Alexander J. Klimas

A description of the solar wind-magnetosphere coupling based on nonlinear filters

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−1. 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 organized nonlinear dynamics of the magnetosphere

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.

Self-organized criticality in the substorm phenomenon and its relation to localized reconnection in the magnetospheric plasma sheet

Evidence is presented that suggests that there is a significant self-organized criticality (SOC) component in the dynamics of substorms in the magnetosphere. We assume that observations of bursty bulk flows, fast flows, localized dipolarizations, plasma turbulence, etc. show that multiple localized reconnection sites provide the basic avalanche phenomenon in the establishment of SOC in the plasma sheet. First results are presented from a study of this avalanche process based on this working assumption. A magnetic field reversal model is discussed. Resistivity, in this model, is self-consistently generated in response to the excitation of an idealized currentdriven instability. When forced by convection of magnetic flux into the field reversal region, the model yields rapid magnetic field annihilation through a dynamic behavior that is shown to exhibit many of the characteristics of SOC. Over a large range of forcing strengths, the annihilation rate is shown to self-adjust to balance the rate at which flux is convected into the reversal region. Several analogies to magnetotail dynamics are discussed: (1) It is shown that the presence of a localized criticality in the model produces a remarkable stability in the global configuration of the field reversal while simultaneously exciting extraordinarily dynamic internal evolution. (2) Under steady forcing it is shown that a loading-unloading cycle may arise that, as a consequence of the global stability, is quasi-periodic and, therefore, predictable despite the presence of internal turbulence in the field distribution. Indeed, it is shown that the global loading-unloading cycle is a consequence of the internal turbulence. (3) It is shown that under steady, strong forcing the loading-unloading cycle vanishes. Instead, a recovery from a single unloading persists indefinitely. The field reversal is globally very steady while internally it is very dynamic as field annihilation goes on at the rate necessary to match the strong forcing. From this result we speculate that steady magnetospheric convection events result when the plasma sheet has been driven close to criticality over an extended spatial domain. During these events we would expect to find localized reconnection sites distributed over the spatial domain of near criticality, and we would expect to find plasma sheet transport in that domain to be closely related to that of BBF and fast flow events.

Phase transition‐like behavior of the magnetosphere during substorms

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.

Substorms: A global instability of the magnetosphere‐ionosphere system

Observational and numerical modeling evidence demonstrates that substorms are a global, coherent set of processes within the magnetosphere and ionosphere. This supports the view that substorms are a configurational instability of the coupled system since the entire magnetosphere changes during the expansion phase onset. It is shown that the magnetosphere progresses through a specific sequence of energy-loading and stress-developing states until the entire system collapses. This energy loading-unloading sequence is the essential basis of the Faraday Loop non-linear dynamics model which has been quite successful in describing the fundamental behavior of substorms without invoking detailed treatments of the internal substorm instability mechanism. Present-day MHD models also are seen to produce substorm-like global instabilities despite the fact that they do not treat realistically the extremely thin current sheets that play such an essential role in the near-tail dynamics prior to substorm onset. This paper discusses three-dimensional kinetic simulations that have recently shown a variety of initial plasma kinetic instability modes which all evolve quickly to a similar, globally unstable reconnection configuration. Continuing research concerning the substorm onset location and mechanisms addresses important questions of when and exactly how the substorm expansion develops. However, the loaded magnetosphere almost always progresses rapidly to the same basic reconnection configuration irrespective of the detailed localized initiation mechanism. This is likened to the catastrophic collapse of a sand dune that has reached a highly unstable configuration: Any small local perturbation can cause a complete and large-scale collapse irrespective of the perturbation details. It is concluded that the global magnetospheric substorm problem has now largely been solved and that future work should be directed toward understanding the detailed plasma physical processes that occur during substorms.

Substorm recurrence during steady and variable solar wind driving: Evidence for a normal mode in the unloading dynamics of the magnetosphere

Farrugia et al. (1993) have recently studied substorm activity driven by the passage of an interplanetary magnetic cloud during which the interplanetary magnetic field turned southward for approximately 18 hours. It was shown that both the ϵ and the V Bs parameters varied slowly on the timescale of a substorm but changed considerably over the interval as a whole. The substorm occurrence rate did not reflect the variation in magnetospheric energy loading rate as measured by these parameters but, rather, remained roughly constant with a 50-min average period. Klimas et al. (1992) showed that the Faraday loop analogue model of geomagnetic activity predicts this single unloading rate under various constant loading rates. However, various model parameters were adjusted to yield a 1-hour unloading period in agreement with the Bargatze et al. (1985) linear prediction filters and in approximate agreement with the Farrugia et al. (1993) results. It has since been found necessary to add a slow relaxation mechanism to the Faraday loop model to allow for its approach to a ground state during long periods of inactivity. It is proposed that the relaxation mechanism is provided by slow convection of magnetic flux out of the magnetotail to the dayside magnetosphere. In addition, a rudimentary representation of magnetotail-ionosphere coupling has been added to enable comparison of model output to measured AL. The present study is of the modified Faraday loop model response to solar wind input from the Bargatze et al. data set with comparison of its output to concurrent AL. This study has removed the degree of freedom in parameter choice that had earlier allowed adjustments toward the 1-hour unloading period and has, instead, yielded the 1-hour unloading period under various constant loading rates. It is demonstrated that the second peak of the bimodal Bargatze et al. linear prediction filters at ≈ 1-hour lag and the approximately constant substorm recurrence rate observed by Farrugia et al. can be interpreted as both being due to the existence of a normal unloading recurrence period in the dynamics of the magnetosphere.

A method for overcoming the velocity space filamentation problem in collisionless plasma model solutions

Abstract A method is introduced for overcoming the velocity space filamentation problem which occurs in solutions of the Vlasov-Maxwell system of equations. This method is shown to introduce no error in the evolution of the Vlasov-Maxwell solutions, to leave the field portion of the solutions unmodified, and to yield velocity-filtered distribution functions which do not carry filamentation in the velocity variable. It is conjectured that the filtered distributions do not develop spatial filamentation as well. It is shown that the method can be applied to the most general three-dimensional, electromagnetic Vlasov-Maxwell model. Several examples are presented in which comparisons between filtered and unfiltered solutions are made. These are numerical solutions of a Fourier-Fourier transformed one-dimensional electron plasma model. In the comparisons, which are favorable, reductions in run time by factors of approximately ten and in necessary machine memory by factors of twenty to thirty are demonstrated.

Generation of Electron Suprathermal Tails in the Upper Solar Atmosphere: Implications for Coronal Heating

We present a mechanism for the generation of non-Maxwellian electron distribution function in the upper regions of the solar atmosphere in the presence of collisional damping. It is suggested that finite-amplitude, low-frequency, obliquely propagating electromagnetic waves can carry a substantial electric field component parallel to the mean magnetic field that can be significantly larger than the Dreicer electric field. This long-wavelength electric fluctuation is capable of generating high-frequency electron plasma oscillations and low-frequency ion acoustic-like waves. The analysis has been performed using 1-1/2D Vlasov and PIC numerical simulations in which both electrons and ions are treated kinetically and self consistently. The simulation results indicate that high-frequency electron plasma oscillations and low-frequency ion acoustic-like waves are generated. The high-frequency electron plasma oscillation drives electron plasma turbulence, which subsequently is damped out by the background electrons. The turbulence damping results in electron acceleration and the generation of non-Maxwellian suprathermal tails on timescales short compared to collisional damping. Bulk heating also occurs if the fluctuating parallel electric field is strong enough. This study suggests that finite-amplitude, low-frequency, obliquely propagating electromagnetic waves can play a significant role in the acceleration and heating of the solar corona electrons and in the coupling of medium and small-scale phenomena.

Dst index prediction using data-derived analogues of the magnetospheric dynamics

The method of Klimas et al. [1997] for constructing dynamical analogues of physical input-output systems is generalized. Higher-order analogues with sensitivity to more features of the input data are derived. Solar wind V Bs parameter data are used for input and Dst index data are used for output to construct analogues of the magnetospheric dynamics responsible for Dst storms. A detailed study of the dynamics involved in a single storm is presented. It is shown that the relationship between V Bs input and Dst output for this storm can be described in the context of the model of Burton et al. [1975] but with variable decay time and strength of coupling to the solar wind V Bs parameter. During the storm recovery it is found that the decay time varies from ≈ 4 hours at the storm maximum to ≈ 20 hours midway in the recovery and then back to ≈ 10 hours. There appears to be nothing in the simultaneous solar wind data to explain this reversal in the evolution of the decay time. It is shown that the strength of coupling to the solar wind V Bs parameter varies considerably. The coupling strength peaks strongly at the time of the storm maximum and decays to low values during the storm recovery. Solar wind V Bs input during the storm recovery does not affect the recovery rate. Using this storm data, empirical nonlinear analogues are constructed. These analogues are tested out of sample for their prediction effectiveness. Comparisons with the predictions of the model due to Burton et al. are given. It is shown that these analogues are promising prediction tools, but their lack of sensitivity to solar wind dynamic pressure must be corrected.

Indications of low dimensionality in magnetospheric dynamics

Using three separate but related approaches, the authors examine the question of whether the dynamic response of the magnetosphere to the solar wind input may be described by a low-order system of equations. First, the authors determine that the dimension of the subset (the attractor) in the high-dimensional magnetospheric phase space associated with the westward auroral electrojet (AL) index for some of the data sets compiled by Bargatze et al. (1985) is 4.0 {plus minus} 0.2, seemingly independent of activity level. Second, direct modeling of the magnetosphere considering the bulk properites of the tail plasma leads to a system of equations that is similar to those previously reported as a dripping faucet model; here they focus specifically on the prediction of a natural frequency in this model. Finally, they identify a peak with the predicted frequency in power spectra of AL computed for intervals with both low and high activity. Peaks at other frequencies also appear in the spectra, and such resonances would be expected for a chaotic nonlinear oscillator. Combining these approaches they conclude that at least some aspects of magnetospheric dynamics may be meaningfully modeled by low-dimensional sets of equations.