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We show that changes in the magnetospheric ring current and auroral currents during the magnetic storms of March 2015 and June 2015, are recorded in several specific ways by ground magnetometers. The ring current changes are detected in geomagnetic field measurements of ground stations at magnetic mid-latitudes from -50 to +50 degrees. The auroral currents changes are detected at high magnetic latitudes from 50 to about 73 degrees. Finally, for stations between 73 and about 85 degrees the measurements of the ground magnetometers seem to be directly correlated with the convection electric field VBSouth of the solar wind. Using the correlations among magnetic fields measured at stations ordered by latitude, a correlation diagram is obtained where the maximum correlation values for fields determined by the ring current form a distinct block. High-latitude magnetic fields from stations at higher latitudes, which are mainly determined by auroral currents, form a different block in the same diagram. This is in agreement with our earlier work using wavelet transforms on ground magnetic-field time series, where mid-latitude fields stations that are influenced mainly by the ring current, give a critical exponent greater than 2 while higher-latitude fields show a more complex dependence with two exponents. The maximum correlation values for mid-latitude fields correlated with the SYM-H index vary from 0.8 to 0.9, and, thus, we infer that those geomagnetic disturbances are mainly due to the ring current. The maximum correlations between the same fields and the solar wind VBSouth vary from 0.5 to 0.7. Fields at magnetic latitudes between 50 and 73 degrees exhibit greater correlation values for the AL index rather than the SYM-H index. This is expected since in the auroral zone, the convection- and substorm-associated auroral electrojets contribute significantly to the deviation of the geomagnetic field from its quiet-time value. In this case, maximum correlations vary between 0.6 and 0.7 for auroral latitude stations when compared with AL, as opposed to 0.4–0.5 when compared with SYM-H. Our results show how different measures of ground geomagnetic variations reflect the time evolution of several magnetospheric current systems and of the solar wind – magnetosphere coupling.

Learning from successful applications of methods originating in statistical mechanics or information theory in one scientific field (e.g. atmospheric physics or weather) can provide important insights or conceptual ideas for other areas (e.g. space sciences) or even stimulate new research questions and approaches. For instance, quantification and attribution of dynamical complexity in output time series of nonlinear dynamical systems is a key challenge across scientific disciplines. Especially in the field of space physics, an early and accurate detection of characteristic dissimilarity between normal and abnormal states (e.g. pre-storm activity vs. magnetic storms) has the potential to vastly improve space weather diagnosis and, consequently, the mitigation of space weather hazards. This presentation reports on the progress of a largely interdisciplinary International Team, combining expertise from both space physics and nonlinear physics communities, which was selected for funding by the International Space Science Institute (ISSI) in 2019. The Team attempts to combine advanced mathematical tools and identify key directions for future methodological progress relevant to space weather forecasting using Swarm, SuperMAG, and other space/ground datasets. By utilizing a variety of complementary modern complex systems based approaches, an entirely novel view on nonlinear magnetospheric variability is obtained. Taken together, the multiplicity of recently developed approaches in the field of nonlinear time series analysis offers great potential for uncovering relevant yet complex processes interlinking different geospace subsystems, variables and spatio-temporal scales. The Team provides a first-time systematic assessment of these techniques and their applicability in the context of geomagnetic variability.

The results of a genetic algorithm optimization of the WINDMI model using the Blanchard-McPherron substorm data set is presented. A key result from the large-scale computations used to search for convergence in the predictions over the database is the finding that there are three distinct types of vx Bs -AL waveforms characterizing substorms. Type I and III substorms are given by the internally-triggered WINDMI model. The analysis reveals an additional type of event, called a type II substorm, that requires an external trigger as in the northward turning of the IMF model of Lyons (1995). We show that incorporating an external trigger, initiated by a fast northward turning of the IMF, into WINDMI, a low-dimensional model of substorms, yields improved predictions of substorm evolution in terms of the AL index. Intrinsic database uncertainties in the timing between the ground-based AL electrojet signal and the arrival time at the magnetopause of the IMF data measured by spacecraft in the solar wind prevent a sharp division between type I and II events. However, within these timing limitations we find that the fraction of events is roughly 40% type I, 40% type II, and 20% type III.

The solar wind velocity is the primary driver of the electron flux variability in Earth's radiation belts. The response of the logarithmic flux (“log-flux”) to this driver has been determined at the geosynchronous orbit and at a fixed energy [Baker, D.N., McPherron, R.L., Cayton, T.E., Klebesadel, R.W., 1990. Linear prediction filter analysis of relativistic electron properties at 6.6 RE. Journal of Geophysical Research 95(A9), 15,133–15,140) and as a function of L shell and fixed energy [Vassiliadis, D., Klimas, A.J., Kanekal, S.G., Baker, D.N., Weigel, R.S., 2002. Long-term average, solar-cycle, and seasonal response of magnetospheric energetic electrons to the solar wind speed. Journal of Geophysical Research 107, doi:10.1029/2001JA000506 ). In this paper we generalize the response model as a function of particle energy (0.8–6.4 MeV) using POLAR HIST measurements. All three response peaks identified earlier figure prominently in the high-altitude POLAR measurements. The positive response around the geosynchronous orbit is peak P 1 ( τ =2±1 d; L =5.8±0.5; E =0.8–6.4 MeV), associated with high-speed, low-density streams and the ULF wave activity they produce. Deeper in the magnetosphere, the response is dominated by a positive peak P 0 (0±1 d; 2.9±0.5 R E ; 0.8–1.1 MeV), of a shorter duration and producing lower-energy electrons. The P 0 response occurs during the passage of geoeffective structures containing high IMF and high-density parts, such as ICMEs and other mass ejecta. Finally, the negative peak V 1 (0±0.5 d; 5.7±0.5 R E ; 0.8–6.4 MeV) is associated with the “ D st effect” or the quasiadiabatic transport produced by ring-current intensifications. As energies increase, the P 1 and V 1 peaks appear at lower L , while the D st effect becomes more pronounced in the region L P 0 effectively disappears for E >1.6 MeV because of low statistics, although it is evident in individual events. The continuity of the response across radial and energy scales supports the earlier hypothesis that each of the three modes corresponds to a qualitatively different type of large-scale electron acceleration and transport.

We examine the magnetospheric wave power in the Pc3–Pc5 range in terms of its growth and decay characteristics and its distribution in L shell in response to the interplanetary plasma bulk velocity, VSW. We use linear and nonlinear (rank-order) correlation and filtering methods to quantify the effective coupling of the wave power to VSW variations. These methods are applied to measurements from 26 ground magnetometers of the IMAGE array and NOAA's GOES-10 spacecraft at geosynchronous orbit, taken over 2 years of solar-maximum activity (2002–2003). We find that the ground ULF wave power is structured in the range 3.5

The outer radiation belt injection, transport, acceleration and loss satellite (ORBITALS) is a small satellite mission proposed as a Canadian contribution to the satellite infrastructure for the International Living With a Star (ILWS) program. The ORBITALS will monitor the energetic electron and ion populations in the inner magnetosphere across a wide range of energies (keV to tens of MeV) as well as the dynamic electric and magnetic fields, waves and cold plasma environment which govern the injection, transport, acceleration and loss of these energetic and space weather critical particle populations. ORBITALS will be launched around 2010–2012 into a low-inclination GTO-like orbit which maximizes the long-lasting apogee-pass conjunctions with both the ground-based instruments of the Canadian Geospace Monitoring (CGSM) array as well as with the GOES East and West and geosynchronous communications satellites in the North American sector. Specifically, the ORBITALS will make the measurements necessary to gain fundamental new understanding of the relative importance of different physical acceleration and loss processes which are hypothesised to shape the energetic particle populations in the inner magnetosphere. The ORBITALS will also provide the raw radiation measurements at MEO altitudes necessary for the development of the next-generation of radiation belt specification models, and on-board experiments will also monitor the dose, single-event upset, and deep-dielectric charging responses of electronic components on-orbit. In this paper we outline the scientific objectives of the ORBITALS mission, discuss how the ORBITALS will lead to solutions to outstanding questions in inner magnetospheric science, and examine how the ORBITALS will complement other proposed inner magnetosphere missions in the ILWS era.

The activity of Earth’s magnetosphere is frequently dominated by sporadic perturbations involving broad ranges of spatial and temporal scales. This complex behavior has recently been shown to possess power-law intermittency statistics implying global and/or local self-organized critical dynamics of the magnetotail plasma sheet. In the present paper, we show that under nonstationary driving conditions, the magnetosphere can deviate from its steady critical state. This transient dynamics is revealed based on spatial fractal analysis of critical fluctuations associated with multiscale turbulent activity in the tail. More specifically, we analyze multiscale correlations of an extended set of high-resolution ultraviolet images of the nighttime sector of the northern aurora provided by the UVI instrument onboard the POLAR spacecraft. The images are represented as an evolving activity surface characterized by a time-dependent roughness critical exponent. We show that the fractal structure of this surface undergoes a systematic reorganization during substorm phases. The expansion phase is typically preceded by a transition from sub- to super-critical behavior associated with enhanced correlations and decreased fractal dimension of the auroral activity surface. This transition manifests itself in increased values of the roughness exponent and the scaling error characterizing the quality of auroral emissions fractal scaling, as well as in the number of simultaneously observed emission events. The results obtained indicate that scaling analysis of critical auroral fluctuations can be a helpful tool for developing spatiotemporal prediction models of high-latitude geomagnetic activity.

High fluxes of relativistic electrons in the inner magnetosphere have been associated with a range of spacecraft anomalies, and therefore the modeling of the flux is of direct relevance to the development of space weather applications. Time variations of the electron flux at a given L shell are ultimately functions of interplanetary parameters as well as of internal magnetospheric dynamics. It is important to resolve which one of the two elements is important for modeling and to what extent. To that end we compare two models of the magnetospheric relativistic electron flux at 2–6 MeV spanning the range L = 1 –10 and driven by the solar wind plasma velocity, V SW . The finite-impulse-response (FIR) model represents the coupling of the flux to the solar wind velocity. It is part of an empirical model chain currently in development at the Center for Integrated Space Weather Modeling. The autoregressive moving-average (ARMA) model also includes a representation of the internal flux dynamics. The comparison is quantified in terms of the prediction accuracy, its variation with season and solar cycle phase, and its dependence on activity level. We find that the FIR model is more accurate than the ARMA model in most radial regions of the radiation belts, including the geosynchronous orbit. The results indicate that the long memory of the FIR model to past solar wind velocity inputs is more important in representing the effective coupling than ARMA's additional internal dynamics.

The Wang–Sheeley–Arge (WSA) method is used to predict the solar wind speed (and certain other parameters) near the Earth’s orbit based upon solar surface measurements. This approach gives a predicted solar wind time series with a lead time of three to four days. Such forecasted solar wind conditions can then be convolved with linear and nonlinear filters in order to provide a predicted set of geomagnetic indices or various particle flux estimates. In order to illustrate the method in a concrete way, we present here a demonstration of an end-to-end empirical forecast of relativistic electrons in the outer Van Allen radiation belt. Past work has shown that radiation belt electron fluxes are highly dependent on the speed of the solar wind striking the magnetosphere. We develop filters that predict electron fluxes using the WSA estimates of solar wind speed at L1, which allows for 3–4 days lead times. We compare the prediction efficiency (PE) provided by these filters with filters developed to use 3–4 day old values of the solar wind velocity measured at L1 and 3–4 day old values of the measured electron fluxes themselves. It is found that the WSA method provides PEs of the electron flux that are slightly lower than that provided by using old L1 or the autocorrelated electron flux data. r 2004 Elsevier Ltd. All rights reserved.

We test the ability of a data-derived model of geomagnetic activity, originally optimized to have a high prediction efficiency (PE), for its ability to predict only large geomagnetic disturbances. Correlation-based metrics, such as prediction efficiency, are often used as a measure of model performance. This metric puts equal weight on prediction of both large and small measurements. However, for space weather purposes, one is often interested in knowing only if a large disturbance event will occur so less emphasis should be placed on small measurements. If only large events are of interest, then a correlation metric is not the best measure of model performance. In this work, we determine how well a data-derived model, originally optimized to have a high prediction efficiency, predicts large geomagnetic events. The ratio of the number of correct to false alarm forecasts, R/sub F/, is used as an event-predictor metric. It is shown that in the electrojet regions the data-derived model that predicts the north-south component of the ground magnetic field B/sub x/ has a spatial R/sub F/ profile similar to that of the prediction efficiency. Maximal values of R/sub F/=4 are found at 0300 MLT when an event is defined as an excursion in the hourly-averaged north-south component of the ground magnetic field below -400 nT. Whereas the local time profile of PE(B/sub x/) is similar to R/sub F/(B/sub x/), the profile of PE(|dB/sub x//dt|) differs substantially from R/sub F/(|dB/sub x//dt|) in the noon sector. Epoch analysis shows that the poor performance in the noon sector is a result of pre-event levels of |dB/sub x//dt| not being clearly separated from post-event levels.

Energy transport from the interplanetary plasma to Earth's inner magnetosphere occurs in a range of time scales and efficiencies. It is often hypothesized that this range is smoothly varying with radial geocentric distance, indicating the transport involves many processes, whose ranges overlap. Here we report evidence from observations, and time series analysis, and other data-based modeling which indicates that the coupling of magnetospheric relativistic electron fluxes to solar wind variables occurs in specific ranges of radial distance (L shell). These findings probably have important consequences for the understanding of physical mechanisms responsible for the acceleration in each region. We identify three distinct regions: P-0 at approximately 37 R-E. Each one responds to a different combination of solar wind variables, and couples to the main driver variable, the solar wind speed V-SW, in a different way. Mode P-1 is the prototypical response of the inner magnetosphere. The electron flux responds more slowly than the other two regions to V-SW (2-3 days): high-speed streams are the most geoeffective structures for that region. Mode P-0 responds significantly faster (

We show that the Lu (Phys. Rev. Lett. 74(13) (1995) 2511) model, which is known to exhibit some properties of a system in self-organized criticality (SOC) [Lu, 1995; Klimas et al. (J. Geophys. Res. 105 (2000) (A8), 18,765–18,780.)], can be obtained through a reduction of the resistive MHD system to an idealized one-dimensional limit. Resistivity in this model is anomalous and localized and is due to the excitation of an idealized current-driven instability at positions where large spatial gradients appear in the magnetic field distribution. We note that, by reversing the reduction to the idealized one-dimensional limit, the Lu model presents an opportunity to construct a true MHD system that incorporates kinetic phenomena when small spatial scales are generated which may evolve into SOC under some conditions. We study the evolution of this model in a driven magnetic field reversal configuration on a high-resolution spatial grid. It has been shown earlier that the behavior of several parameters that are global measures of the state of the field reversal suggests that the reversal can evolve into SOC (Klimas et al., 2000). Here, we study the internal dynamics of the field reversal during the unloading phase of a loading–unloading cycle. Unloading is due to internal, localized, dynamic field annihilation; no flux is lost by the system through its boundaries. For this continuum model, we define an “avalanche” as a group of unstable grid points that are contiguous in position and time. We demonstrate scale-free power-law size and duration distributions for these avalanches during the unloading phase of a loading–unloading cycle. We further demonstrate the stability of these distributions; they do not evolve significantly as the unloading progresses. Box counting statistics on the position–time plane show that the avalanches can be characterized as intermittent one-dimensional structures; gaps in these otherwise one-dimensional structures lower their dimension to below one. The stable scale-free avalanche size and duration distributions, plus the fractal structure of the avalanches at small scales, provide further evidence that solutions of the continuum Lu model in a field reversal configuration can evolve into SOC.

A magnetic field model of the magnetotail current sheet in the form of a coupled-map lattice (CML) is presented. It is continuously driven (“running”) and based on the MHD diffusion equation. Solar wind vBS data (solar wind speed multiplied by the southward component of IMF) are used for driving the model, and it is shown to exhibit perturbations (avalanches) with power-law scalings in their distributions of duration and size. Such distributions may indicate self-organized critical (SOC) behavior. Furthermore, it is shown that the power spectra of the model outputs are of bicolor power-law form with different slopes for high and low frequencies. Although the “running” model gives power-law distributions independent of the strength of the driver, it is argued that the model is in SOC state only when driven slowly. When the driver is strong the model acts more like an input–output system, and the power laws are possibly due to the statistics of the driver. This is supported by the fact that durations of southward turnings of IMF have also a power-law distribution. It is also shown that by driving the model very strongly we can reproduce AE data with correlation 0.74 by using large resistivity, and Dst with correlation 0.79 by using small resistivity.

The behavior of substorms as sudden transitions of the magnetosphere is studied using the Bargatze et al. [1985] data set of the solar wind induced electric field vBs and the auroral electrojet index AL. The data set is divided into three subsets representing different levels of activity, and they are studied using the singular spectrum analysis. The points representing the evolution of the magnetosphere in the subspace of the eigenvectors corresponding to the three largest eigenvalues can be approximated by two-dimensional manifolds with a relative deviation of 10–20%. For the first two subsets corresponding to small and medium activity levels the manifolds have a pleated structure typical of the cusp catastrophe. The dynamics of the magnetosphere near these pleated structures resembles the hysteresis phenomenon typical of first-order phase transitions. The reconstructed manifold is similar to the “temperature-pressure-density” diagrams of equilibrium phase transitions. The singular spectra of vBs, AL, and combined data have the power law dependence typical of second-order phase transitions and self-organized criticality. The magnetosphere thus exhibits the signatures of both self-organization and self-organized criticality. It is concluded that the magnetospheric substorm is neither a pure catastrophe of the low-dimensional system nor a random set of avalanches of different scales described by the simple sandpile models. The substorms behave like nonequilibrium phase transitions, with features of both first- and second-order phase transitions.

We examine the dependence of the Dst timescales on storm conditions and its implications for the storm-substorm relationship. The growth, decay and oscillation timescales are expressed as functions of the storm magnitude and phase, and the solar wind electric-field input VBs. Nonlinear, second-order autoregressive moving average (ARMA) models are fit to 5-min data and yield two timescales, an exponential decay with an average e-folding time τ1 = −4.69 hours (−7.26 hours for the pressure-corrected Dst(0)) and an inductive time τ2 = −0.81 hours (−0.05 hours for Dst(0)). Around these average values there is a systematic variation: (1) For most of the storm duration, τ1 is negative representing the rapid adjustment of the inner magnetosphere to the imposed electric field. (2) In the early main phase, however, τ1 = 5.29 hours (1.76 hours for Dst(0)), so the disturbance grows as a slow exponential. (3) During commencement and main phase, the timescales are complex conjugate and the response is oscillatory. Fast oscillations during storm commencement (period 1.13 hours: 8.48 min for Dst(0)) are a “ringing” response to interplanetary pressure enhancements. Slow oscillations in the main phase have an average period of 1.96 hours (1.55 hours for Dst(0)) and coincide with AL intensifications. The main phase can be separated into periods of oscillatory, fast decay (coincident with AL activity and probably due to injections) and monotonic slow decay (regular convection). (4) All timescales decrease with increasing interplanetary activity because high activity involves acceleration and loss of heavy ions with shorter lifetimes than protons. (5) Also, decay times are about twice as long during recovery than during main phase. (6) Similar dependences are found for the solar wind coupling coefficients. The models are similar to linear models in predictability and are stable with respect to perturbation in the initial conditions.

The Earth’s magnetosphere exhibits substantial complexity in many of its physical properties. Particle populations wax and wane and magnetic fields fluctuate on virtually all observed time scales, from less than 1 minute to many days. Much of the variability of the magnetosphere and its interaction with the ionosphere can be ascribed to the phenomena termed “substorms” and “storms.” Ample evidence is found that these geospace disturbances, though exhibiting event-to-event differences, are remarkably repetitive and have basic underlying similarities. The ring current development, radiation belt particle changes, and basic substorm patterns suggest a high degree of coherence in the phenomena. Observations, modeling, and basic physical properties are discussed here that point to a relatively ordered, low-dimensional underlying dynamics in the magnetosphere. These results suggest that nonlinear processes and couplings introduce much of the observed complexity in magnetospheric particle and field changes.

Previous input–output analysis of the electrojet indices has been generalized to a spatio-temporal dynamical model of the high latitude magnetic perturbation (HLMP) by using the spatially dependent measurements that can be provided by a ground magnetometer array of latitudinal coverage. A technique that utilizes the daily rotation of the Earth as a longitudinal, or local time, sampling mechanism is used to construct a two-dimensional representation of the high latitude magnetic perturbations, both in magnetic latitude and local time, from the single latitudinal chain of magnetometers. Two-dimensional static, linear dynamical and nonlinear dynamical models for the evolution of the spatial structure of the HLMP are constructed by including a coupling to the solar wind as the energy input. The nonlinear spatial model of the HLMP produces better predictions than the linear one, reducing the average error from 65 to 50 nT for the Hx component. This can be taken as an indication that during intense activity, th...

A magnetic field model of the magnetotail current sheet in the form of a coupled-map lattice (CML) is presented. It is a continuously driven and based on the MHD diffusion equation. Solar wind vBs data (solar wind speed multiplied by the southward component of IMF) are used for driving the model, and it is shown to exhibit perturbations (avalanches) with power-law scalings in their distributions of duration and size. Such distributions may indicate self-organized critical (SOC) behavior. Furthermore, it is shown that the power spectra of the model outputs are of bicolor power-law form with different slopes for high and low frequencies. The model parameters determine the frequency of the break points of the spectra, and the slopes of their low and high frequency regimes.

A magnetic field model of the magnetotail current sheet based on cellular automaton (CA) is presented. The present isotropic model is a continuously driven, two-dimensional running CA. The model has a physical interpretation in terms of magnetohydrodynamic (MHD) equations, and features self-organized critical (SOC) behavior with power-law scalings both in durations and sizes of instabilities (avalanches). The model has nonlinear energy dissipation, and shows avalanches with and without an external trigger. Thus the model reproduces some of the statistical features recently observed in the magnetotail.

We have constructed a data-derived model of the evolution of the spatial structure of the ring current geomagnetic signature during storms. A spatially dependent generalization of the Dessler-Parker-Skopke relation has been derived to explain the spatial structure in the midlatitude magnetic fluctuations (MLMF) as observed by ground magnetometers. Such a relation is used as a basis for constructing solar-wind-driven, data-derived models of the MLMF. The model includes a coupling to the solar wind as the energy driver and also includes a nonlocal coupling as an explanation of the inhomogeneity in the energy density that appears in the ring current during the main phase of a storm. Both linear and nonlinear models for the evolution of the spatial structure of the MLMF are constructed, and the nonlinear spatial model of the ring current produces better predictions than the linear one. This can be taken as an indication that during strong magnetic storms the ring current evolves in a nonlinear fashion. The spatial data used in the generation of the models are rotated to a frame “fixed” with the ring current, and presure effects were accounted through a kinematic relation. The techniques developed in this paper are very general and can be used to study other systems that show spatial structure, such as the high-latitude current system.

Nonlinear dynamics methods have been applied successfully to predict various aspects of geomagnetic activity. In the local-linear prediction method past input and output data are convolved with filter functions to produce a prediction of future output. For solar wind input and geomagnetic activity output, the local-linear filter functions constitute a low-dimensional nonlinear model of the magnetospheric dynamics. This prediction model is data-derived; it is an unbiased representation of the magnetospheric dynamics. In principle this model contains a wealth of data-derived information concerning substorm and storm processes. Such models, however, are not amenable to physical interpretation. We present a method for transforming a local-linear prediction model to dynamical system analogues of two types: (1) A local-linear analogue composed of readily recognized physical components, suitable for identifying time-scales, coupling strengths, dissipation rates, etc. implied by the input-output data. (2) For prediction applications, a nonlinear analogue containing a small number of free parameters which are fixed from a training interval in the input-output data. Both of these are data-derived, low order, ordinary differential equations. They represent the collective effects of the many magnetospheric phenomena that couple the solar wind driver to the geomagnetic response. We illustrate the method using intervals of ISEE-3 and IMP-8 solar wind data for input, and D st and AL index data for output.

The International Symposium on Solar-Terrestrial Coupling Processes was held in Paros, Greece, on June 23–27, 1997. The Symposium was sponsored by NASA, the European Geophysical Society, the Greek Ministry of the Aegean, and the Greek Ministry of Development. It was attended by 85 scientists from 13 countries, and included six sessions on topics ranging from Interplanetary Disturbances to Particle Acceleration. In addition to the six sessions a panel discussion session was held. Eight scientists reported on recent advances, open questions and future directions in solar-terrestrial research. This review paper is based on the panelists' reports and includes individual sections on seven particular topics of special interest to solar-terrestrial research. The topics range from the significance of solar wind composition and interplanetary disturbances to promising new technologies and methods. Solar-terrestrial research deserves the special attention of the scientific community, both because of the attractive physics underlying the various phenomena associated with them, as well as because of the applied aspect of the sometimes destructive effects of solar-terrestrial coupling on a wide variety of technological systems.

Nonlinear filters have provided high-accuracy mid-latitude geomagnetic effects, mainly due to the ring predictions of geomagnetic activity indices from solar wind current and magnetopause current, but also smaller effects key parameters. Here we extend the nonlinear prediction of other current systems (Mayaud, 1980; Campbell, 1996; methods to derive closed-form analytical models for the so- Tsurutani et al., 1997). In particular, magnetopause currents lar wind-geomagnetic coupling. For each phase of either are enhanced and move earthward following increases in the storm or magnetopause compression as identified by D,,, we solar wind ram pressure Psw. The magnetopause current calculate nonlinear, piecewise-constant models of the rela- effect can be reduced by defining the pressure corrected tion between the ring current index D,, and the solar wind index, DJ+ Dst + ba + c, where representative electric field components. The time scales of storm main values are b = 25.32 nT/(nP)"* and c = -10.6 nT (from phase and recovery depend on storm phase, and the pres- McPherron, 1995). The standard Dst model (Burton et al., ence of solar wind VB, and pressure. Then, going beyond 1975) is a linear response of the pressure-corrected index piecewise constant models, we use state space methods to to the "injection function" Q(t) (McPherron, 1997), usually reveal the fine structure of the D,, dynamics in detail. written as a simple function of the solar wind electric field

We have investigated the excitation of electrostatic and electromagnetic lower hybrid waves in the magnetic field reversal region of the plasma sheet using a two-fluid approach. We consider a two-dimensional tail configuration that includes the Bx and Bz magnetic field components and examine the nonlocal properties of lower hybrid modes near the weak field region, where the field Bx(z) reverses sign. We have shown that an electrostatic lower hybrid mode is excited by the magnetic field gradient while electromagnetic modes are driven unstable by the combined effects of the magnetic field gradient and the electron fluid drift across the Bx field. We have shown that the electrostatic and electromagnetic lower hybrid modes grow in a few milliseconds and a few tens of milliseconds, respectively, the former for wavelengths shorter than the current sheet width (that is, for kyλ ≥ 1, where λ is the current sheet width) and the latter for long wavelengths (kyλ ≪ 1).

A method is presented for transforming a local-linear prediction model into dynamical analogues of the coupling between the input and output data that enters and forms the prediction model. Two types of analogues are produced: (1) local-linear analogues composed of readily recognized physical components and (2) nonlinear analogues suitable for prediction purposes; both are data derived. Second-order analogues of the magnetospheric dynamics are examined in detail using the composite ISEE 3 solar wind parameter VBs for input and simultaneous Dst index data for output. An optimized local-linear analogue is constructed which minimizes the rms difference between analogue output and measured Dst. It is shown that the optimized local-linear analogue reduces, in behavior, to that of the first-order Burton et al. [1975] Dst model during periods of Dst recoveries, both large and small. During those periods, however, the analogue effectively decouples from the solar wind VBs driver. At other times the coupling strength is found in general agreement with the value deduced by Burton et al., but, at those times, the analogue behavior is beyond the scope of their first-order equation. Nonlinear analogues are also constructed and studied. These are driven, damped, harmonic oscillators in which the dissipation rate, restoring force, and coupling strength to the VBs driver are expressed as functions of the Dst and VBs variables; these expressions are data derived. It is found that these analogues couple to the solar wind through the expression (VBs/Dst) VBs, rather than through the usual linear dependence on VBs. The suitability of these nonlinear analogues for prediction purposes is discussed.

It is widely accepted that substorms consist of both directly driven and loading-unloading processes. However, a recent study has presented results which suggested that over 90% of the auroral electrojet (AE) variation was directly predictable from the solar wind variations alone. This would imply that only a small residual in the AE variability is due to internal magnetospheric dynamics. The present paper considers nonlinear dynamical models of the global solar wind-magnetosphere interaction and uses the observed, highly variable solar wind electric field (VBs) to drive the Faraday loop analogue model. It is found that it is critically important to include magnetotail unloading in the model in order to replicate the main features of geomagnetic activity: with just the driven response in the model, one does not obtain realistic time behavior of the model AL index. Thus these results show quite clearly that both driven and unloading processes must be included in a realistic model of geomagnetic activity.

The polar cap (PC) index is a measure of the high-latitude geomagnetic disturbances due to Hall and field-aligned currents. The index is well correlated with the auroral electrojet AL and AU indices (correlation with the PC index is 76% and 66%, resp.). Here we obtain several types of data-based models that relate the PC to the AL and AU indices in the wintertime, when the ionospheric conductivity is mostly due to the precipitating particles of the field-aligned currents. The new models predict AL and AU from PC with correlations much higher than those found by earlier studies. Thus linear moving-average filters reproduce the observed AL with a correlation of 88% (AU : 75%) while linear autoregressive moving-average (ARMA) models based on the PC index produce in-sample single-step predictions with 98% and 97% correlations with AL and AU respectively. For long-term, out-of-sample prediction, the linear ARMA prediction from the PC index has an asymptotic prediction error which is at least 25% more accurate than the prediction from solar wind input. Nonlinear models are slightly more accurate than their linear counterparts, indicating a weak nonlinearity in the relation between the polar cap and auroral zone indices. The prediction-observation correlations are sufficiently high that models based on the PC index can be used for specification of the auroral geomagnetic activity.

We study the solar wind-geomagnetic activity coupling by analyzing time series of vBsouth and AL data in the period of December 29–31, 1974. We construct state-space models whose parameters are adjusted so that when their input is vBsouth their output is as close to AL as possible and find that nonlinear models are significantly more accurate than linear models in short-term predictions. Because the real dynamics is unknown, we measure the degree of nonlinearity indirectly as the number of geomagnetic/solar wind events required to make the best prediction. Linear models are related to large event numbers, comparable to the size of the database (>40 k of samples, or 2 months of data). Small numbers of events (values between 10 and 100 are typical) correspond to nonlinear models. Model performance is measured by the short-term time-aver aged prediction error. Nonlinear models have consistently lower prediction error than linear ones, often by as much as an order of magnitude. In testing the above result (1) we show that conclusions regarding model nonlinearity are biased if the prediction error is averaged over many prediction runs with different levels of activity. When we average over activity level, nonlinear and linear models appear to be equally accurate. (2) There is a range of prediction times over which linear and nonlinear models are adequately separated in accuracy. However, the models are similarly accurate if the prediction time is too short (such as 1–2 min, when the models fit high-frequency effects and noise) or for long prediction times (> 1 hour, when the prediction error stops increasing). (3) The model nonlinearity is an indication for nonlinearity in the physical coupling. We show that two alternative explanations, namely nonstationarity and non-Gaussian nature of the data, are not sufficient: nonlinear models predict better even after we suppress these properties in the data. (4) The prediction error depends on the location in the state-input space, or roughly, on the activity level. In conclusion, this study further confirms the nonlinear character of the vBsouth-AL coupling.

The linear prediction filters computed by Bargatze et al. [1985] have resulted in a turning point in the study of solar wind-magnetosphere coupling. The evolution of the filters with varying activity provides a clear demonstration that the coupling is nonlinear. The filters have thus brought about the end of one era of linear correlative studies and the beginning of a new era of nonlinear dynamical studies. Two separate, but complementary, approaches have emerged in these dynamical studies, analogue modeling and data-based phase space reconstruction. The reconstruction research has evolved from the original autonomous method studies, which were not conclusive, to the more recent input-output studies that are more appropriate for the solar wind-driven magnetosphere and have produced more reliable results. At present it appears that the modeling and reconstruction approaches may be merged in future attempts to produce analogue models directly from the results of the input-output data-based methods. If this can be accomplished, it will constitute a major step forward toward the goal of a low-dimensional analogue model of the magnetospheric dynamics derived directly from data and interpreted in terms of magnetospheric physics. These developments are reviewed in three sections: autonomous data analysis methods, analogue models, and input-output data analysis methods. The introduction provides sufficient information to read each of these sections independently.

Azimuthal convective flow and density-depleted magnetic field-aligned current co-located in the helium plasma produced in the large plasma device (LAPD-U) at UCLA (Gekelman et al 2016 Rev. Sci. Instrum. 87 025105) support an Alfvenic perturbation that is static in the laboratory frame. Electrostatic probes measure the flow and static density perturbations in the 72 cm-diameter, 12 m-long, afterglow plasma, wherein a radially segmented electrode creates the convective flow and an off-cylindrical-axis planar-mesh electrode draws current in a channel parallel to the background magnetic field. This stationary 'wave' is measured as a fixed (in the laboratory frame) ion density structure.

A nonlinear filtering method is introduced for the study of the solar wind -- magnetosphere coupling and related to earlier linear techniques. The filters are derived from the magnetospheric state, a representation of the magnetospheric conditions in terms of a few global variables, here the auroral electrojet indices. The filters also couple to the input, a representation of the solar wind variables, here the rectified electric field. Filter-based iterative prediction of the indices has been obtained for up to 20 hours. The prediction is stable with respect to perturbations in the initial magnetospheric state; these decrease exponentially at the rate of 30/min. The performance of the method is examined for a wide range of parameters and is superior to that of other linear and nonlinear techniques. In the magnetospheric state representation the coupling is modeled as a small number of nonlinear equations under a time-dependent input.

The coupling of energy between the solar wind and the magnetosphere has been studied using many different techniques. Early research used simple statistical methods and cross-correlation analyses. Such work suggested that solar wind-magnetosphere coupling is strongly controlled by the interplanetary electric field (-V × B). Later studies have used more sophisticated techniques such as linear prediction filtering to understand quantitatively the time scales and efficiency of such coupling. In fact, there emerge two distinct aspects and time scales for coupling processes: (1) Directly-driven ionospheric dissipation with response time scales of 10-20 min.; and (2) Storage-release mechanisms involving energy loading in the magnetotail for-1 hour. Very recent research has used nonlinear dynamical models and nonlinear filter techniques to incorporate both directly driven and loading-unloading behavior. The result is that very accurate predictions of magnetosphere-ionosphere response are possible using state-input space reconstruction and “nearest neighbor” nonlinear filters.

The presented method of adaptive control corrects perturbations in the parameters of a system based on observations of its variables. After a transient during which the desired parameter setting is reached exponentially quickly, the system exhibits the goal behavior - which can be a periodic, quasiperiodic, or chaotic solution of the equations of motion. The length of the control transient scales inversely with the control strength and logarithmically with the magnitude of the original parameter perturbation. It is shown that time series-based models are capable of substituting for detailed knowledge of the system's nonlinear dynamics. The method can be generalized to control more than one parameters, to rely on observations of a single variable, or to utilize a variety of control functions. Finally, a method of parameter identification dual to the adaptive control is also discussed.

Planetary magnetospheres are prime examples of interacting plasma regimes at different scales. There is the principal interaction with the solar wind that seems to be the main driver of the dynamics at Mercury and Earth. But these inner planet magnetospheres are relatively simple when compared to those of the outer planets which are primarily driven by planetary rotation and include internal plasma sources from various moons and rings, in addition to those from the planetary ionospheres and the solar wind. Io’s volcanic source at Jupiter is a prime example, but now Enceladus at Saturn has joined the fray, while Titan is a surprisingly minor player despite its thick nitrogen atmosphere and its continued bombardment by energetic particles. Mass loading of plasma leads to interchange instability in the inner magnetospheres at both Jupiter and Saturn, while ionospheric slippage, among other processes, seems to contribute to a variable rotation period in the spin‐aligned dipole field of Saturn, manifested in a...

The evolution of magnetic reconnection in large‐scale systems often gives rise to extended current layers that are unstable to the formation of secondary magnetic islands. The role of these islands in the reconnection process and the conditions under which they form remains a subject of debate. In this work, we benchmark two different kinetic particle‐in‐cell codes to address the formation of secondary islands for several types of global boundary conditions. The influence on reconnection is examined for a range of conditions and collisionality limits. Although secondary islands are observed in all cases, their influence on reconnection may be different depending on the regime. In the collisional limit, the secondary islands play a key role in breaking away from the slow Sweet‐Parker scaling and pushing the evolution towards small scales where kinetic effects can dominate. In the collisionless limit, fast reconnection can proceed in small systems (30× ion inertial scale) without producing any secondary islands. However, in large‐scale systems the diffusion region forms extended current layers that are unstable to the formation of secondary islands, giving rise to a time‐dependent reconnection process. These instabilities provide one possible mechanism for controlling the average length of the diffusion region in large systems. New results from Fokker‐Planck kinetic simulations are used to examine the role of secondary islands in electron‐positron plasmas for both collisional and kinetic parameter regimes. Simple physics arguments suggest the transition should occur when the resistive layers approach the inertial scale. These expectations are confirmed by simulations, which demonstrate the average rate remains fast in large systems and is accompanied by the continuous formation of secondary islands.

In this study, we present evidence for the co‐existence of a SOC‐like mechanism, of intermittent turbulence and a hidden low dimensional chaotic process underlying the solar activity. In particular, the original signal reveals a high dimensional stochastic character and a critical state according to a SOC process, since there in no clear discrimination between the original signal and its surrogate data concerning geometrical and dynamical characteristics of the solar time series. Furthermore, using the flat coefficient F we found evidence for intermittent turbulence behaviour. This result was based on the non‐Gaussian character and the presence of long‐range correlated plasma vorticity. This is in agreement with the low dimensional chaotic self‐organization that was revealed after the application of a high pass filter to the original solar flares signal and provides further evidence for self organization in solar activity dynamics. Finally, the above results indicate the existence of a phase transition‐li...

It is well known that strong electron heating by a powerful HF‐facility can lead to the formation of electron and ion density perturbations that stretch along the magnetic field line. Those density perturbations can serve as ducts for ELF waves, both of natural and artificial origin. This paper presents observations of the plasma density perturbations caused by the HF‐heating of the ionosphere by the HAARP facility. The low orbit satellite DEMETER was used as a diagnostic tool to measure the electron and ion temperature and density along the satellite orbit overflying close to the magnetic zenith of the HF‐heater. Those observations will be then checked against the theoretical model of duct formation due to HF‐heating of the ionosphere. The model is based on the modified SAMI2 code, and is validated by comparison with well documented experiments.

We show how a general class of spatio‐temporal nonlinear impulse‐response forecast networks (Volterra networks) can be constructed from a taxonomy of nonlinear autoregressive integrated moving average with exogenous inputs (NAR‐MAX) input‐output equations, and used to model the evolution of energetic particle f uxes in the Van Allen radiation belts. We present initial results for the nonlinear response of the radiation belts to conditions a month earlier. The essential features of spatio‐temporal observations are recovered with the model echoing the results of state space models and linear f nite impulse‐response models whereby the strongest coupling peak occurs in the preceding 1–2 days. It appears that such networks hold promise for the development of accurate and fully data‐driven space weather modelling, monitoring and forecast tools.

A variety of in‐situ measurements in space plasmas point out to an intermittent formation of distribution functions with elongated tails and power‐law at high energies. Power‐laws form ubiquitous signature of many complex systems, plasma being a good example of a non‐Boltzmann behavior for distribution functions of energetic particles. Particles, which either undergo mutual collisions or are scattered in phase space by electromagnetic fluctuations, exhibit statistical properties, which are determined by the transition probability density function of a single interaction, while their non‐asymptotic evolution may determine the observed high‐energy populations. It is shown that relaxation of the Brownian motion assumptions leads to non‐analytical characteristic functions and to generalization of the Fokker‐Planck equation with fractional derivatives that result in power law solutions parameterized by the probability density function.

Professor K. Papadopoulos, or Dennis, who we have all come to him as, has had a profound influence over my career as a scientist as well as my private life. Here I provide a brief account of the events that led me to Dennis as my PhD thesis advisor at University of Maryland and what that has meant to me.

To understand particle acceleration during magnetospheric substorms we must consider the problem on multple scales ranging from the large scale changes in the entire magnetosphere to the microphysics of wave particle interactions. In this paper we present two examples that demonstrate the complexity of substorm particle acceleration and its multi-scale nature. The first substorm provided us with an excellent example of ion acceleration. On March 1, 2008 four THEMIS spacecraft were in a line extending from 8 R{sub E} to 23 R{sub E} in the magnetotail during a very large substorm during which ions were accelerated to >500 keV. We used a combination of a global magnetohydrodynamic and large scale kinetic simulations to model the ion acceleration and found that the ions gained energy by non-adiabatic trajectories across the substorm electric field in a narrow region extending across the magnetotail between x = -10 R{sub E} and x = -15 R{sub E}. In this strip called the 'wall region' the ions move rapidly in azimuth and gain 100s of keV. In the second example we studied the acceleration of electrons associated with a pair of dipolarization fronts during a substorm on February 15, 2008. During this substorm three THEMIS spacecraftmore » were grouped in the near-Earth magnetotail (x {approx}-10 R{sub E}) and observed electron acceleration of >100 keV accompanied by intense plasma waves. We used the MHD simulations and analytic theory to show that adiabatic motion (betatron and Fermi acceleration) was insufficient to account for the electron acceleration and that kinetic processes associated with the plasma waves were important.« less

Resonant three‐wave interactions (R3WIs) and their dynamical counterpart, three‐oscillator interactions (R3OIs) play a fundamental role in many fields of physics. Consequently, controlling R3WI/R3OIs is an important goal of both basic and applied physics research. We have developed new control schemes based on a recent approach of wave autoresonance. This approach is based on the intrinsic property of many nonlinear waves and oscillations to stay in resonance (phase‐lock) even when parameters of the system vary in time and/or space. We review autoresonance in several new coupled wave systems including externally driven R3OI systems and multidimensional R3WIs. Particularly, we have focused on autoresonant stimulated Raman scattering in nonuniform plasmas. This research comprises an important step toward understanding of adiabatic synchronization of nonlinear waves in space‐time varying media with a potential of many new applications in plasma physics and related fields, such as fluid dynamics, nonlinear optics, and acoustics.

This paper presents recent results of the nonlinear processes associated with energy transfer between the solar wind and the magnetosphere—ionosphere system. The work concentrates on results arising from global magnetohydrodynamic simulations, but combines observational data where appropriate to support the conclusions drawn from the simulations.

Turbulence at MagnetoHydroDynamics (MHD) scales of the solar wind has been studied for more than three decades, using data analyzes, theoretical and numerical modeling. However smaller scales have not been explored until very recently. Here, we review recent results on the first observation of cascade and dissipation of the solar wind turbulence at the electron scales. Thanks to the high resolution magnetic and electric field data of the Cluster spacecraft, we computed the spectra of turbulence up to {approx}100 Hz (in the spacecraft reference frame) and found two distinct breakpoints in the magnetic spectrum at 0.4 Hz and 35 Hz, which correspond, respectively, to the Doppler-shifted proton and electron gyroscales, f{sub {rho}p} and f{sub {rho}e}. Below f{sub {rho}p} the spectrum follows a Kolmogorov scaling f{sup -1.62}, typical of spectra observed at 1 AU. Above f{sub {rho}p} a second inertial range is formed with a scaling f{sup -2.3} down to f{sub {rho}e}. Above f{sub {rho}e} the spectrum has a steeper power law {approx}f{sup -4.1} down to the noise level of the instrument. Solving numerically the linear Maxwell-Vlasov equations combined with recent theoretical predictions of the Gyro-Kinetic theory, we show that the present results are fully consistent with a scenario of amore » quasi-two-dimensional cascade into Kinetic Alfven modes (KAW).« less

This paper reviews space plasma physics in Dennis Papadopoulos’ group in the 1980s and early 1990s.

We present the results of a study of Electrostatic Solitary Waves (ESWs) in which propagation of a series of noncyclical ESWs is observed from one Cluster spacecraft to another over distances as great as tens of km and time lags as great as a few tens of ms. This propagation study was conducted for locations near the magnetopause on the magnetosheath side. Propagation was found primarily toward the earth with speeds on the order of 1500 to 2400 km/s. The sizes of the ESWs obtained from these velocities were on the order of 1 km along the magnetic field direction and several tens of km perpendicular. These results are consistent with measurements on single spacecraft in which the ESW propagation is observed with time lags of only {approx}0.1 ms. Our results thus show the stability of ESWs over time periods much greater than their own characteristic pulse durations of a few 100s of microseconds. We present also the results of a study of ESW modulation at the magnetopause on the earthward side. We found that ESWs were modulated at {approx}1.3 Hz, consistent with a Pc1 wave which was observed concurrently. During this time, tens of eV electron beams are present.more » We propose a Buneman type instability in which the E{sub ''''} component of the Pc1 waves provides a mechanism for accelerating electrons, resulting in the generation of the ESWs modulated at the Pc1 frequency.« less