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1.
Although the auroral substorm has been long regarded as a manifestation of the magnetospheric substorm, a direct relation of active auroras to certain magnetospheric processes is still debatable. To investigate the relationship, we combine the data of the UV imager onboard the Polar satellite with plasma and magnetic field measurements by the Geotail spacecraft. The poleward edge of the auroral bulge, as determined from the images obtained at the LHBL passband, is found to be conjugated with the region where the oppositely directed fast plasma flows observed in the near-Earth plasma sheet during substorms are generated. We conclude that the auroras forming the bulge are due to the near-Earth reconnection process. This implies that the magnetic flux through the auroral bulge is equal to the flux dissipated in the magnetotail during the substorm. Comparison of the magnetic flux through the auroral bulge with the magnetic flux accumulated in the tail lobe during the growth phase shows that these parameters have the comparable values. This is a clear evidence of the loading–unloading scheme of substorm development. It is shown that the area of the auroral bulge developing during substorm is proportional to the total (magnetic plus plasma) pressure decrease in the magnetotail. These findings stress the importance of auroral bulge observations for monitoring of substorm intensity in terms of the magnetic flux and energy dissipation.  相似文献   

2.
Consequences of the solar wind input observed as large scale magnetotail dynamics during substorms are reviewed, highlighting results from statistical studies as well as global magnetosphere/ionosphere observations. Among the different solar wind input parameters, the most essential one to initiate reconnection relatively close to the Earth is a southward IMF or a solar wind dawn-to-dusk electric field. Larger substorms are associated with such reconnection events closer to the Earth and the magnetotail can accumulate larger amounts of energy before its onset. Yet, how and to what extent the magnetotail configuration before substorm onset differs for different solar wind driver is still to be understood. A strong solar wind dawn-to-dusk electric field is, however, only a necessary condition for a strong substorm, but not a sufficient one. That is, there are intervals when the solar wind input is processed in the magnetotail without the usual substorm cycle, suggesting different modes of flux transport. Furthermore, recent global observations suggest that the magnetotail response during the substorm expansion phase can be also controlled by plasma sheet density, which is coupled to the solar wind on larger time-scales than the substorm cycle. To explain the substorm dynamics it is therefore important to understand the different modes of energy, momentum, and mass transport within the magnetosphere as a consequence of different types of solar wind-magnetosphere interaction with different time-scales that control the overall magnetotail configuration, in addition to the internal current sheet instabilities leading to large scale tail current sheet dissipation.  相似文献   

3.
The magnetotail and substorms   总被引:5,自引:0,他引:5  
The tail plays a very active and important role in substorms. Magnetic flux eroded from the dayside magnetosphere is stored here. As more and more flux is transported to the magnetotail and stored, the boundary of the tail flares more, the field strength in the tail increases, and the currents strengthen and move closer to the Earth. Further, the plasma sheet thins and the magnetic flux crossing the neutral sheet lessens. At the onset of the expansion phase, the stored magnetic flux is returned from the tail and energy is deposited in the magnetosphere and ionosphere. During the expansion phase of isolated substorms, the flaring angle and the lobe field strength decrease, the plasma sheet thickens and more magnetic flux crosses the neutral sheet.In this review, we discuss the experimental evidence for these processes and present a phenomenological or qualitative model of the substorm sequence. In this model, the flux transport is driven by the merging of the magnetospheric and interplanetary magnetic fields. During the growth phase of substorms the merging rate on the dayside magnetosphere exceeds the reconnection rate in the neutral sheet. In order to remove the oversupply of magnetic flux in the tail, a neutral point forms in the near earth portion of the tail. If the new reconnection rate exceeds the dayside merging rate, then an isolated substorm results. However, a situation can occur in which dayside merging and tail reconnection are in equilibrium. The observed polar cap electric field and its correlation with the interplanetary magnetic field is found to be in accord with open magnetospheric models.  相似文献   

4.
At the ionospheric level, the substorm onset (expansion phase) is marked by the initial brightening and subsequent breakup of a pre-existing auroral arc. According to the field line resonance (FLR) wave model, the substorm-related auroral arc is caused by the field-aligned current carried by FLRs. The FLRs are standing shear Alfvén wave structures that are excited along the dipole/quasi-dipole lines of the geomagnetic field. The FLRs (that can cause auroral arc) thread from the Earthward edge of the plasma sheet and link the auroral arc to the plasma sheet region of 6–15 R E. The region is associated with magnetic fluctuations that result from the nonlinear wave-wave interactions of the cross-field current-instability. The instability (excited at the substorm onset) disrupts the cross-tail current which is built up during the growth phase of the substorms and results in magnetic fluctuations. The diversion of the current to polar regions can lead to auroral arc intensification. The current FLR model is based on the amplitude equations that describe the nonlinear space-time evolution of FLRs in the presence of ponderomotive forces exerted by large amplitude FLRs (excited during substorms). The present work will modify the FLR wave model to include the effects arising from magnetic fluctuations that result from current disruption near the plasma sheet (6–15 R E). The nonlinear evolution of FLRs is coupled with the dynamics of plasma sheet through a momentum exchange term (resulting from magnetic fluctuations due to current disruption) in the generalized Ohm's law. The resulting amplitude equations including the effects arising from magnetic fluctuations can be used to study the structure of the auroral arcs formed during substorms. We have also studied the role of feedback mechanism (in a dipole geometry of the geomagnetic field) in the formation of the discrete auroral arc observed on the nightside magnetosphere. The present nonlinear dispersive model (NDM) is extended to include effects arising from the low energy electrons originating from the plasma sheet boundary layer. These electrons increase the ionospheric conductivity in a localized patch and enhance the field-aligned current through a feedback mechanism. The feedback effects were studied numerically in a dipole geometry using the the NDM. The numerical studies yield the magnitude of the field-aligned current that is large enough to form a discrete auroral arc. Our studies provide theoretical support to the observational work of Newell et al. that the feedback instability plays a major role in the formation of the discrete auroral arcs observed on the nightside magnetosphere.  相似文献   

5.
Substorm timings and timescales: A new aspect   总被引:1,自引:0,他引:1  
Meng  Ching-I  Liou  Kan 《Space Science Reviews》2004,113(1-2):41-75
The magnetospheric substorm is a fundamental element of magnetospheric disturbances. After more than 40 years of intensive studies, various aspects of substorm morphology have been qualitatively established. Observations from the International Solar-Terrestrial Physics (ISTP) mission during the last decade have provided more detailed and complete pictures of substorms than before and, consequently, have provided new insights into substorm mechanisms. From the global auroral imaging it is shown that substorm onsets are locally confined; however, the effects of substorms involve a very large space at different times. Observations relying on in situ techniques can be misleading and can introduce confusion if not properly interpreted. On the other hand, remote sensing techniques such as global auroral imaging not only provide a robust means for studying substorm phenomenology but also yield relatively consistent results. This article reviews and summarizes a number of substorm studies conducted based primarily on global auroral images from NASA's Polar satellite, with a main focus on “quantitative” substorm morphology (i.e., onset timing, locations, energy input, and substorm timescales). These studies conclude that (1) auroral breakups are the most reliable substorm indicator, whereas other commonly used onset proxies may not always be associated with substorms and are subject to a propagation delay; (2) after breakup, the expanded auroral bulge can move either westward (60%) or eastward (40%); and (3) a typical substorm expansion phase lasts ~10 minutes and increases with increasing distances from the onset. A key conclusion from some recent studies seems to suggest that magnetotail reconnection, if it ever exists, is a consequence of substorm expansion onset. These findings provide constraints for substorm models and theories.  相似文献   

6.
Transient phenomena in the magnetotail and their relation to substorms   总被引:1,自引:0,他引:1  
Recent observations of magnetic field, plasma flow and energetic electron anisotropies in the magnetotail plasma sheet during substorms have provided strong support for the idea that a magnetospheric substorm involves the formation of a magnetic neutral line (the substorm neutral line) within the plasma sheet at X SM — 10R E to -25R E. An initial effect, in the tail, of the neutral line's formation is the severance of plasma sheet field lines to form a plasmoid, i.e., a closed magnetic loop structure, that is quickly (within 5–10 min) ejected from the tail into the downstream solar wind. The plasmoid's escape leaves a thin downstream plasma sheet through which plasma and energetic particles stream continuously into the solar wind, often throughout the duration of the substorm's expansive phase. Southward oriented magnetic field threads this tailward-flowing plasma but its detection, as an identifier of the occurrence of magnetic reconnection, is made difficult by the thinness and turbulence of the downstream plasma sheet. The thinning of the plasma sheet downstream of the neutral line is observed, by satellites located anywhere but very close to the tail's midplane, as a plasma dropout. Multiple satellite observations of plasma droputs suggest that the substorm neutral line often extends across a large fraction (> ) of the tail's breadth. Near the time of substorm recovery the substorm neutral line moves quickly tailward to a more distant location, progressively inflating the closed field lines earthward of it, to reform the plasma sheet.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.  相似文献   

7.
Causality between near-Earth and midtail substorm processes is one of the most controversial issues about the substorm trigger mechanism. The currently most popular model, the outside-in model, assumes that near-Earth reconnection is initiated in the midtail region before substorm onset and that the associated flow burst causes tail current disruption in the near-Earth region. However, there remain some outstanding issues that may serve as critical tests of this model. The present article reviews recent satellite and ground observations addressing three such critical issues with a focus on substorm-related auroral features. First, near-Earth reconnection, even if it reaches the lobe magnetic field, does not necessarily trigger a global substorm, but it is often related to a pseudobreakup. This fact suggests that there is an additional or alternative condition for substorm development. Secondly, although there appears to be one-to-one correspondence between flow bursts in the plasma sheet and equatorward-moving auroral structures (auroral streamers), no such auroral feature that can be associated with the fast plasma flow can be identified prior to auroral breakups. On the other hand, the flow burst is widely regarded as a manifestation of reconnection and therefore, according to the outside-in model, should be created in the near-Earth plasma sheet before substorm onset. Finally, auroral arcs poleward of a breakup arc are not affected until the front of auroral intensification reaches those arcs. The last two points suggest that if substorm is triggered as the outside-in model describes, the ionosphere is electromagnetically detached from the magnetosphere, which, however, has not been addressed theoretically. Thus, it should be crucial for a better understanding of the substorm trigger process to implement the magnetosphere-ionosphere coupling in future modeling efforts and to address those basic issues as a guide for critically evaluating each model.  相似文献   

8.
Wave-particle effects are implicit in most models of radial diffusion and energization of Van Allen belt particles; they were explicitly used in the wave turbulence model for trapped particle precipitation and trapped flux limitations by Kennel and Petschek, Cornwall and by many others. Liemohn used wave-particle interactions to work out a theory of path-integrated whistler amplification process to explain the lack of large per-hop attenuation of multiple-hop LF whistlers.Others have now used wave-particle interactions to construct theories of ELF and VLF chorus. In the present paper we shall review the observations and some of the pertinent theoretical interpretations of wave-particle effects as they relate to substorm and storm-time phenomena. If substorms develop as a result of magnetic merging, then it seems clear that wave-particle interactions in the dissipative or so-called diffusion region of the reconnection zone may be of great importance. The plasma sheet thinning and flow towards the Earth lead inevitably to the development of particle distribution functions that contain free energy in a pitch-angle anisotropy. Such free energy can be released via plasma wave instabilities. The subsequent wave-particle interactions can result in both strong and weak diffusion of particles into loss cones with consequent precipitation fluxes into the auroral zone. Ring current proton spectra also should be unstable against various plasma instabilities with consequent ring current decay and precipitations. Wave-particle interactions must play some important roles in auroral arcs, electrojets and other phenomena related to substorms. These aspects of wave-Paticle interaction will be covered  相似文献   

9.
The morphology of development of auroral flares (magnetospheric substorms) for both electron and proton auroras is summarized, based on ground-based as well as rocket-borne and satellite-borne data with specific reference to the morphology of solar flares.The growth phase of an auroral flare is produced by the inflow of the solar wind energy into the magnetosphere by the reconnection mechanism between the solar wind field and the geomagnetic field, thus the neutral and plasma sheets in the magnetotail attaining their minimum thickness with a great stretch of the geomagnetic fluxes into the tail.The onset of the expansion phase of an auroral flare is represented by the break-up of electron and proton auroras, which is associated with strong auroral electrojets, a sudden increase in CNA, VLF hiss emissions and characteristic ULF emissions. The auroral break-up is triggered by the relaxation of stretched magnetic fluxes caused by cutting off of the tail fluxes at successively formed X-type neutral lines in the magnetotail.The resultant field-aligned currents flowing between the tailward magnetosphere and the polar ionosphere produce the field-aligned anomalous resistivity owing to the electrostatic ion-cyclotron waves; the electrical potential drop thus increased further accelerates precipitating charged particles with a result of the intensification of both the field-aligned currents and the auroral electrojet. It seems that the rapid building-up of this positive feedback system for precipitating charged particles is responsible for the break-up of an auroral flare.  相似文献   

10.
This paper deals with acceleration processes in the magnetotail and the processes that enhance particle precipitation from the tail into the ionosphere through electric fields in the auroral acceleration region, generating or intensifying discrete auroral arcs. Particle acceleration in the magnetotail is closely related to substorms and the occurrence, and consequences, of magnetic reconnection. We discuss major advances in the understanding of relevant acceleration processes on the basis of simple analytical models, magnetohydrodynamic and test particle simulations, as well as full electromagnetic particle-in-cell simulations. The auroral acceleration mechanisms are not fully understood, although several, sometimes competing, theories and models received experimental support during the last decades. We review recent advances that emphasize the role of parallel electric fields produced by quasi-stationary or Alfvénic processes.  相似文献   

11.
Theoretical pressure balance arguments have implied that steady convection is hardly possible in the terrestrial magnetotail and that steady energy input necessarily generates a cyclic loading-unloading sequence, i.e., repetitive substorms. However, observations have revealed that enhanced solar wind energy input to the magnetospheric system may either lead to substorm activity or enhanced but steady convection. This topic is reviewed with emphasis on several recent case studies of the Steady Magnetospheric Convection (SMC) events. In these cases extensive data sets from both satellite and ground-based instruments from various magnetospheric and ionospheric regions were available.Accurate distinction of the spatial and temporal scales of the magnetospheric processes is vital for correct interpretation of the observations during SMC periods. We show that on the large scale, the magnetospheric configuration and plasma convection are stable during SMC events, but that both reveal considerable differences from their quiet-time assemblies. On a shorter time scale, there are numerous transient activations which are similar to those found during substorms, but which presumably originate from a more distant tail reconnection process, and map to the poleward boundary of the auroral oval. The available observations and the unresolved questions are summarized here.The tail magnetic field during SMC events resembles both substorm growth and recovery phases in the neartail and midtail, respectively, but this configuration may remain stable for up to ten hours. Based on observations and model results we discuss how the magnetospheric system avoids pressure balance problems when the plasma convects earthward.Finally, the importance of further coordinated studies of SMC events is emphasized. Such studies may shed more light on the substorm dynamics and help to verify quantitatively the theoretical models of the convecting magnetosphere.  相似文献   

12.
It is a crucial issue to know where magnetic reconnection takes place in the near-Earth magnetotail for substorm onsets. It is found on the basis of Geotail observations that the factor that controls the magnetic reconnection site in the magnetotail is the solar wind energy input. Magnetic reconnection forms close to (far from) the Earth in the magnetotail for high (low) solar wind energy input conditions.With the early Vela spacecraft observations, it was believed that magnetic reconnection started inside the Vela position, likely at 15 RE. The later ISEE/IRM observations put magnetic reconnection beyond 20 RE. The Vela event studies were made for highly active conditions, while the ISEE/IRM survey studies were made for moderate or quiet conditions. The finding of the factor that controls the site of magnetic reconnection in the magnetotail resolves the apparent discrepancy among various spacecraft results, and suggests solar cycle variation of the magnetotail reconnection site.  相似文献   

13.
The characteristics of inverted-V electron precipitation fluxes deduced predominantly from observations by the Atmosphere Explorer satellites are reviewed. The energy and pitch angle distributions are presented and shown to be generally in agreement with acceleration by a parallel electrostatic potential. Characteristics of secondary electrons are examined, and effects of beam plasma instabilities on these electrons are discussed. The properties of the monoenergetic component are compared with theoretical models of creating parallel DC electric fields, and found to favor the anomalous resistivity model. The article also discusses relations of inverted-V events with other auroral phenomena including auroras, electrostatic shocks, convective electric field reversals, field-aligned currents and wave emissions. The principal conclusions are: (1) plasma sheet electrons are continuously accelerated to form inverted-V structures in the pre-midnight hemisphere independent of substorm phase, (2) the acceleration processes are probably related to large scale electrostatic wave turbulence observed at altitudes of a few thousand kilometers, (3) narrow bursts of intense electron precipitation fluxes are found to be imbedded within some inverted-V's. It is argued that the narrow bursts of intense electron precipitation have the proper characteristics to cause discrete auroral arcs in the atmosphere. We suggest that these narrow bursts are accelerated by an electrostatic shock at higher altitude and capable of producing discrete auroral arcs below the observing satellite.  相似文献   

14.
Mende  S.B.  Frey  H.U.  Immel  T.J.  Gerard  J.-C.  Hubert  B.  Fuselier  S.A. 《Space Science Reviews》2003,109(1-4):211-254
The IMAGE spacecraft carries three FUV photon imagers, the Wideband Imaging Camera (WIC) and two channels, SI-12 and SI-13, of the Spectrographic Imager. These provide simultaneous global images, which can be interpreted in terms of the precipitating particle types (protons and electrons) and their energies. IMAGE FUV is the first space-borne global imager that can provide instantaneous global images of the proton precipitation. At times a bright auroral spot, rich in proton precipitation, is observed on the dayside, several degrees poleward of the auroral zone. The spot was identified as the footprint of the merging region of the cusp that is located on lobe field lines when IMF Bz was northward. This identification was based on compelling statistical evidence showing that the appearance and location of the spot is consistent with the IMF Bz and By directions. The intensity of the spot is well correlated with the solar wind dynamic pressure and it was found that the direct entry of solar wind particles could account for the intensity of the observed spot without the need for any additional acceleration. Another discovery was the observation of dayside sub-auroral proton arcs. These arcs were observed in the midday to afternoon MLT sector. Conjugate satellite observations showed that these arcs were generated by pure proton precipitation. Nightside auroras and their relationship to substorm phases were studied through single case studies and in a superimposed epoch analysis. It was found that generally there is substantial proton precipitation prior to substorms and the proton intensity only doubles at substorm onset while the electron auroral brightness increases on average by a factor of 5 and sometimes by as much as a factor of 10. Substorm onset occurs in the central region of the pre-existing proton precipitation. Assuming that nightside protons are precipitating from a quasi-stable ring current at its outer regions where the field lines are distorted by neutral sheet currents we can associate the onset location with this region of closed but distorted field lines relatively close to the earth. Our results also show that protons are present in the initial poleward substorm expansion however later they are over taken by the electrons. We also find that the intensity of the substorms as quantified by the intensity of the post onset electron precipitation is correlated with the intensity of the proton precipitation prior to the substorms, highlighting the role of the pre-existing near earth plasma in the production of the next substorm.  相似文献   

15.
This paper reviews recent developments in the understanding of the solar-wind magnetosphere interaction process in which the interplanetary magnetic field has been found to play a key role. Extensive correlative studies between the interplanetary magnetic field and the magnetospheric parameters have in the past few years yielded detailed information on the nature of the interaction process and have made possible to follow the sequence of events that are produced inside the magnetosphere in consequence of the solar-wind energy transfer. We summarize the observed effects of the interplanetary magnetic field, its north-south and east-west components in particular, found in various domains of the magnetosphere — dayside magnetopause, polar cap, magnetotail, auroral zone —, and present an overall picture of the solar-wind magnetosphere interaction process. Dungey's reconnected magnetosphere model is used as a frame of reference and the basic compatibility of the observations with this model is emphasized. In order to avoid overlap with other review articles in the series discussion on the energy conversion process inside the magnetosphere leading to the substorm phenomenon is kept to the minimal.  相似文献   

16.
The V-shock is identified as the primary mechanism for the acceleration of electrons responsible for the discrete aurora. A brief review of the evidence supporting the V-shock model is given, including the dynamics of auroral striations, anomalous motion of barium plasma at high altitudes and in-situ observations of large electric fields. The V-shock is a nonlinear, n = 0 ion cyclotron mode soliton, Doppler shifted to zero frequency. The V-shock is also shown to be a generalization of the one-dimensional double layer model, which is an ion acoustic soliton Doppler shifted to zero frequency. The essential difference between the double layer theory and the theory for the oblique, current-driven, laminar electrostatic shock is that the plasma dielectric constant in directions perpendicular to the magnetic field is c 2/V a /2 , where V a is the Alfvén velocity; but the plasma dielectric constant parallel to the magnetic field is unity. Otherwise, in the limit that the shock thickness perpendicular to the magnetic field is much larger than an ion gyroradius, the equations describing the double layer and the oblique shock are the same. The V-shock, while accounting for the acceleration of auroral electrons, requires an energy source and mechanism for generating large potential differences perpendicular to the magnetic field. An energy source is the earthward streaming protons coming from the distant magnetospheric tail. It is shown how these protons can be energized by the cross-tail electric field, which is the tailward extension of the polar cap dawn-to-dusk electric field. The local, large cross-field potential differences associated with the V-shock are seen to be the result of a non-linear, E × B drift turbulent cascade which transfers energy from small- to large-scale sizes. Energy at the smallest scale sizes comes from the kinetic energy in the ion cyclotron motion of the earthward streaming protons, which are unstable against the zero-frequency flute-mode instability. The review points out the gaps in our understanding of the mechanism of the diffuse aurora and the mechanism of the auroral substorm.  相似文献   

17.
Mars and Venus do not have a global magnetic field and as a result solar wind interacts directly with their ionospheres and upper atmospheres. Neutral atoms ionized by solar UV, charge exchange and electron impact, are extracted and scavenged by solar wind providing a significant loss of planetary volatiles. There are different channels and routes through which the ionized planetary matter escapes from the planets. Processes of ion energization driven by direct solar wind forcing and their escape are intimately related. Forces responsible for ion energization in different channels are different and, correspondingly, the effectiveness of escape is also different. Classification of the energization processes and escape channels on Mars and Venus and also their variability with solar wind parameters is the main topic of our review. We will distinguish between classical pickup and ??mass-loaded?? pickup processes, energization in boundary layer and plasma sheet, polar winds on unmagnetized planets with magnetized ionospheres and enhanced escape flows from localized auroral regions in the regions filled by strong crustal magnetic fields.  相似文献   

18.
The Earth’s magnetotail is an extremely complex system which—energized by the solar wind—displays many phenomena, and Alfvén waves are essential to its dynamics. While Alfvén waves were first predicted in the early 1940’s and ample observations were later made with rockets and low-altitude satellites, observational evidence of Alfvén waves in different regions of the extended magnetotail has been sparse until the beginning of the new millennium. Here I provide a phenomenological overview of Alfvén waves in the magnetotail organized by region—plasmasphere, central plasma sheet, plasma sheet boundary layer, tail lobes, and reconnection region—with an emphasis on spacecraft observations reported in the new millennium that have advanced our understanding concerning the roles of Alfvén waves in the dynamics of the magnetotail. A brief discussion of the coupling of magnetotail Alfvén waves and the low-altitude auroral zone is also included.  相似文献   

19.
Several recent results concerning the nature of the Earth's magnetotail are briefly reviewed. These observational findings include: (1) the three-dimensional character of the plasma sheet via a comprehensive survey of proton bulk flows, (2) a region of earthward flowing plasmas at the interfaces of the plasma sheet and magnetotail lobes during magnetic substorm recovery, and (3) the signature of electrostatic acceleration for protons within the jetting plasmas from magnetotail fireballs.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.  相似文献   

20.
Most substorm researchers assume substorms to be caused by a unique large-scale process. However, a critical evaluation of substorm observations indicates that a new paradigm is needed to understand the substorm phenomenon and the magnetospheric dynamics in general. It is proposed here that substorms involve a number of physical processes covering over a wide range of spatial and temporal scales. Potential candidates include the kinetic or shear ballooning instability, the Kelvin-Helmholtz instability, the cross-field current instability, the tearing instability, and magnetic reconnection. An observational constraint on the qualified process for substorm onset is that it must be associated with magnetic field lines of auroral arcs since substorm onsets start with brightening of a pre-existing auroral arc. Which particular process dominates in a given substorm depends on the present and past states of the magnetosphere as well as the external solar wind. The magnetosphere is almost perpetually driven by the solar wind to be near a critical point and in a metastable state. Magnetospheric disturbances occur sporadically in multiple localized sites. A substorm is realized when the combined effect of these localized disturbances become global in extent, much like the system-wide activity in a sandpile or avalanche model.  相似文献   

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