Ring Current Region Research Articles

A quantitative model of the magnetosphere with poloidal vector fields

Abstract. A quantitative model of the magnetospheric magnetic field is developed using poloidal vector fields. This formalism is applied to the ring current region, the distant field and the return currents. The tail model is similar to the unwarped model of Tsyganenko. Several sets of coefficients are obtained for different Kp through a fit of the NSSDC data base. Experimental ΔB contours and theoretical distributed currents contours are correctly described and are Kp-dependent. Field line topology problems and poor ring current description observed in models of similar complexity are avoided. Computer time has been kept reasonable and makes this model particularly adapted to intensive-type calculations.Key words. Magnetospheric physics (magnetospheric · configuration and dynamics).

Structure of the low‐latitude boundary layer: A case study with Geotail data

A case study of the structure of the low‐latitude boundary layer (LLBL) on dawnside (0600–0900 MLT) is reported. It is shown that the LLBL consists of two regions, the sheath‐like region and the mixing region. The sheath‐like region is where cold ions from the magnetosheath are flowing tailward. Detailed study has shown that this region is produced by reconnection and subsequent draping of open field lines over the dayside magnetosphere [Fujimoto et al., 1997]. The mixing region, on the other hand, is characterized by mixing of cold ions from the magnetosheath with the magnetospheric hot ions. Thermal electrons (< 500 eV) enhanced bidirectionally along field lines are detected to accompany these mixed ions. The balanced bi‐directional flux is taken to indicate the closed topology of the field lines. An interesting finding is that the flow direction in this region tends to be sunward. Flow in the mixing region and the adjacent plasma sheet is faster sunward. than in the ring current region, suggesting that these two constitute a channel of sunward returning convection in the dayside outer magnetosphere for this particular case. More new information on the mixing region from the present study is the ion distribution function showing a three‐component feature and autocorrelation between plasma density and the degree of electron bidirectional heating. These observational facts would offer clues for understanding of the mixing region formation, which still remains open.

Theory of magnetospheric standing hydromagnetic waves with large azimuthal wave number: 4. Standing waves in the ring current region

There is a rich variety of observations of long‐period pulsations in the ring current region. One class of such pulsations is characterized by large azimuthal wave numbers and close confinement to a field line. In this paper, computations are made of the eigenfrequencies and fields of standing oscillations which can exist in a realistic self‐consistent magnetohydrodynamic model of such a region. The model, which depends on a few simple parameters, allows for the shape of the field line to be distorted from a dipole. In this paper it is limited to isotropic pressure. The magnetic field and transverse gradient of pressure can be defined. It is assumed that growth and loss processes are small and in balance because the plasma has reached a quasi‐linear equilibrium state. The computations show that a rich variety of compressional modes can exist. They are much more complex than simple coupled Alfvén and magnetosonic modes which are often invoked in such circumstances. At some points along the field line, such modes may be closely coupled while at other points they are essentially uncoupled with different wavelengths. This leads to modes with complex nonharmonic structures. It is noted that the transverse pressure gradient allows an MHD instability, related to the flute instability, to exist in appropriate circumstances. Such calculations should allow good comparison of theory and observation.

Geomagnetic storms, the Dst ring-current myth and lognormal distributions

The definition of geomagnetic storms dates back to the turn of the century when researchers recognized the unique shape of the H-component field change upon averaging storms recorded at low latitude observatories. A generally accepted modeling of the storm field sources as a magnetospheric ring current was settled about 30 years ago at the start of space exploration and the discovery of the Van Allen belt of particles encircling the Earth. The Dst global ‘ring-current’ index of geomagnetic disturbances, formulated in that period, is still taken to be the definitive representation for geomagnetic storms. Dst indices, or data from many world observatories processed in a fashion paralleling the index, are used widely by researchers relying on the assumption of such a magnetospheric current-ring depiction. Recent in situ measurements by satellites passing through the ring-current region and computations with disturbed magnetosphere models show that the Dst storm is not solely a main-phase, growth to disintegration, of a massive current encircling the Earth. Although a ring current certainly exists during a storm, there are many other field contributions at the middle-and low-latitude observatories that are summed to show the ‘storm’ characteristic behavior in Dst at these observatories. One characteristic of the storm field form at middle and low latitudes is that Dst exhibits a lognormal distribution shape when plotted as the hourly value amplitude in each time range. Such distributions, common in nature, arise when there are many contributors to a measurement or when the measurement is a result of a connected series of statistical processes. The amplitude-time displays of Dst are thought to occur because the many time-series processes that are added to form Dst all have their own characteristic distribution in time. By transforming the Dst time display into the equivalent normal distribution, it is shown that a storm recovery can be predicted with remarkable accuracy from measurements made during the Dst growth phase. In the lognormal formulation, the mean, standard deviation and field count within standard deviation limits become definitive Dst storm parameters.

Lower hybrid turbulence and ponderomotive force effects in space plasmas subjected to large‐amplitude low‐frequency waves

It is demonstrated that large‐amplitude low‐frequency waves (LFW) can generate lower hybrid waves (LHW) in the auroral zone and ring current region. The LHW could then heat the ions. The ion energization due to the LHW may be comparable with that produced by the ponderomotive force of the LFW.

Low-frequency electric field fluctuations excited by ring current protons

Energetic protons haying ring type distributions are shown to generate low-frequency electrostatic waves, propagating nearly transverse to the geomagnetic field lines, in the ring current region by exciting Mode 1 arid Mode 2 nonresonant instabilities and a resonant instability. Mode 1 nonresonant instability has frequencies around ~4 Hz with transverse wavelengths of ~(8–80) km, and it is likely to occur in the region L = (7–8). Mode 2 nonresonant instability can generate frequencies ~(850–1450) Hz with transverse wavelengths ~(2–20) km. The typical frequencies and transverse wavelengths associated with the resonant instability are (950–1250) Hz and (30–65) km. Both the Mode 2 nonresonant instability and the resonant instability can occur in the ring current region with L = (4–6). The low-frequency modes driven by energetic protons could attain maximum saturation electric field amplitude varying from 0.8 mV/m to 70 mV/m. It is suggested that the turbulence produced by the low-frequency modes may cause pitch angle scattering of ring current protons in the region outside the plasmapause resulting in the ring current decay.

One‐ and two‐dimensional simulations of whistler mode waves in an anisotropic plasma

We present results from self‐consistent, one‐ and two‐dimensional, electromagnetic simulations of the electron whistler mode instability relevant to the near‐Earth nightside plasma sheet region during geomagnetically disturbed times. Specifically, we study the evolution of energetic, anisotropic (T⊥ > T∥) electron distributions that are injected into the nightside ring current region at geomagnetically disturbed times, the resulting growth of electron whistler mode waves, and subsequent electron pitch angle diffusion via electron whistler wave‐particle interactions. Growth of whistler mode waves from an initial pitch angle anisotropy (T⊥ ≈ 4 T∥) is studied in the strong pitch angle diffusion regime (defined as having scattering times much shorter than a typical electron bounce time in the near Earth's dipolar field). The quasi‐linear and subsequent nonlinear evolution of waves and the corresponding migration of electrons in velocity space is followed over timescales such that ion motion may be neglected. Our simulations contain wave frequencies and growth rates that are a significant fraction of the electron gyrofrequency (ω ∼ 0.5ωce, γ ∼ 0.1ωce being typical) and the simultaneous evolution of waves propagating both parallel and nonparallel to the ambient magnetic field direction. Effects due to these are not usually accounted for in applications of quasi‐linear theory to the problem of electron whistler wave‐particle interactions, so that our self‐consistent simulations of the electron whistler instability provide an important insight into the applicability of quasi‐linear theory to the velocity space diffusion of electrons due to electron whistler wave‐particle interactions. We examine the dependence of whistler mode wave growth rates, nonlinear wave mode saturation, and pitch angle diffusion rates on the β value of the hot electron species which contains the resonant population, and we compare the differences between results of one‐ and two‐dimensional simulations. In general, we have found significantly larger average growth rates in a one‐dimensional than in a two‐dimensional geometry, by up to a factor of ∼2–3, with the difference between such growth rates becoming larger as β increases. As a result, we find pitch angle diffusion rates are significantly larger (by up to a factor of ∼10) in a one‐dimensional geometry, and pitch angle diffusion rates increase as β increases. During the early wave growth period of the instability, pitch angle diffusion rates Dα have been found to scale to magnetic wave energy Bw², approximately Dα ∝ Bw². We also show that in the self‐consistently evolved system (containing several wave modes), the pitch angle diffusion is still consistent with a usual quasi‐linear approach in which resonant particles are taken to diffuse along surfaces of constant wave frame energy.

Generation mechanisms for magnetosphere‐ionosphere current systems deduced from a three‐dimensional MHD simulation of the solar wind‐magnetosphere‐ionosphere coupling processes

Mechanisms that generate the field‐aligned current (FAC) systems in the magnetosphere‐ionosphere coupling scheme by virtue of the solar wind‐magnetosphere interaction are investigated with a three‐dimensional magnetohydrodynamic (MHD) simulation. As a simulation scheme, the finite volume total variation diminishing (TVD) scheme on an unstructured grid system is employed for precise calculations of the ionospheric region. In the ionosphere, the divergence of the Pedersen and Hall currents is matched with FAC, mainly assuming uniform conductivity. The present calculation reproduces the traditional region 1 and 2 currents in the polar ionosphere, for both the northward and southward interplanetary magnetic fields (IMFs). The calculated magnitude of the region 1 current becomes large on the dayside, in agreement with observational results. For the northward IMF, NBZ currents that dominate the entire polar cap are obtained, with a maximum on the dayside. This current is totally absent in the southward IMF result. Corresponding to the FACs, the northward IMF results in multicell convection in the polar ionosphere, and the southward IMF results in two‐cell convection. On the evening side, the calculated region 1 currents flow almost along the field lines away from the Earth toward the magnetospheric low‐latitude boundary layer (LLBL), then flow up the magnetopause across the field lines to high latitudes. The region 1 currents in the morning side are similar but opposite in direction. In the noon‐midnight meridian (xz) plane, the main part of the region 1 current passes the tailward side of the cusp in the magnetosphere. The region 1 current converges to a very narrow region in the noon‐midnight meridian (xz) plane when the IMF is northward, whereas it passes the noon‐midnight meridian (xz) plane diverging to wide regions in the x direction when the IMF is southward. These differences are attributed to the efficient current‐driving effect (J · E < 0) of the high‐latitude boundary layer (HLBL) for the southward IMF. The calculated region 2 currents on the evening (morning) side flow toward (away from) the Earth and close in the inner magnetosphere near the equator. The evening region 2 currents flow azimuthally from the inner boundary of the plasma sheet and show a sharp turn toward the Earth at the ring current region where strong drivers are distributed. For the northward IMF, the NBZ current that flows toward (away from) the evening (morning) polar cap ionosphere is connected with currents in the magnetotail. In the NBZ current loop, there is no remarkable driver or load (J · E > 0). In the evening magnetosphere, the NBZ current that flows into the dayside ionosphere passes the low‐latitude side of the NBZ current that flows into the nightside ionosphere, then it turns aside to the outward (+y) direction and turns back before reaching the dayside ionosphere. Consequently, the dayside NBZ current flows from the low‐latitude side of the lobe, while the nightside NBZ current flows from the high‐latitude side of the lobe. Calculation assuming nonuniform ionospheric conductivity results in a wedge‐current‐like structure in the evening side. This result indicates that the current generated in the ionosphere cannot be ignored in the magnetosphere‐ionosphere current systems.

The Inner Magnetosphere: A Review

This paper addresses research achievements during roughly the period 1991–1993 pertaining to the inner magnetosphere including the radiation belts, plasmasphere, and ring current region. It also addresses issues concerning the magnetic fields, electrical currents, and particle precipitation properties that relate to this region of the solar-terrestrial system. Recent analysis and modeling of magnetospheric substorms and geomagnetic storms affecting the inner edge of the plasma sheet are discussed and the regions from the geostationary orbit inward toward the Earth are examined in light of new observational and theoretical tools.

Magnetic Storm Development and Its Quantification for Aims of Modeling.

Using a large sample of storms of different intensity the ring current magnetic field development is followed in terms of varying interplanetary conditions. It is shown that although the storm depression field is associated with energy input into the magnetosphere, the sustained IEF intensity <-5 mV/m as a condition for the occurrence of intense storms appears not to be of general validity. Quantification of the magnetic storm development indicates the role of the actual state of the magnetosphere in the development of its response on interplanetary medium forcing. Ring current energization is considered for some storm models represented by pairs of energy injection rate and time decay parameter. A number of models are juxtaposed quantitatively. The adequacy of modeling of storm profiles and the significance of decay parameter in the magnetic storm development is discussed from the viewpoint of consistency of energy injection rate and energy decay rate and also with regard to an adequate distribution of dissipated energy within the ring current region and auroral ionosphere.

Ion transport and loss in the Earth's quiet ring current: 1. Data and standard model

We have studied the transport and loss of ions in the Earth's quiet time ring current, comparing the standard radial diffusion model developed for the higher‐energy radiation belt particles with measurements of the lower‐energy ring current ions. We compiled a data set with full local time coverage from the quietest days seen by the AMPTE/CCE/CHEM instrument in near‐equatorial orbit at L=2‐9 RE. This data set provides, for the first time, ionic composition information in an energy range that includes the bulk of the ring current energy density, 1‐300 keV/e. Protons were found to dominate the quiet time energy density at all altitudes, peaking near L∼4 at 60 keV cm−3, with much smaller contributions from O+ (1‐10%), He+ (1‐5%), and He++ (&lt;1%). The proton densities were azimuthally symmetric excepting a small dawn‐dusk distortion caused by the cross‐tail electric field, and a plasma sheet contribution for L&gt;6 near midnight. Thus the standard radial diffusion model, which incorporates an outer source boundary at 7.5 RE from the Earth, and diffuses ions earthward while undergoing charge exchange and Coulomb energy loss, should fit the data. We improved on previously used model loss processes by incorporating the latest atomic physics cross sections from the literature, updating the last survey done 15 years ago. We also included the effects of finite electron temperature on Coulomb drag. A χ² minimization procedure was used to fit the amplitudes of the standard electric radial diffusion coefficient, giving DLLE = 5.8 × 10−11 RE²/s. Yet the model was unable to fit the data (to within a factor of 10) over 50% of the energy and radial ranges of the data set, particularly at L&lt;4 or E&lt;30 keV. Assuming that the loss terms in the model are correct, the data can be inverted to extract a radial diffusion coefficient that had nearly constant amplitude from 2‐7 RE. This suggests that another transport mechanism is operating in the ring current region, which is strongest at smaller radial distances. We speculate that fluctuating ionospheric electric fields may be the source of this additional diffusion.

A study of low‐latitude VHF scintillations in relation to electric fields during magnetic storms

Nighttime VHF scintillations observed at Lunping (magnetic latitude 14.7°N) during four specific seasonal storms showed four different types of behaviour: Scintillation activity was found to be either inhibited or triggered during magnetic storms depending on the phase of the storm and its local time. A qualitative explanation for this behaviour is attempted in terms of storm time electric fields. The triggering of postmidnight scintillation activity during the recovery phase seems to be a result of penetration of the dusk‐dawn electric fields due to shielding charges developed in the ring current region,while inhibition of usual premidnight scintillation activity seems to be related to the ionospheric disturbance dynamo electric fields acting opposite to normal fields. One case where postsunset scintillation activity was triggered seems to be a result of penetration of dawn‐dusk convection electric field which developed following the main phase onset.

An empirical static model of low energy ring current ions

The empirical model consists of a set of average equatorial energy and pitch‐angle distributions of fluxes of H+ and O+ in the energy range 110 eV to 35 keV for a number of local time and L ranges. It was constructed from data acquired by the Lockheed IMS‐LO ion mass spectrometer on CRRES (apogee 6.3 RE, inclination 18°) which sampled a substantial portion of the ring current region. Equatorial distributions were constructed by mapping the ion data adiabatically from the satellite location to the equatorial plane, which was taken to be the minimum B surface. There the data were binned by their energy and equatorial pitch angle and sorted into ranges of L and local time. Equatorial distributions from many orbits were accumulated and averaged to construct the average equatorial distributions. This static model represents the average magnetosphere during the CRRES mission, August 1990 through October 1991, regardless of magnetic activity. In the absense of parallel electric fields and wave‐particle interactions, the model may be used to estimate the ion distributions at non‐equatorial magnetic latitudes by adiabatic mapping.

Radial transport of storm time ring current ions

Radial transport of energetic ions for the development of the main phase of geomagnetic storms is investigated with data from the medium energy particle analyzer (MEPA) on the Charge Composition Explorer (CCE) spacecraft, which monitored protons (Ep &gt; 56 keV), helium ions (EHe &gt; 72 keV), and the carbon‐nitrogen‐oxygen group, which is mostly dominated by oxygen ions (E0 &gt; 137 keV). From a study of four geomagnetic storms, we show that the flux increase of these ions in the inner ring current region (L ≲ 5) can be accounted for by an inward displacement of the ring current population by ∼0.5 to 3.5 RE. There is a general trend that a larger inward displacement occurs at higher L shells than at lower ones. These results are in agreement with previous findings. The radially injected population consists of the prestorm population modified by substorm injections which occur on a much shorter time scale than that for a storm main phase. It is also found that the inward displacement is relatively independent of ion mass and energy, suggesting that the radial transport of these energetic ions is effected primarily by convective motion from a large electric field or by diffusion resulting from magnetic field fluctuations.

Saturation of Alfven oscillations in the ring current region due to generation of lower hybrid waves

The possibility of flux generation of lower hybrid oscillations in the ring current region of the Earth's magnetosphere is suggested in this paper. The energy level of lower hybrid oscillations can exceed the modulational instability threshold, which leads to the formation of caverns. The consequences of this are qualitatively analysed. Also, an assumption is made that the flux instability of lower hybrid oscillations may limit the level of Alfvén oscillations in the ring current region.

Effects of the Magnetospheric Currents on the Sq-Field and a New Magnetic Index Characterizing Sq Dynamo Current Intensity.

The magnetic fields caused by the magnetospheric and ionospheric current systems are calculated. These current systems are Chapman-Ferraro current system (C-F), magnetotail current system (MTL), symmetric ring current system (SRC), region 1 field-aligned current system (FAC1), partial ring current-region 2 field-aligned current-ionospheric current system (PRFI), and the ionospheric dynamo current system (IDC). The variable magnetic fields recorded at the ground surface are the superposition of these fields and other disturbance fields. The spatial-temporal characteristics of these fields are comparatively studied, and a method for separating dynamo-field from the total field is developed. In order to describe conveniently dynamo-field intensity, a new magnetic index, “Sq index”, is proposed.

Plasma Pressure Profile in Ring Current Region

The equilibrium equation in the field line coordinate system is derived in the ring current region where the Tsyganenko and Usmanov (TU) model of magnetic field is adopted. A generalized Euler difference method for solving two-dimensional equilibrium equations is developed. The numerical result show that a nearly isotropic plasma pressure profile exists in the ring current region. On the equator, with increasing L, the plasma pressure attend to more isotropic. Most of the results are in good agreement with observations.

An evaluation of the Tsyganenko Magnetic Field Model

A data set of more than 22,000 vector averages of the magnetosphere magnetic field over 0.5 RE regions is used to evaluate Tsyganenko's 1982 and 1987 magnetospheric magnetic field models. The magnetic field predicted by the model in various regions is compared to observations to find systematic discrepancies which future models might address. While agreement is generally good, discrepancies are noted which include: (1) a lack of adequate field line stretching in the tail and ring current regions; (2) an inability to predict weak enough fields in the polar cusps; and (3) a deficiency of Kp as a predictor of the field configuration.

Energetic particles in the environment of the Earth's magnetosphere

This review summarizes the work in the field of magnetospheric energetic particles during the years 1987–1989. Out of a wealth of contributions it concentrates on a few topics. First it follows the path of ions extracted out of the polar ionosphere and their acceleration parallel and perpendicular to the magnetic field, as well as their subsequent transport into the equatorial magnetosphere and tail region. Then it focuses on acceleration of ions in the magnetotail and the related characteristics in the boundary layers including consequences for current substorm modeling. In the ring current region, the AMPTE and VIKING missions have made possible detailed studies of charge state and pitch-angle distributions as well as their variations during magnetospheric storms and substorms, from which conclusions on the transport and loss processes can be drawn. Recently, observations of energetic particles from orbiting nuclear reactors in the magnetosphere, which can be used as tracers for these satellites, have been made public. However, this may also constitute a serious background problem for future γ-astronomy missions with an increased sensitivity of the instrumentation. Finally, leading beyond the boundaries of the magnetosphere, attention is drawn to the still ongoing debate on the source of energetic particles upstream of the Earth's bow-shock and the respective importance of particle leakage and/or acceleration at the magnetospheric boundaries.

Dynamics of single‐particle orbits during substorm expansion phase

Features of ion trajectories during “taillike” to “dipolelike” magnetic transitions are examined by means of three‐dimensional particle codes. It is demonstrated that the large electric fields induced by the “collapse” of the geomagnetic tail result in enhanced earthward convection of the midtail (∼10 RE) magnetospheric populations. It is shown that the particle motion is controlled, to a major extent, by drifts that are negligible in steady state, namely, (1) in the direction parallel to the magnetic field, a centrifugal acceleration related to the rapid E×B transport, which can account for creation of new high‐altitude mirror points, (2) perpendicularly to the magnetic field, a drift of polarization which possibly yields “frozen‐in” violation and transient breaking of the first adiabatic invariant. In this latter case the simulations emphasize that the guiding center validity is at stake depending upon particle mass and/or charge state and allow us to distinguish three types of ion behavior (adiabatic, nonadiabatic and gyrophase dependent, nonadiabatic and gyrophase independent) according to injection depth in the plasma sheet. Also, systematic orbit calculations show that the low‐latitude populations are most affected by the “collapse” of the geomagnetic tail and reveal possible dramatic (from hundreds of eV up to hundreds of keV) accelerations of the particles. These trajectory results are of relevance to explain various storm time signatures at geosynchronous altitudes and provide a populating mechanism for the ring current region.