Combining global and multi-scale features in a description of the solar wind-magnetosphere coupling

Abstract

Abstract. The solar wind-magnetosphere coupling during substorms exhibits dynamical features in a wide range of spatial and temporal scales. The goal of our work is to combine the global and multi-scale description of magnetospheric dynamics in a unified data-derived model. For this purpose we use deterministic methods of nonlinear dynamics, together with a probabilistic approach of statistical physics. In this paper we discuss the mathematical aspects of such a combined analysis. In particular we introduce a new method of embedding analysis based on the notion of a mean-field dimension. For a given level of averaging in the system the mean-filed dimension determines the minimum dimension of the embedding space in which the averaged dynamical system approximates the actual dynamics with the given accuracy. This new technique is first tested on a number of wellknown autonomous and open dynamical systems with and without noise contamination. Then, the dimension analysis is carried out for the correlated solar wind-magnetosphere database using vB S time series as the input and AL index as the output of the system. It is found that the minimum embedding dimension of vB S − AL time series is a function of the level of ensemble averaging and the specified accuracy of the method. To extract the global component from the observed time series the ensemble averaging is carried out over the range of scales populated by a high dimensional multiscale constituent. The wider the range of scales which are smoothed away, the smaller the mean-field dimension of the system. The method also yields a probability density function in the reconstructed phase space which provides the basis for the probabilistic modeling of the multi-scale dynamical features, and is also used to visualize the global portion of the solar wind-magnetosphere coupling. The structure of its input-output phase portrait reveals the existence of two energy levels in the system with non-equilibrium dynamical features such as hysteresis which are typical for non-equilibrium phase transitions. Further improvements in space weather forecasting tools may be achieved by a combiCorrespondence to: A. Y. Ukhorskiy (sasha@astro.umd.edu) nation of the dynamical description for the global component and a statistical approach for the multi-scale component.

Dynamical critical scaling of electric field fluctuations in the greater cusp and magnetotail implied by HF radar observations of F-region Doppler velocity

“…Some aspects of magnetospheric dynamics are directly driven by the solar wind, yet others seem to arise from internal interactions, and it is possible the dynamics are often driven yet self-organised, behaving in a way analogous to phase transitions (Ukhorskiy et al, 2003). The driver might dominate the magnetospheric dynamics when and where the coupling is strong, yet self-organisation might prevail when and where the coupling is weak.…”

Evidence of low-dimensional chaos in magnetized plasma turbulence

“…By applying the meanfield dimensional method [3], we conclude that the dynamics underlying these data is low-dimensional on the larger scales, and its attractor can be unfolded in the embedding dimension of 4 ≈ D . Recurrence plot analysis reveals deterministic behavior in both plasma potential and density as well as correlation between them.…”

“…However, it has been shown in [6] that for analysis of experimental data more accurate phase space reconstruction can be obtained if data representing different observables can be applied. The low-dimensional character of the Helimak streamer dynamics can be put to a test by employing the mean-field dimensional method developed in [3]. In the following, we briefly review this method.…”

“…As a consequence, there is no smooth manifold containing the dynamical trajectories in any dimension of the reconstructed phase space, and standard methods such as correlation dimension analysis or false nearest neighbors method would indicate that the system is high-dimensional. On the other hand, the mean-field dimensional method, developed in [3] can be successfully applied to the experimental data. In this method the probability density function ) (D P is introduced.…”

Complexity in the high latitude HF radar spectral width boundary region

“…Chang, 1992;Ukhorskiy et al, 2003). In the current disruption paradigm for substorm onset, the cross tail current may undergo a transition to multi-fractal plasma turbulence in which current and magnetic fluctuations interact (Lui, 2001;Vörös et al, 2003).…”