double‐hump f(H+). Also, more sophisticated (than the existing bi‐Maxwellian 16‐moment) generalized transport equations might be needed to properly handle problems such as the one considered here.

Effects of spatial diffusion in the inner plasma sheet and the structure of the diffusion tensor

Abstract. A standard pair of equations is used to describe the behaviour of a single monoenergetic particle (proton or electron) population on a geomagnetic flux tube drifting in the magnetosphere. When particle losses from the drifting flux tube into the ionosphere are neglected, this behaviour is adiabatic in a thermodynamic sense. For a population of particles with an isotropic pitch-angle distribution, the generalization of that system of equations is obtained by adding radial and azimuthal spatial diffusion terms. The magnetic field is taken to be dipolar in the inner magnetosphere. The potential electric field is assumed to consist of magnetospheric convection and corotation components. Experimental data are used to estimate the radial equatorial profiles of the plasma sheet pressure. Assuming that the local time and L-shell variations are separable and supposing steady-state conditions, the expressions for the diffusion tensor components are evaluated. The influence of spatial diffusion on the radial and azimuthal profiles of the plasma pressure in the inner plasma sheet is also discussed.

Effects of spatial diffusion in the inner plasma sheet and the structure of the diffusion tensor

<strong class="journal-contentHeaderColor">Abstract.</strong> A standard pair of equations is used to describe the behaviour of a single monoenergetic particle (proton or electron) population on a geomagnetic flux tube drifting in the magnetosphere. When particle losses from the drifting flux tube into the ionosphere are neglected, this behaviour is adiabatic in a thermodynamic sense. For a population of particles with an isotropic pitch-angle distribution, the generalization of that system of equations is obtained by adding radial and azimuthal spatial diffusion terms. The magnetic field is taken to be dipolar in the inner magnetosphere. The potential electric field is assumed to consist of magnetospheric convection and corotation components. Experimental data are used to estimate the radial equatorial profiles of the plasma sheet pressure. Assuming that the local time and <i>L</i>-shell variations are separable and supposing steady-state conditions, the expressions for the diffusion tensor components are evaluated. The influence of spatial diffusion on the radial and azimuthal profiles of the plasma pressure in the inner plasma sheet is also discussed.

Dynamics of the generation of magnetic‐field‐aligned electric fields by drift currents

A study is made of the process of generation and evolution of parallel electric fields on closed geomagnetic field lines. Charge separation that is due to the different character of the drift of energetic electrons and protons of inhomogeneous magnetospheric plasma in the geomagnetic field is considered to be the factor responsible for the generation of the electric field. In a magnetic flux tube that drifts together with the cold plasma, this separation of charges is manifested as the injection of energetic electrons or protons. A numerical self‐consistent calculation of the evolution of the distribution functions of particles and of the parallel electric field is carried out for the injection of energetic electrons into the geomagnetic flux tube. An analytical investigation of the macroscopic and microscopic processes accompanying such injection is carried out. The calculations take into account cold ionospheric particles and energetic magnetospheric protons and electrons. It was found that an intense parallel electric field is produced in the form of two collisionless rarefaction shock waves that separate from the equatorial plane in the northward and southward directions. Below the front of each shock wave, there is mainly the ionospheric plasma, while behind the front there are the upward accelerated ionospheric ions and the hot magnetospheric plasma. Microscopic structure behind the shock front is formed by electrostatic oscillations of a large amplitude. Generation conditions for intense longitudinal fields are formulated: The difference in densities of injected energetic electrons and protons near the equatorial plane must exceed the initial density of cold particles, and the current‐associated velocity of cold electrons must be larger than the ion sound velocity. It is shown that these conditions can be satisfied, owing to a drift mechanism of charge separation. A rarefaction shock wave is excited with substantially smaller field‐aligned currents as compared with anomalous resistance or double layers. The observed manifestations of the rarefaction shock waves are auroral plasma cavities.

Global dynamics of the magnetosphere for northward IMF conditions

Ground-based and spacecraft observations of polar cap geophysical phenomena during periods of northward interplanetary magnetic field (IMF) show specific patterns of electric fields, field-aligned currents, aurora and particle precipitation. These are basically different from those when the IMF is southward. The total combination of observational data for northward IMF indicates rather a closed magnetosphere. This topology has led to the formation of a specific convection pattern in the distant plasma sheet. As different theoretical studies show, the connection of the IMF to geomagnetic flux tubes poleward of the cusp region may serve as the driving mechanism for plasma sheet convection and as the dynamo of current systems. Unfortunately, the direct observations of processes in the distant magnetosphere are too scarce either to accept or reject the concept of a closed magnetosphere. There are also some experimental data that are inconsistent with the closed magnetosphere topology. Definitive open or closed models must await future measurements.

Geomagnetic field‐line resonant harmonics measured by the Viking and Ampte/CCE magnetic field experiments

We report the first simultaneous observations of multiple harmonic, azimuthally polarized, ULF pulsations at two points along a geomagnetic flux tube in space. In March 1986, the elliptically orbiting equatorial AMPTE/CCE satellite was oriented with the apogee near 0830 hours magnetic local time (MLT), and the orbital plane of the polarorbiting Viking satellite was at 1000 MLT. The satellites were situated within approximately the same flux tube but with an effective separation of approximately 10 Re near L = 8 on the inbound pass of the AMPTE/CCE orbit. Structured harmonic pulsations were observed by the magnetic field experiments on both spacecraft, and they appeared to turn off and on simultaneously at both locations. Both the observations and the relative amplitudes along the magnetic field lines support recent ideas of multiple field‐line resonances of Alfvén waves.

Temporal features of the refilling of a plasmaspheric flux tube

Time‐dependent hydrodynamic equations were solved in order to study the refilling of plasmaspheric flux tubes depleted during magnetic storms. Depending on the initial density profiles in the depleted flux tube, a variety of shock formations occur during the early stage (∼1 hour) of the refilling. After this early stage, an important feature of the flow is the formation of a pair of shocks, which propagate down, one in each hemisphere. The refilling occurs by the downward propagating shocks with speeds &lt;1.5 km/s and by a simultaneous increase in the plasma density between the two shocks. The time rates of this increase in the density are given for magnetic shells L = 4 and 6.6. These rates depend on the density (N0) at the ionospheric boundaries. Depending on N0, a fair agreement is found between the refilling rates obtained from our calculations for L = 6.6 and those determined from the GEOS 2 observations. The refilling of a flux tube with different densities in the conjugate ionospheres was also considered, and it was found that after the initial stage of about one hour, the filling occurs through the propagation of only one shock from the hemisphere of the weak ionospheric source to that of the strong one. An interesting feature of the temporal evolution of the density of the shocked plasma after the early stage is the persistence of fluctuations with time periods ranging from about 2 to 10 minutes and corresponding wavelengths ranging from about one to several thousand kilometers. These fluctuations appear to be sound waves. Prior to the shock formation, counterstreaming of the ions is expected to occur in the equatorial region. The single‐fluid hydrodynamic model used in the present study is not suited to handle such multiple plasma streams. Therefore, some kinetic considerations for the formation of shocks are given. Results from the particle simulations of counterstreaming plasma expansion show that a potential hill, which eventually slows down the ion streams, leads to the formation of a shock pair in the “equatorial plane.” These shocks propagate in opposite directions in a manner analogous to that obtained with the hydrodynamic model of a geomagnetic flux tube. However, the kinetic calculations show that the shock formation occurs only when the electron temperature Te &gt; 3Ti, where Ti is the ion temperature.

Studies on Counterstreaming Plasma Expansion

Counterstreaming plasma expansion occurs in a variety of physical situations ranging from laboratory devices to plasmas in space. In such situations, the counterstreaming plasma streams consisting of accelerated ions, collide with each other. Upon this collision, the interaction of the ion streams can lead to a variety of plasma physical phenomena such as the excitation of waves and instabilities and formations of shocks. In order to study these phenomena, several types of numerical simulations were carried out. One-dimensional Vlasov simulations with Boltzmann electrons showed that the H+ streams produced by the counterstreaming expansion of an O+ - H+ ion plasma in which H+ is minor, do not couple with each other. The H+ streams pass through each other without exciting any instability which turns out to be in agreement with the linear stability of the plasma. Thus, the streams do not thermalize in the expansion region and penetrate the source plasmas, where they slow down and interact with the ambient plasmas exciting relatively strong oscillations. In order to remove the limitations on the above type of simulations, such as the plasma being one dimensional and the electrons obeying the Boltzmann law, two-dimensional particle simulations, in which electrons and ions were treated like particles, were carried out. Despite the limitations imposed by computer resources, the 2-D simulations brought out some interesting results as follows. The ion streams were seen to mix together via the ion-ion instability when Te/Ti ≳ 3, where Te and Ti are the electron and ion temperatures in the source plasmas. For Te/Ti ≳ 5, the collisions of the ion streams produced a pair of electrostatic shocks propagating in opposite directions. On the other hand, for smaller temperature ratio (5 < Te/Ti ≲ 3), the instability resulted into short wavelength waves, which evolved into highly structured nearly stationary waveforms giving spiky electric fields. Since the small scale Vlasov or particle simulations are limited in their spatial extent, their applicability to large scale counterstreaming plasma expansions in space cannot be easily appreciated. This led to the studies on counterstreaming ionospheric plasma expansion along the closed geomagnetic flux tubes in the outer region of the terrestrial plasmasphere. In such studies the hydrodynamic equations were solved. The formation of a shock pair, upon the collision of the ion streams, was always seen, irrespective of the electron-ion temperature ratio, as expected from hydrodynamic calculations. The refilling of the flux tube occurs by the downward propagation of the shocks. The refilling rates derived from the hydrodynamic calculations are found to be in fair agreement with satellite observations. The kinetic aspects of the shock formations as derived from the small-scale simulations are discussed.

A model for conjugate coupling from ionospheric dynamos in the acoustic frequency range

A model is developed for estimating the Pedersen currents driven in the conjugate ionosphere by an oscillatory ionospheric dynamo associated with acoustic waves in the upper atmosphere. The model is electrostatic within each ionosphere but uses Alfvén waves in the intervening geomagnetic flux tube. The acoustic frequency range (f ∼ 10¹–10² mHz) considered here allows for coupling to the geomagnetic micropulsation spectrum. Exercises of the model show that the conjugate coupling could be both efficient and observable (by HF sounding). During the daytime the preferred observational mode would be of plasma compression in the upper E region. During the nighttime, only observations of F‐region plasma convection would be possible. Daytime and nighttime coupling efficiencies differ markedly because of a variation in ionospheric boundary condition at the foot of the flux tube.

An updated theory of the polar wind

The ‘classical’ polar wind is an ambipolar outflow of thermal plasma from the terrestrial ionosphere at high latitudes. As the plasma escapes along diverging geomagnetic flux tubes, it undergoes four major transitions, including a transition from chemical to diffusion dominance, a transition from subsonic to supersonic flow, a transition from collision-dominated to collisionless regimes, and a transition from a heavy to a light ion. A further complication arises because of horizontal convection of the flux tubes owing to magnetospheric electric fields. Recent modelling predictions indicate that the polar wind has the following characteristics: (1) The ion and electron distributions are anisotropic and asymmetric in the collisionless regime; (2) Elevated electron temperatures ( ∼ 10,000 K) act to produce significant escape fluxes of suprathermal O + ions; (3) The interaction of the hot magnetospheric and cold ionospheric electron populations leads to a localized (double layer) electric field which accelerates the polar wind ions; (4) A time-dependent expansion produces suprathermal ions; and (5) Large perturbations lead to the formation of forward and reverse shocks. These and other results are reviewed.

Equatorial scintillations: advances since ISEA-6

Since the last equatorial aeronomy meeting in 1980, our understanding of the morphology of equatorial scintillations has advanced greatly due to more intensive observations at the equatorial anomaly locations in the different longitude zones. The unmistakable effect of the sunspot cycle in controlling irregularity belt width and electron concentration responsible for strong scintillation in the GHz range has been demonstrated. The fact that night-time F-region dynamics is an important factor in controlling the magnitude of scintillations has been recognized by interpreting scintillation observations in the light of realistic models of total electron content at various longitudes. A hypothesis based on the alignment of the solar terminator with the geomagnetic flux tubes as an indicator of enhanced scintillation occurrence and another based on the influence of a transequatorial thermospheric neutral wind have been postulated to describe the observed longitudinal variation. A distinct class of equatorial irregularities known as the bottomside sinusoidal (BSS) type has been identified. Unlike equatorial bubbles, these irregularities occur in very large patches, sometimes in excess of several thousand kilometers in the E-W direction and are associated with frequency spread on ionograms. Scintillations caused by such irregularities exist only in the VHF band, exhibit Fresnel oscillations in intensity spectra and are found to give rise to extremely long durations (~ several hours) of uninterrupted scintillations. These irregularities maximize during solstices, so that in the VHF range, scintillation morphology at an equatorial station is determined by considering occurrence characteristics of both bubble type and BSS type irregularities. The temporal structure of scintillations in relation to the in situ measurements of irregularity spatial structure within equatorial bubbles has been critically examined. A two-component irregularity spectrum with a shallow slope ( p 1 ~ 1.5) at long scalelengths (> 1km) and steep slope ( p 2 ~−3) at shorter scalelengths has been found in both vertical and horizontal spectra. Phase and intensity scintillation modelling was found to be consistent with this two-component irregularity spectrum. Finally, the information provided by the major experimental undertaking represented by Project Condor in the fields of night-time scintillations and zonal irregularity drifts with be briefly outlined.

Control of the seasonal and longitudinal occurrence of equatorial scintillations by the longitudinal gradient in integrated E region Pedersen conductivity

An enigma of equatorial research has been the observed seasonal and longitudinal occurrence patterns of equatorial scintillations (and range‐type spread F). We resolve this problem by showing that the seasonal maxima in scintillation activity coincide with the times of year when the solar terminator is most nearly aligned with the geomagnetic flux tubes. That is, occurrence of plasma density irregularities responsible for scintillations is most likely when the integrated E‐region Pedersen conductivity is changing most rapidly. Hence the hitherto puzzling seasonal pattern of scintillation activity, at a given longitude, becomes a simple deterministic function of the magnetic declination and geographic latitude of the magnetic dip equator. This demonstrated relationship is consistent with equatorial irregularity generation by the collisional Rayleigh‐Taylor instability and irregularity growth enhancement by the current convective and (wind‐driven) gradient drift instabilities. Some discrepancies in this relationship, however, have been found in scintillation data obtained at lower radio frequencies (below, say, 300 MHz) that suggest the presence of other irregularity‐influencing processes. The role of field‐aligned currents, associated with the longitudinal gradient in integrated E‐region Pedersen conductivity produced at the solar terminator, in equatorial irregularity generation via the current convective instability has not been discussed previously.

A flux preserving method of coupling first and second order equations to simulate the flow of plasma between the protonosphere and the ionosphere

This paper describes a numerical method developed to solve the interhemispheric flow of thermal plasma, heat and momentum along closed magnetic field tubes in the plasmasphere. The essence of our technique incorporates the best aspects of two former approaches into a single unified code. The first is the so-called shooting or searching method, which employs integro-differential equations, and the second involves the solution of second order nonlinear partial differential equations by conventional iterative techniques. The former method attains optimal performance above ∼2000 km, and the latter below this altitude. The combined approach yields a satisfactory solution over an entire geomagnetic flux tube, encompassing two low altitude regimes, in the northern and southern ionospheres, and a high altitude regime spanning the distance between them. We demonstrate that the solution is stable and simulate the collapse of the postsunset ionosphere.

True height calculation from ionograms

Since the last equatorial aeronomy meeting in 1980, our understanding of the morphology of equatorial scintillations has advanced greatly due to more intensive observations at the equatorial anomaly locations in the different longitude zones. The unmistakable effect of the sunspot cycle in controlling irregularity belt width and electron concentration responsible for strong scintillation in the GHz range has been demonstrated. The fact that night-time F-region dynamics is an important factor in controlling the magnitude of scintillations has been recognized by interpreting scintillation observations in the light of realistic models of total electron content at various longitudes. A hypothesis based on the alignment of the solar terminator with the geomagnetic flux tubes as an indicator of enhanced scintillation occurrence and another based on the influence of a transequatorial thermospheric neutral wind have been postulated to describe the observed longitudinal variation.A distinct class of equatorial irregularities known as the bottomside sinusoidal (BSS) type has been identified. Unlike equatorial bubbles, these irregularities occur in very large patches, sometimes in excess of several thousand kilometers in the E-W direction and are associated with frequency spread on ionograms. Scintillations caused by such irregularities exist only in the VHF band, exhibit Fresnel oscillations in intensity spectra and are found to give rise to extremely long durations (~ several hours) of uninterrupted scintillations. These irregularities maximize during solstices, so that in the VHF range, scintillation morphology at an equatorial station is determined by considering occurrence characteristics of both bubble type and BSS type irregularities.The temporal structure of scintillations in relation to the in situ measurements of irregularity spatial structure within equatorial bubbles has been critically examined. A two-component irregularity spectrum with a shallow slope (p1 ~ 1.5) at long scalelengths (> 1km) and steep slope (p2 ~−3) at shorter scalelengths has been found in both vertical and horizontal spectra. Phase and intensity scintillation modelling was found to be consistent with this two-component irregularity spectrum.Finally, the information provided by the major experimental undertaking represented by Project Condor in the fields of night-time scintillations and zonal irregularity drifts with be briefly outlined.

Electron density in the plasmasphere: Whistler data on solar cycle, annual, and diurnal variations

Whistler data are used to present a statistical view of equatorial plasmaspheric electron density neq and associated tube electron content NT (defined as the number of electrons in a geomagnetic flux tube of 1cm² cross‐sectional area at 1000km altitude and extending to the magnetic equator). The data were acquired between 1959 and 1973 at Byrd (L ≃ 7), Eights (L ≃ 4), and Siple (L ≃ 4), Antarctica, which are within 1 hour of the same geomagnetic meridian, and from Stanford, California (L ≃ 2). The plasmaspheric neq profile beyond L ≃ 3 is dominated by variations associated with magnetic disturbances and subsequent recovery. In the aftermath of disturbances the plasmasphere tends to be divided into an inner ‘saturated’ region, which is in equilibrium with the underlying ionosphere in a diurnal average sense, and an outer ‘unsaturated’ region, which is still filling with plasma from below. In the outer plasmasphere byond ˜3.5 RE, diurnal variations appear as relatively small effects superimposed on larger storm‐associated variations. Large numbers of whistler traces (as many as 3000 in some cases) were scaled for each of several months. These data sets form the basis for approximations to neq profiles to form log10 (neq) = aL + b. These profiles are offered for reference use in estimating plasmasphere density levels. The previously reported annual and solar cycle variations are further documented by new evidence that these effects diminish with increasing L beyond L ≃ 3.

The electrostatic field at the magnetopause

The discharge through the magnetosphere-ionosphere circuit of the electrostatic field at the magnetopause is examined quantitatively using an idealized circuit analogue. The two geomagnetic flux tubes linking the magnetopause to the ionosphere are treated as uniform transmission lines and the magnetopause and ionosphere are regarded as terminal impedances. It is argued that the electrostatic field is neutralized predominantly by the polarization of the ambient magnetospheric plasma at the magnetopause. The characteristic time constant for the discharge of the residual electrostatic field through the magnetosphere-ionosphere circuit is of the order of a few hours. Therefore the residual field seems unlikely to be completely discharged unless the solar wind flux remains steady for about a day. Nevertheless, the tendency for the residual field to be discharged through the magnetosphere-ionosphere circuit generates hydromagnetic ‘twist’ (TEM) waves which travel along the geomagnetic lines of force to the polar ionosphere. These waves generate Hall currents in the ionosphere, which contribute to the magnetic agitation observed at high latitudes.

An approximate flow equation for geomagnetic flux tubes and its application to polar substorms

A recent model of polar substorms suggests they are the result of an impulsive recombination of magnetic field lines across the neutral sheet in the tail of the magnetosphere. The flow of flux tubes within the magnetosphere is shown to be dominated by the discharging action of the ionosphere on flux tubes. This fact enables an approximate flow equation for flow within the magnetosphere to be developed by integrating along flux tubes. This equation is applied to the above model of polar substorms and is shown to give reasonable agreement with the following experimental observations: (i) the velocity and flow pattern of auroral patches; (ii) the height and shape of the auroral breakup bulge; and (iii) the bay current system, including the westward electrojet under the assumption that the westward electrojet is current-induced by the southward component of flow of flux tube feet in the high conductivity strips under auroral arcs. These strips are expected to exhibit a Cowling conductivity. The westward traveling surge is probably caused by an increasing width of the recombination slot in the tail of the magnetosphere. The current flow down field lines and through the ionosphere results in a density (and hence pressure) decrease in the neutral sheet at the west edge of the recombination slot, and thus causes a corresponding westward propagation of the west edge of the recombination slot. Application of the flow equations to the viscous bounday layer problem indicates an exponential falloff in velocity from the magnetosphere boundary with a 1/e distance of 5 × 104 m.

Cyclotron-resonance amplification of VLF and ULF whistlers

Electromagnetic signals that propagate through the magnetosphere exchange energy with nonthermal charged particles by the cyclotron-resonance mechanism. The interaction is due to a Doppler shift of the propagation frequency ω to the cyclotron frequency ωc of the charged particle that allows the particle to resonate with the electromagnetic fields. The dominant exchange is between electrons around 1 kev and VLF whistlers that propagate in the right-hand mode and between protons around 1 kev and ULF whistlers (Pc 1 geomagnetic micropulsations) that propagate in the left-hand mode. The complex wave number k(ω) = kr + iki for propagation in a hot uniform plasma parallel to a static magnetic field is assumed to describe whistler properties locally in the magnetosphere. The power transfer function A(ω), which relates the input and output power spectrums, is determined by the path integral of ki along a geomagnetic flux tube. Spectrums of A for both VLF and ULF whistlers have been evaluated for a variety of energy and pitch-angle distributions of the form E−n sinm α. In general, A has an amplification maximum just below a sharp absorption cutoff, which is consistent with observations. The detailed input-output spectrums of whistlers that are necessary to test the theory are not available yet. When these spectrums are measured, this interaction may provide a possible method for mapping the phase space distribution of nonthermal particles in the magnetosphere.