NG21A-01 INVITED 08:00h
What We Can Learn From Solar Flare Statistics
Solar flares are caused by the rapid release of magnetic energy. Related events corresponding to the release of smaller energies such as microflares and transient brightenings occur more frequently. It has been found that the frequency of events is related to their energy by an inverse power law. This and several other statistical relationships have been used by several investigators as clues to the fundamental nature of solar flares. This talk will review some of the recent models, including cellular automata, relating the nature of flares to their statistics. This work was supported by NSF grant ATM 97227
NG21A-02 INVITED 08:15h
Magnetohydrodynamic turbulence in the solar corona
I will discuss the manifestation of MHD turbulence in different situations in the solar corona, modeled through direct numerical simulations of the MHD equations. These include dissipation rate scalings, impulsive events and their power-law distributions in a coronal loop model, heating profiles and current sheet formation in a low frequency wave-driven model of a coronal hole. These processes have in common a strong nonlinearity, anisotropic behavior and the formation of coherent structures, properties which are important for energy dissipation mechanisms in the solar corona.
NG21A-03 08:30h
Multi-Scale Probability Distributions of Solar Wind Speed and Magnetic Field Strength Fluctuations at 1 AU Described by a Generalized Tsallis PDF
This paper describes the multi-scale structure of fluctuations in the solar wind speed V and magnetic field strength B at 1 AU in 2003, during the declining phase of the solar cycle 23 and of fluctuations in V during 1999 approaching solar maximum. There were many types of physical structures (intermittent turbulence at the smallest scales; corotating streams, ejecta, compound streams, and interaction regions at intermediate scales; and the collection of streams and ejecta of different sizes and shapes at the largest scales). The probability distribution functions (PDFs) of changes of V and B on scales from 64 sec to 171 days can be described by a generalization of the PDF derived by Tsallis from a non-additive entropy function in the context of nonextensive statistical mechanics.
NG21A-04 08:45h
Scaling and a Fokker-Planck model for AU and AL- Solar Cycle Dependence.
Scaling and a departure from Gaussian statistics has been identified as a key property of magnetospheric energy release in the form of bursty bulk flows in the magnetotail, ``blobs" in the aurora, non-Gaussian fluctuations in geomagnetic indices and in single station magnetometer data. Models include Self-Organized Criticality (SOC) and multi-fractal models related to those of turbulence. We study scaling in fluctuations of the AU and AL geomagnetic indices that provide a measure of magnetospheric activity, and of the epsilon parameter which is a measure of the solar wind driver. We perform analyses that provide quantitative measures within the framework of models for turbulence and for critical phenomena; that is, we find the exponent that captures the self-similarity in the time series, and the functional form of the non-Gaussian Probability Density Function (PDF) that expresses its intermittency. Generalized structure function analysis is accompanied by PDF rescaling. Fluctuations in all quantities are found to exhibit self-similar statistics for up to 1-2 hours for fluctuation size up to 10 standard deviations. We divide the data into intervals of solar maximum and minimum and find that whereas fluctuations in epsilon and AU change their properties with the solar cycle, fluctuations in AL do not. This places strong statistical constraints on the propagation of information from these below-substorm scale fluctuations from the solar wind to the magnetosphere as seen by the indices. Having established scaling in AU and AL we then develop a Fokker-Planck model for their timeseries which we test against the PDF of the fluctuation timeseries. This provides a Langevin (stochastic dynamical) equation for the fluctuations in the indices.
NG21A-05 INVITED 09:00h
Quantifying Self-Organization and Coherent Structures with Statistical Complexity
Despite broad interest in self-organizing systems, there are few quantitative criteria for self-organization which can be applied to dynamical models, let alone experimental data. The existing criteria all give counter-intuitive results in important cases. A resolution is offered by a recently-proposed criterion, namely an internally-generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. This complexity can be precisely defined for spatially-extended dynamical systems, using the probabilistic ideas of mutual information and minimal sufficient statistics. The definition also leads to a general method for predicting such systems, and a simple algorithm for estimating statistical complexity. Examining the variation in the statistical complexity over space and time provides a way of automatically identifying the coherent structures generated by the system. The results of applying this algorithm to two important classes of cellular automata (CA) --- cyclic CA, which model excitable media, and sandpile CA, which are prototypes of self-organized criticality --- illustrate the general ideas.
http://bactra.org/research/
NG21A-06 INVITED 09:15h
Susceptibility Divergence at the Mean-Field SOC Limit in a 2-D Driven Current-Sheet Model
Uritsky et al. [JGR, 2002; GRL, 2003] have shown that the evolution of bright night-side auroral emission regions shares several important properties with that of avalanches in numerical models of self-organized criticality (SOC). Klimas et al. [JGR, 2000] have suggested that this result is a reflection of the statistical behavior of reconnection in the magnetotail plasma sheet. They hypothesize that the spatiotemporal distribution of reconnection events in the plasma sheet is a reflection of an avalanching process in that region that is scale-free over a broad range of scales. The nature of this hypothetical avalanching process is presently under investigation. Klimas et al. [JGR, 2004] are considering a 2-D driven current-sheet model that exhibits scale-free avalanche distributions associated with bursty, intermittent reconnection and field annihilation in the modeled current sheet. The indices that define these power-law avalanche distributions and the range of scales contained in the distributions are quite similar to those of the auroral emission regions. For a broad class of sandpile-like models, Vespignani and Zapperi [Phys. Rev. E, 1998] have constructed a mean-field theory of SOC that describes the divergence of the susceptibility of the models as the SOC limit is approached. Results will be presented to show that the susceptibility of the 2-D driven current-sheet model mentioned above diverges in agreement with this SOC theory. As in a 1-D driven current-sheet model discussed earlier by Uritsky et al. [Phys. Rev. E, 2002], this divergence is governed by a reduced control parameter that allows a finite input rate in the scaling-neighborhood of the SOC limit. We will conclude that, over a range of finite driving rates, the behavior of the 2-D driven current sheet model is consistent with the mean-field SOC theory of Vespignani and Zapperi.
NG21A-07 09:30h
A new exact solution of finite amplitude Alfven wave in a relativistic pair plasma
The dispersion relation of a finite amplitude, parallel, circularly polarized Alfven wave in a relativistic electron-positron plasma is derived exactly, without assuming weak relativistic effects, for the first time to the authors' knowledge. As usual, the dispersion relation consists of electromagnetic (light) waves and Alfven waves, both degenerated due to identical mass of electrons and positrons. However, when the relativistic effects are fully taken into account, there appears a critical wave number above which the Alfven wave ceases to exist. Details of the dispersion relation as well as its implications to astro-plasma physics will be discussed.
NG21A-08 09:45h
Observational Evidence for Nonlinear Charged Particle Dynamics in the Magnetotail.
Computer simulations of nonlinear charged particle dynamics in magnetotail-like magnetic fields have pointed towards the existence of a phase space resonance effect that manifests itself in the preferential forward or back scattering as a function of the energy of incoming particles as they interact with the current sheet. This resonance has been shown to manifest itself as a series of peaks in the ion distribution function where the separation of the peaks is proportional to the fourth root of the normalized particle energy. The normalization in turn depends on parameters that describe the magnetic field structure, i.e. the current sheet half-thickness and the ratio of the magnetic field strength at the midplane, $B_z$, to the magnetic field strength far from the field reversal but still in the plasma sheet, $B_0$. In this paper we will examine the underlying physics of the current sheet as a chaotic scattering system and demonstrate how the energy resonance signature in the ion distribution function may be used to determine the current sheet structure. We also present the results of a survey of the current sheet structure as determined using the energy resonance signature in the region from 20 to 100 earth radii downtail.