NG23A-1181 1340h
Fluctuations in Total Quantities as a Probe of Complex Behaviour
Very frequently in physics one studies a macroscopic variable which averages the effect of N microscopic degrees of freedom (dof). In equilibrium systems, where the dof are uncorrelated, the fluctuations are forced to a Gaussian form quite rapidly with increasing N by the central limit theorem. Increasingly, however, attention is focused on the non-Gaussian fluctuations seen in long-range correlated, critical systems. Recent progress was made by Bramwell ${\it et \ al}$ [Nature, 1998; PRL, 2000] who observed a particular non-Gaussian fluctuation probability density (pdf) in both confined laboratory turbulence and the XY model of critical phenomena, subsequently reporting it in many other critical models such as sandpiles. Chapman ${\em et \ al }$ [2000] proposed that the similar functional form of this pdf to the Gumbel distribution of extreme statistics might be due to the fluctuations in patches of activity in a complex system being dominated by the largest event. This is counter-intuitive, because of the behaviour of the short-ranged distributions with which we are more familiar, but similar questions been the subject of recent interest in solid state physics [Romeo ${\em et \ al}$, Eur. Phys. J. B, 2003]. We here examine this idea using a lognormal random process, showing under which circumstances the sums and maxima are similarly distributed. We also examine the effect of breaking statistical independence by means of a Hurst exponent not equal to 0.5. We also discuss applications to burst pdfs of the type first calculated for the auroral indices by Takalo [1993] and Consolini [1997].
NG23A-1182 1340h
Modelling the multi-scale coupling in solar reconnection
Solar reconnection is a typical example of a nonlinear, multi-scale phenomenon which follows as a direct consequence from the fundamental nonlinearity of plasma physical equations and the variety of complicated initial and boundary conditions in a non-uniform plasma. Reconnection needs dissipation, which has to be treated microscopically but it also needs magnetic energy accumulation at large scale. The inter-scale coupling between the two is the real open question in this strongly nonlinear problem. Any proper treatment of reconnection has to combine both aspects, which appeared to be an non-trivial problem, impossible to be solved directly even using for modern massively parallelized computer simulation techniques. We are considering the follwoing way out of this dilemma: let us start with known boundary and initial conditions as the input to large scale modelling based on truncated equation. This allows to obtain the times and critical regions, where small-scale phenomena have to be taken into account and the truncation is inappropriate. Next we use these results about critical regions as boundary and initial conditions for the analysis of microphysical processes at their naturally shorter temporal and spatial scales. Feeding this information back to the large scale truncated system in terms of an appropriate parametrization we than investigate the further evolution of the large scale system already including the small-scale microphysical results extending the truncated macroscopic evolution equations in an appropriate way. We demonstrate the workability of such approach applying it to model the heating of EUV and X-ray Bright Points in the solar corona. The initial system of MHD equations uses a severely truncated energy equation which does, nevertheless, describe the large corona appropriately. This allows us to identify the potential sites of non-force-free current sheets, where the current carriers will be accelerated until their velocity exceeds the theshold of microinstabilities. The latter are considered kinetically, which in turn provides transport equations and coefficients for the large scale MHD approach. The feedback of microphysical processes to the large scale system is especially strong where the large scale topology and geometry tends to form deformations or even singularities. This allowed us already, for example, to localize the energization of the solar corona better as approaches could do which did not consider the specific feedback of microprocesses. As an example, we identified the locations of coronal Bright Points based on solar photospheric observations.
NG23A-1183 1340h
Characterising the Scaling Properties of the Local Rate of Dissipation in Incompressible Isotropic Three-Dimensional MHD Turbulence
Recent improvements in the scale and accuracy of direct numerical simulations (DNS) of three-dimensional incompressible isotropic MHD turbulence enable many of its fundamental properties to be investigated anew. Here we report progress on several questions, achieved using the DNS of Biskamp and Muller [Phys. Plasmas 7, 4889 (2000)]. This employs the incompressible resistive MHD equations to simulate decaying isotropic turbulence, with finite magnetic helicity and initially equal magnetic and kinetic energy densities. It has a spatial resolution of $512^3$ Fourier modes. Central questions include the nature, including dimensionality, of the localised turbulent structures that give rise to intermittency in the local rate of dissipation; and the relation of their role to that of less strongly dissipative turbulent structures that are more widely distributed. There is also the question of the extent and nature of any universal scaling properties of the turbulent fluctuations. Here the scaling of the local rate of dissipation (both viscous and Ohmic), and of its one-dimensional surrogate, are compared with the picture gained from the study of the Elsasser field variables. A range of techniques is used to characterise any universal scaling behaviour that arises from the relatively low Reynolds number flows obtainable by DNS. These include extended self-similarity (ESS), which extends a variant of inertial range scaling into the dissipative range. Intermittency in these measures is then analysed in the framework of the generalised theory of the intermittency correction proposed by She and Leveque [Phys. Rev. Lett. 72, 336 (1994)].
NG23A-1184 1340h
Nearly incompressible fluid III: Hydrodynamics and large-scale inhomogeneity
The solar wind is an excellent example of a turbulent MHD fluid, and models based on an incompressible MHD description have had considerable success in explaining observations such as the Kolmogorov-like power spectrum in magnetic field fluctuations. However, fully developed solar wind fluctuations also show a Kolmogorov like density spectrum with spectral index $\kappa^{-5/3}$. These weakly compressible fluctuations cannot be described by isotropic homogeneous and isothermal incompressible fluid models. Nearly incompressible (NI) fluid theory, developed by Zank, Matthaeus and Brown is an appropriate model to describe the weakly compressible solar wind fluctuations. The theory is primarily developed for isotropic homogeneous fluctuations in solar wind. However, the solar wind possesses large scale gradients in the magnetic field, density and temperature. In order to describe these fluctuations in a self consistent manner, it is necessary to include large scale inhomogeneities in the NI model. Here we present an extension of the theory of NI fluids that includes large scale gradients in the solar wind background. The inhomogeneous flow modifies the leading order incompressible behavior of the fluid substantially in that: i) the divergence of the solar wind velocity fluctuations is non-solenoidal. ii) Incompressible density and pressure fields are driven by large-scale gradients in the solar wind. iii) Higher order compressible pressure fluctuations couple to large-scale gradients in the solar wind pressure and velocity fields. iv) The complete inhomogeneous NI hydrodynamics model, describing high plasma beta solar wind, possesses rich and complex nonlinear interactions that couple to the large scale gradients through a weak aspect ratio parameter (defined by the ratio of ambient small scale turbulence to the large scale solar wind).
NG23A-1185 1340h
Density and Temperature Spectra in the Solar Wind: Nearly Incompressible Modelling
Density and temperature spectra in the solar wind frequently exhibit a Kolmogorov-like spectrum. Remarkably, interstellar scintillation and angular radio wave broadening measurements also show that interstellar (electron) density fluctuations exhibit a Kolmogorov-like $k^{-5/3}$ power spectrum extending over many decades in wavenumber space. The ubiquity of the Kolmogorov-like interplanetary and interstellar medium (ISM) density spectrum led to an explanation based on the coupling of incompressible magnetohydrodynamic (MHD) fluctuations to density fluctuations through a ``pseudosound'' relation within the context of ``nearly incompressible'' (NI) hydrodynamics (HD) and MHD models. The NI theory provides a fundamentally different explanation for the observed ISM density spectrum in that density fluctuations can be a consequence of passive scalar convection due to background incompressible fluctuations. Depending upon the amplitude of thermal, pressure and density fluctuations, there exist two distinct approaches to incompressibility. When density and temperature dominate the pressure fluctuations, the NI regime is called heat fluctuation dominated (HFD). On the other hand, when all the fluctuations are comparable heat fluctuation modified (HFM) NI regime results. Here, we present results of our two dimensional nonlinear fluid simulations, exploring various nonlinear aspects, that lead to inertial range ISM turbulence within the context of the NI hydrodymanics models. In qualitative agreement with the NI predictions and in-situ observations, we find that the density fluctuations exhibit a Kolmogorov-like spectrum via a passive convection in the field of the background incompressible fluctuations in both the regimes.
NG23A-1186 1340h
Properties of Chaotic Scattering in Current Sheets
We investigate the Hamiltonian system of a charged particle in the modified Harris magnetic field model, relevant to the dynamics of current sheets in space plasmas. It is a localized scattering system as the particle stays in the current sheet or scattering region for a finite time interval before it escapes from the region. For some initial conditions, the motion of the particle has been found to be chaotic and the statistical properties of an ensemble of particle trajectories with a fixed energy have been shown to critically depend on the energy. At the resonant energies, the particle on a chaotic trajectory tends to stay in the current sheet region much longer than the particle on a chaotic trajectory with energy away from the resonant energies. Our numerical results show that the average Lyapunov exponent increases for higher resonant energies whereas away from the resonant energies it remains relatively small. In the talk, we will also show that the distribution of the Lyapunov exponents follows a universal functional form at both the resonant and the off-resonant energies.
NG23A-1187 1340h
On the Characteristics and Generation of Magnetosheath Solitary Waves
Observations made by the Cluster WBD plasma wave instruments have recently revealed that solitary waves in Earth's magnetosheath have significantly shorter time durations (tens to a few hundreds of microseconds) than those in all other regions of Earth from the solar wind to the inner magnetosphere (several tenths to several ones of milliseconds). However, the peak-to-peak electric field amplitudes of the magnetosheath solitary waves appear to follow the general trend of solitary waves in the other regions, that being increasing electric field amplitudes with increasing local magnetic field strength. We expand on these findings by providing the results of a survey of the magnetosheath solitary waves in which we compare their amplitudes and time durations to the spacecraft distance from the bow shock, to the magnitude of the local ion flow velocity and to the angle of the local ion flow velocity to the magnetic field. The results of this survey would tend to support the conclusion that these solitary waves are locally generated rather than propagating to the measurement point from the bow shock or other location. We examine the low frequency (few hundred Hz to a few kHz) wave, electron density, and electron and ion data for further insight into the possibility that the magnetosheath solitary waves are locally generated.
NG23A-1188 1340h
Scaling and Markov properties of magnetic field fluctuations in the geotail plasma sheet
In a recent paper by Chang et al. (2004) it has been shown that the evolution of magnetic coherent structures in space plasmas can generate nonpropagating spatiotemporal fluctuations which are characterized by non-Gaussian probability distribution functions (PDFs). The central regions (plasma sheet and neutral sheet) of the Earth's magnetospheric tail provide a natural laboratory for the observation and the study of the aforementioned intermittent fluctuations over a wide range of spatiotemporal scales. Here, we investigate the statistical features of the turbulent magnetic field fluctuations, as observed by satellite measurements, in the tail plasma sheet region by studing the scaling features of the PDFs in a wide range of scales from the non-MHD scales up to the MHD scales. The Markov nature of the aforementioned fluctuations is also investigated.
NG23A-1189 1340h
Scaling Properties of Magnetic Fluctuations in the Earth's Plasma Sheet
In situ observations of the ion velocity and magnetic field in the plasma sheet have revealed intermittent fluctuations in the temporal and spatial domains. These observations were attributed to turbulence. Any description of fluctuating fields in terms of turbulence, however, requires certain multi-scaling characteristics to be present in the observed data. Since the specific occurrence of magnetic fluctuations strongly depends on the spatio-temporal non-steady conditions in the plasma sheet, the application of turbulence methodology should always be accompanied by a thorough analysis of the multi-scaling features in relation to the physical conditions during the analyzed intervals. In order to investigate the scaling properties of magnetic fluctuations, we employ wavelet methods together with a rescaling technique of empirical probability density functions for bursty-bulk flow and non-flow associated intervals in the plasma sheet. We show that both non-scaling and multi-scaling fluctuations are present. In the latter case the scalings, and the range of scales exhibiting characteristics of magnetohydrodynamic turbulence, differ significantly from the fluctuations occurring below the dissipation scale.
NG23A-1190 1340h
Intermittency Analyses on the SIERRA Measurements of the Electric Field Fluctuations in the Auroral Zone
We perform intermittency analyses on the electric field data obtained by the SIERRA sounding rocket in the auroral zone. The electric field fluctuations are broadband, covering the extremely low-frequency range with a power-law relation, similar to the type of fluctuations commonly observed at various altitudes of the auroral region. Our preliminary analyses of the data based on the technique of probability distribution functions indicate that the electric field fluctuations are intermittent. Using the methods of wavelet analyses and local intermittency measures, we determine the degree of intermittency of the fluctuations at various scales. It is found that the electric field fluctuations are more intermittent at smaller scales.
NG23A-1191 1340h
A Structure Function Analysis of Ionospheric Velocity and Ground-Based Magnetic Field Fluctuations.
A number of recent studies have investigated temporal structuring within the magnetosphere ionosphere system. Studies of ground magnetometer measurements, ionospheric velocity fluctuations, inter FTE intervals, and the AE index, have shown evidence of scale free behaviour. In contrast little work has been done to characterise the spatial structuring. With the large field of view of the SuperDARN radars we have the facility to investigate the spatial structure of ionospheric flows. We present a structure function analysis of 5 years of data from the Halley radar in Antarctica comparing contemporaneous measurements of ionospheric meridional velocities at different range separations. We find strong evidence for scale free behaviour both above and below the open-closed field line boundary and show that it is possible to collapse the distributions of fluctuations at different separations to a single distribution using appropriate scaling. We complement these results with a temporal and spatial structure function analysis of ground-based magnetometer data from the British Antarctic Survey's Low Power Magnetometer network.
NG23A-1192 1340h
Correlation Dimension Analysis Applied to a Magnetotail Coupled-Map Lattice Model
It has been suggested that slowly driven dynamical systems, with many degrees of freedom, self-organise into a critical state, with avalanches of all sizes obeying power law characteristics. Various recent observations and numerical simulations suggest that the Earth's magnetotail system, a highly complex system, could exist in a near-critical configuration. Although no experiment exists to prove entirely that a system is self-organised critical (SOC), several pieces of evidence can be collected to support the idea, e.g.\ exhibition of power-law scaling in distribution functions. An additional tool that can be used to reveal information from an observed time-series is correlation dimension analysis. The goal of a correlation dimension analysis is to extract, from a highly complex system with many degrees of freedom, the dimension of an underlying chaotic attractor. The existence of such a dimension may be used as evidence to argue whether a system is in a SOC state or otherwise. The numerical simulation used in this work, a magnetic field model of the magnetotail current sheet, has been developed by, amongst others, {Takalo, Timonen et al., (1999)}. It is in the form of a Coupled-Map Lattice (CML) and is based on the MHD diffusion equation and is continuously driven by solar wind \emph{vBs} data. It has been shown by {Takalo, Timonen et al., (1999)} that the model exhibits perturbations (avalanches) with power-law scalings in their distributions of duration and size. Such distributions may indicate SOC behaviour. This paper presents the results of a correlation dimension analysis of the numerical outputs of the CML model and discusses the implications.
http://www.acse.shef.ac.uk/~bates/research/?file=abstracts
NG23A-1193 1340h
Scale-Invariance and Universality in a 2-D Turbulent Current Sheet Model
Magnetospheric substorm is a complex and partially unpredictable phenomenon involving vast ranges of spatial and temporal scales. Recently, it has been revealed based on POLAR UVI observations that multiscale dynamics of auroral active areas associated with multiscale activity in the magnetotail (BBFs, pseudo-breakups, intermittent turbulence) is arranged across different time, space and energy scales in a scale-invariant way typical for many-body nonlinear systems in the vicinity of a nonequilibrium critical point. Remarkable stability of the observed phenomenon under changeable solar wind conditions has been interpreted as a manifestation of self-organized critical (SOC) dynamics in the magnetotail plasma sheet. In this paper, we present first numerical results leading to the identification of the universality class of such dynamics as represented by the 2-D current sheet model (CSM) proposed by A. Klimas et al. [JGR, 2004, 109(A2)]. Based on the analysis of power-law critical relations characterizing statistical scaling, spreading behavior and fractal properties of current-driven instabilities in CSM, it is shown that the model belongs to the universality class of stochastic directed sandpiles (SDSP) characterized by strongly anisotropic energy transfer, and seems to operate in the regime that can be described using a relatively simple dynamic mean-field approximation. A number of scaling relations for different groups of critical exponents is verified, and a quantitative agreement between CSM exponents and the exponents reported in the literatures for other SDSP models is demonstrated. Most of the critical exponents obtained for CSM are shown to be reasonably close to the exponents calculated earlier for POLAR UVI data, which suggests possible casual relation between the SOC dynamics in the magnetotail plasma sheet and scale-invariant high-latitude geomagnetic perturbations.