A. S. Sharma

Thin current sheet embedded within a thicker plasma sheet: Self‐consistent kinetic theory

A self-consistent theory of thin current sheets, where the magnetic field line tension is balanced by the ion inertia rather than by the pressure gradient, is presented. Assuming that ions are the main current carriers and their dynamics is quasi-adiabatic, the Maxwell-Vlasov equations are reduced to the nonlocal analogue of the Grad-Shafranov equation using a new set of integrals of motion, namely, the particle energy and the sheet invariant of the quasi-adiabatic motion. It is shown that for a drifting Maxwellian distribution of ions outside the sheet the equilibrium equation can be reduced in the limits of strong and weak anisotropy to universal equations that determine families of equilibria with similar profiles of the magnetic field. In the region Bn/B0 < vT/vD ≪ 1 (B0, Bn, vD, and vT are the magnetic fields outside the sheet and close to its central plane, the ion drift velocity outside the sheet, and the ion thermal velocity, respectively) the thickness of such similar profiles is of the order of (vT/vD)1/3 ρ0, where ρ0 is the thermal ion gyroradius outside the sheet. In the limit of weak anisotropy (vT/vD ≫ 1) the self-consistent current sheet equilibrium may also exist with no indications of the catastrophe reported earlier by Burkhart et al. [1992a]. On the contrary, it is found that in this limit the magnetic field profiles again become similar to each other with the characteristic thickness ∼ ρ0. The profiles of plasma and current densities as well as the components of the pressure tensor are calculated for arbitrary ion anisotropy outside the sheet. It is shown that the thin current sheet for the equilibrium considered here is usually embedded into a much thicker plasma sheet. Moreover, in the case of weak anisotropy the perturbation of the plasma density inside the sheet is shown to be proportional to the parameter vD/vT, and as a result the electrostatic effects should be small, consistent with observations. This model of the thin current sheet satisfies the basic force balance equations including the marginal fire-hose condition and preserves the nonguiding center effects including the pressure nongyrotropy.

Reconstruction of low‐dimensional magnetospheric dynamics by singular spectrum analysis

The low dimensionality of magnetospheric activity indicated by previous phase space reconstructions using the AE and AL data suffer from the limitations of these techniques. In this paper the singular spectrum analysis is used to study the global magnetospheric dynamics using the AE data and it yields a correlation dimension ≃2.5, thus confirming the low dimensionality published earlier. Further, this technique shows that the global magnetospheric dynamics can be described by 3 variables whose dynamical features are obtained from the AE data.

Prediction of magnetic storms by nonlinear models

The strong correlation between magnetic storms and southward interplanetary magnetic field (IMF) is well known from linear prediction filter studies using the Dst and IMF data. However, the linear filters change significantly from one storm to another and thus are limited in their predicting ability. Previous studies have indicated nonlinearity in the magnetospheric re- sponse as the ring current decay rate varies with the Dst value during storms. We present in this letter non- linear models for the evolution of the Dst based on the OMNI database for 1964-1990. When solar wind data are available in advance, the evolution of storms can be predicted from the Dst and IMF data. Solar wind data, however, are not available most of the time or are avail- able typically an hour or less in advance. Therefore, we have developed nonlinear predictive models based on the Dst data alone. In the absence of solar wind data, these models cannot predict the storm onset, but can predict the storm evolution, and may identify intense storms from moderate ones. The input-output model based on IMF and Dst data, the autonomous model based on Dst alone, and a combination of the two can be used as forecasting tools for space weather.

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.

Effects of the solar wind electric field and ionospheric conductance on the cross polar cap potential: Results of global MHD modeling

[1] The behavior of the cross polar cap potential, PC, under strong solar wind conditions is studied using global MHD simulations. Simulations using two typical values of the ionospheric Pedersen conductance in agreement with others show that the cross polar cap potential is reduced compared to the corresponding potential in the solar wind due to the stagnation of the magnetosheath flow and the existence of parallel potentials. However, it is the ionospheric conductance that affects the value of PC the most: the transpolar potential saturates only for high enough ionospheric conductance. A mechanism in which the ionospheric conductance changes the properties of the magnetosheath flow is proposed. This mechanism assumes mapping of the electrostatic potential in the ideal MHD system and yields a self-consistent response of the reconnection and transpolar potentials to changes in the ionospheric conductance. INDEX TERMS: 2736 Magnetospheric Physics: Magnetosphere/ionosphere interactions; 2753 Magnetospheric Physics: Numerical modeling; 2776 Magnetospheric Physics: Polar cap phenomena; 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions. Citation: Merkine, V. G., K. Papadopoulos, G. Milikh, A. S. Sharma, X. Shao, J. Lyon, and C. Goodrich, Effects of the solar wind electric field and ionospheric conductance on the cross polar cap potential: Results of global MHD modeling, Geophys. Res. Lett., 30(23), 2180, doi:10.1029/2003GL017903, 2003.

Data‐derived forecasting model for relativistic electron intensity at geosynchronous orbit

[1] In this paper we present a data-derived model of relativistic electron flux at geosynchronous orbit. The model is driven by multiple solar wind and magnetospheric inputs and combines the deterministic approach of nonlinear dynamics with conditional probability consideration. The model is used for one-day predictions of daily flux maxima for the years 1995–2000. The deterministic part of the model yields average prediction efficiency of 0.77 and linear correlation coefficient of 0.89. It identifies solar wind velocity and SymH index as most relevant input parameters. The probabilistic part of the model quantifies the risks of deviations from deterministic predictions as a function of average solar wind and magnetosphere conditions. INDEX TERMS: 2720 Magnetospheric Physics: Energetic particles, trapped; 2722 Magnetospheric Physics: Forecasting; 2730 Magnetospheric Physics: Magnetosphere— inner; 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions; 3220 Mathematical Geophysics: Nonlinear dynamics. Citation: Ukhorskiy, A. Y., M. I. Sitnov, A. S. Sharma, B. J. Anderson, S. Ohtani, and A. T. Y. Lui (2004), Data-derived forecasting model for relativistic electron intensity at geosynchronous orbit, Geophys. Res. Lett., 31, L09806,

Modeling the spatial structure of the high latitude magnetic perturbations and the related current systems

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...

Lyapunov exponent of magnetospheric activity from AL time series

A correlation dimension analysis of the AE index indicates that the magnetosphere behaves as a low-dimensional chaotic system with a dimension close to 4. Similar techniques are used to determine if the systems behavior is due to an intrinsic sensitivity to initial conditions and thus is truly chaotic. The quantity used to measure the sensitivity to initial conditions is the Lyapunov exponent. Its calculation for AL shows that it is nonzero (0.11±0.05 min−1). This gives the exponential rate at which initially similar configurations of the magnetosphere evolve into completely different states. Also predictions of deterministic nonlinear models are expected to deviate from the observed behavior at the same rate.

Spatiotemporal activity of magnetic storms

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.

Characterization Of Asymmetric Fragmentation Patterns In Spatially Extended Systems

Spatially extended systems yield complex patterns arising from the coupled dynamics of its different regions. In this paper we introduce a matrix computational operator, , for the characterization of asymmetric amplitude fragmentation in extended systems. For a given matrix of amplitudes this operation results in an asymmetric-triangulation field composed by L points and I straight lines. The parameter (I-L)/L is a new quantitative measure of the local complexity defined in terms of the asymmetry in the gradient field of the amplitudes. This asymmetric fragmentation parameter is a measure of the degree of structural complexity and characterizes the localized regions of a spatially extended system and symmetry breaking along the evolution of the system. For the case of a random field, in the real domain, which has total asymmetry, this asymmetric fragmentation parameter is expected to have the highest value and this is used to normalize the values for the other cases. Here, we present a detailed description of the operator and some of the fundamental conjectures that arises from its application in spatio-temporal asymmetric patterns.