Vadim M. Uritsky

Low frequency 1/f-like fluctuations of the AE-index as a possible manifestation of self-organized criticality in the magnetosphere

Low frequency stochastic variations of the geomagnetic AE-index characterized by 1/fb-like power spectrum (where f is a frequency) are studied. Based on the analysis of experimental data we show that the Bz-component of IMF, velocity of solar wind plasma, and the coupling function of Akasofu are insufficient factors to explain these behaviors of the AE-index together with the 1/fb fluctuations of geomagnetic intensity. The effect of self-organized criticality (SOC) is proposed as an internal mechanism to generate 1/fb fluctuations in the magnetosphere. It is suggested that localized spatially current instabilities, developing in the magnetospheric tail at the initial substorm phase can be considered as SOC avalanches or dynamic clusters, superposition of which leads to the 1/fb fluctuations of macroscopic characteristics in the system. Using the sandpile model of SOC, we undertake numerical modeling of space-localized and global disturbances of magnetospheric current layer. Qualitative conformity between the disturbed dynamics of self-organized critical state of the model and the main phases of real magnetospheric substorm development is demonstrated. It is also shown that power spectrum of sandpile model fluctuations controlled by real solar wind parameters reproduces all distinctive spectral features of the AE fluctuations.

Comparative study of dynamical critical scaling in the auroral electrojet index versus solar wind fluctuations

Based on an analysis of auroral electrojet (AE) index data, we demonstrate that the temporal evolution of magnetospheric perturbations exhibits non-trivial power-law relations consistent with the behavior of a general class of statistical physical models in the vicinity of a stationary critical point. We show that the ensemble average dynamics of the activity bursts in the AE index is essentially scale-free and can be characterized in terms of spreading critical exponents and δ. The lifetime T and the size S of the bursts show strong algebraic correlation that is approximated by the dependence S ∼ T 1+η+δ . For times shorter than 3.5 hours, we find scaling features in the AE index that are independent of the solar wind input, thus indicating the internal magnetospheric origin of the revealed effects.

25 Years of Self-Organized Criticality: Solar and Astrophysics

Shortly after the seminal paper “Self-Organized Criticality: An explanation of 1/fnoise” by Bak et al. (1987), the idea has been applied to solar physics, in “Avalanches and the Distribution of Solar Flares” by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.

Kinetic‐scale magnetic turbulence and finite Larmor radius effects at Mercury

We use a nonstationary generalization of the higher-order structure function technique to investigate statistical properties of the magnetic field fluctuations recorded by MESSENGER spacecraft during its first flyby (01/14/2008) through the near Mercurys space environment, with the emphasis on key boundary regions participating in the solar wind -- magnetosphere interaction. Our analysis shows, for the first time, that kinetic-scale fluctuations play a significant role in the Mercurys magnetosphere up to the largest resolvable time scale ~20 s imposed by the signal nonstationarity, suggesting that turbulence at this planet is largely controlled by finite Larmor radius effects. In particular, we report the presence of a highly turbulent and extended foreshock system filled with packets of ULF oscillations, broad-band intermittent fluctuations in the magnetosheath, ion-kinetic turbulence in the central plasma sheet of Mercurys magnetotail, and kinetic-scale fluctuations in the inner current sheet encountered at the outbound (dawn-side) magnetopause. Overall, our measurements indicate that the Hermean magnetosphere, as well as the surrounding region, are strongly affected by non-MHD effects introduced by finite sizes of cyclotron orbits of the constituting ion species. Physical mechanisms of these effects and their potentially critical impact on the structure and dynamics of Mercurys magnetic field remain to be understood.

Coexistence of self-organized criticality and intermittent turbulence in the solar corona.

An extended data set of extreme ultraviolet images of the solar corona provided by the SOHO spacecraft is analyzed using statistical methods common to studies of self-organized criticality (SOC) and intermittent turbulence (IT). The data exhibit simultaneous hallmarks of both regimes: namely, power-law avalanche statistics as well as multiscaling of structure functions for spatial activity. This implies that both SOC and IT may be manifestations of a single complex dynamical process entangling avalanches of magnetic energy dissipation with turbulent particle flows.

Geomagnetic substorms as perturbed self-organized critical dynamics of the magnetosphere

The e0ect of self-organized criticality (SOC), known from the theory of complex nonlinear systems, is considered as an internal mechanism of geomagnetic 4uctuations accompanying the development of magnetospheric substorms. It is suggested that spatially localized current sheet instabilities, followed by magnetic reconnection in the magnetotail, can be considered as SOC avalanches, the superposition of which leads naturally to the 1=fpower spectra (f — frequency, � — numerical parameter) of geomagnetic activity. A running 2D avalanche model with controlled dissipation rate is proposed for numerical investigation of the multi-scale plasma sheet behavior in stationary and nonstationary states of the magnetosphere. Two basic types of perturbations have been studied, the 9rst induced by an increase in the solar wind energy input rate and the second induced by a decrease in critical current density in the magnetotail. The intensity of large-scale perturbations in the model depends on accumulated energy level and internal dissipation in a manner similar to the dependence characteristic of real magnetospheric substorms. A spectral structure of model dynamics exposed to variations of solar wind parameters reveals distinctive features similar to natural geomagnetic 4uctuations, including a spectral break at 5h separating frequency bands with di0erent spectral slopes. c � 2001 Elsevier Science Ltd. All rights reserved.

Stable critical behavior and fast field annihilation in a magnetic field reversal model

Abstract 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.

Observations and Implications of Large-amplitude Longitudinal Oscillations in a Solar Filament

On 2010 August 20, an energetic disturbance triggered large-amplitude longitudinal oscillations in a nearby filament. The triggering mechanism appears to be episodic jets connecting the energetic event with the filament threads. In the present work, we analyze this periodic motion in a large fraction of the filament to characterize the underlying physics of the oscillation as well as the filament properties. The results support our previous theoretical conclusions that the restoring force of large-amplitude longitudinal oscillations is solar gravity, and the damping mechanism is the ongoing accumulation of mass onto the oscillating threads. Based on our previous work, we used the fitted parameters to determine the magnitude and radius of curvature of the dipped magnetic field along the filament, as well as the mass accretion rate onto the filament threads. These derived properties are nearly uniform along the filament, indicating a remarkable degree of cohesiveness throughout the filament channel. Moreover, the estimated mass accretion rate implies that the footpoint heating responsible for the thread formation, according to the thermal nonequilibrium model, agrees with previous coronal heating estimates. We estimate the magnitude of the energy released in the nearby event by studying the dynamic response of the filament threads, and discuss the implications of our study for filament structure and heating.

Stochastic Coupling of Solar Photosphere and Corona

The observed solar activity is believed to be driven by the dissipation of nonpotential magnetic energy injected into the corona by dynamic processes in the photosphere. The enormous range of scales involved in the interaction makes it difficult to track down the photospheric origin of each coronal dissipation event, especially in the presence of complex magnetic topologies. In this paper, we propose an ensemble-based approach for testing the photosphere-corona coupling in a quiet solar region as represented by intermittent activity in Solar and Heliospheric Observatory Michelson Doppler Imager and Solar TErrestrial RElations Observatory Extreme Ultraviolet Imager image sets. For properly adjusted detection thresholds corresponding to the same degree of intermittency in the photosphere and corona, the dynamics of the two solar regions is described by the same occurrence probability distributions of energy release events but significantly different geometric properties. We derive a set of scaling relations reconciling the two groups of results and enabling statistical description of coronal dynamics based on photospheric observations. Our analysis suggests that multiscale intermittent dissipation in the corona at spatial scales >3 Mm is controlled by turbulent photospheric convection. Complex topology of the photospheric network makes this coupling essentially nonlocal and non-deterministic. Our results are in an agreement with the Parkers coupling scenario in which random photospheric shuffling generates marginally stable magnetic discontinuities at the coronal level, but they are also consistent with an impulsive wave heating involving multiscale Alfv?nic wave packets and/or magnetohydrodynamic turbulent cascade. A back-reaction on the photosphere due to coronal magnetic reconfiguration can be a contributing factor.

A survey of hot flow anomalies at Venus

We present the first survey of hot flow anomalies (HFAs) at the bow shock of Venus, expanding on our recent initial case study. A 3.06 sol (774 Earth day) survey of Venus Express magnetometer, ion spectrometer, and electron spectrometer data was undertaken in order to identify Cytherian HFAs. Seven events were discovered, corresponding to a statistical frequency ≈1.2±0.8 per day, approximately the same rate as at the Earth. All seven HFAs were centered on a discontinuity in the solar wind, with inward pointing motional electric fields on at least one side, and exhibited electron and ion perturbations consistent with heating. For one event the calculation of continuous electron moments is possible, revealing that electron temperature increased from ≈2×105 K to 8×105 K in the HFA core (comparable to terrestrial and Kronian HFA observations), and density increased from ≈1 cm−3 to ~2[RIGHTWARDS ARROW]2.5 cm−3 in the bounding compression regions. Cytherian HFAs were found to be physically smaller (0.4[RIGHTWARDS ARROW]1.7 Venus radii (RV)) than their terrestrial or Kronian counterparts, although are much larger when compared to the overall size of the system (≈130% of the subsolar bow shock distance), and occur very close (1.5[RIGHTWARDS ARROW]3.0RV) to the planet. Thus, we hypothesize that HFAs have a much more dominant role in the dynamics of the induced magnetosphere of Venus relative to the magnetospheres of magnetized planets.