NG31B-1194
The Spatial Correlation Lengthscale of Evolving Nonlinear Fluctuations in the Driven Solar Wind
One of the key quantitative observables of nonlinear phenomena is that of the spatial correlation lengthscale. Using simultaneous multiple spacecraft observations it is possible to directly infer the spatial correlation properties of solar wind parameters such as magnetic field and density. The focus of this work is to determine these using both linear and nonlinear estimators of correlation lengthscale, namely linear cross correlation, and mutual information. One method for investigating the imprint of the corona as a driver on the solar wind, and any associated modulation of cosmic ray flux is to study the differences between solar wind magnetic field properties at solar activity maximum, when the corona magnetic field structure is complex, and at solar minimum, when the coronal magnetic field is simple. Any parameter that does not vary with the solar cycle is likely to be independent of the formation process of the solar wind, and to be dominated by local turbulent behaviour. Changing parameters are likely to be directly affected by the corona and could be a source of cosmic ray modulation. We investigate the spatial correlation properties of the solar wind in the ecliptic at 1AU using simultaneous in-situ observations by the ACE and WIND spacecraft. We present the first direct study of the spatial correlation lengthscale λ of solar wind ion density fluctuations and find it to be smaller than that of the magnetic field. We find that there is the same statistically significant increase in λ by a factor ≈ 2 from maximum to minimum of the solar cycle, for both density and magnetic field magnitude. This is in contrast to the components of the magnetic field, whose λ shows no discernible solar cycle variation. This behaviour is present in the inertial range of turbulence and on larger scales. For the components of the magnetic field the measured correlation lengths are found to lie in the inertial range. Our results suggest long range correlation in ion density and |B| which is of direct coronal origin, in contrast to that found in the B components, which is more strongly dominated by in-situ evolving turbulence. The distinct correlation lengths of the density and magnetic field, and their solar cycle variation, thus provide new quantitative insights into the mapping of the coronal driver out into the solar wind. The lack of variation in the correlation length of the components of the magnetic field implies the continual presence of evolving shear Alfvénic turbulence throughout the solar cycle. The difference between the correlation lengths of the magnetic field magnitude and the magnetic field components could indicate the relative scales of compressive versus shear Alfvénic fluctuations or, at larger temporal scales, different aspects of propagating coherent structures of coronal origin. Thus we have a picture of the solar wind as a combination of imposed correlation from the coronal driver in density and |B| but evolving Alfvénic turbulence in the components of B. Measuring the correlation length of these parameters allows quantitative study of the in-situ behaviour of the solar wind and provides an insight into the formation of the solar wind in the solar corona. The correlation length is also a parameter in the scattering of cosmic rays as they pass through the Heliosphere. We acknowledge the ACE and WIND magnetometer and SWE teams for data provision and the EPSRC and UKAEA for support.
NG31B-1195
Dissipative Relaxed State for Plasma with External Drive: Application to Solar Coronal Magnetic Field
In astrophysical context, systems occurring in nature such as solar corona are open and externally driven . Here we investigate the relaxed states of plasma with an external drive, based on the principle of minimum dissipation. The principle minimum dissipation rate (MDR) is closely related to a well-known theorem of irreversible thermodynamics, viz. the principle of minimum entropy production rate. Such relaxed states with magnetic fields are coupled with flows are non-force free and can support finite pressure gradient. . A full 3- D numerical simulation principle of minimum dissipation rate under the constraint of (approximate) conservation of global helicity is a viable approach for plasma relaxation for a closed system. In a recent simulation by Dastgeer et al. (unpublished) we have shown that for a plasma with external drive a perpendicular component of current develops, which shows that a plasma can relax to a non-force free state. We demonstrate that Solar arcade structures can be modeled as a minimum dissipative relaxed state, and different types of arcade structures can be generated.Further, we demonstrate briefly a newly developed approach to solar coronal magnetic field extrapolation from vector magnetograms, based on MDR.
NG31B-1196
Dynamical complexity detection in geomagnetic activity indices using wavelet transforms and Tsallis entropy
Dynamical complexity detection for output time series of complex systems is one of the foremost problems in physics, biology, engineering, and economic sciences. Especially in magnetospheric physics, accurate detection of the dissimilarity between normal and abnormal states (e.g. pre-storm activity and magnetic storms) can vastly improve space weather diagnosis and, consequently, the mitigation of space weather hazards. Herein, we examine the fractal spectral properties of the Dst data using a wavelet analysis technique. We show that distinct changes in associated scaling parameters occur (i.e., transition from anti- persistent to persistent behavior) as an intense magnetic storm approaches. We then analyze Dst time series by introducing the non-extensive Tsallis entropy, Sq, as an appropriate complexity measure. The Tsallis entropy sensitively shows the complexity dissimilarity among different "physiological" (normal) and "pathological" states (intense magnetic storms). The Tsallis entropy implies the emergence of two distinct patterns: (i) a pattern associated with the intense magnetic storms, which is characterized by a higher degree of organization, and (ii) a pattern associated with normal periods, which is characterized by a lower degree of organization.
NG31B-1197
Investigation of Small-Scale/Dispersive Solar Wind Turbulence Using Cluster Data
Most observational work on solar wind turbulence has been devoted to MHD scales where the Kolmogovov scaling k-5/3 is frequently observed. Turbulence at frequencies above the proton gyrofrequency (fci≈ 0.1Hz) has not been thoroughly investigated and remains far less well understood. Above fci the spectrum steepens to ≈ f-2.5 and a debate exists as to whether the turbulence has become dominated by dispersive kinetic Alfvén waves and is dissipative, or has evolved into a new dispersive turbulent cascade dominated by whistler waves. Here we present recent results on the nature of this small-scale turbulence using magnetic field data from Cluster. These studies are made using two complementary methods: the k-filtering and the surrogate data. The k-filtering is a multipoint measurement technique that allows one to identify the nature of the turbulence and to calculate 3D k- spectra from the ω-ones (Sahraoui et al, PRL, 2006). To investigate small-scale solar wind turbulence, one needs to take advantage of the times when the separation of the four Cluster spacecraft was small. Given separations of 200km, and a typical speed of the solar wind of 600km/s, one expects to be able to study frequencies down to 3Hz. The surrogate data technique completes the previous studies that use only the power spectra (where the phases of the fluctuations are ignored) by making extensive use of the Fourier phases of the turbulent signals. Doing so allows one to detect any coherent structures present within the data. The technique has been applied successfully to magnetosheath compressible turbulence (Sahraoui, Phys. Rev. E, 2008), where the relationship between the identified phase coherence and intermittency, as well as the energy cascade, has been studied.
NG31B-1198
Use of multi-point analysis and modelling to address cross-scale coupling in space plasmas: lessons from Cluster
Fundamental outstanding problems in the physics of plasmas (in space) may be defined in terms of 'cross- scale' coupling, and comparative temporal behaviour, operating over the micro-, meso-, and (MHD-) fluid regimes under contitions of turbulence, during magnetic reconnection and in shocks. The proposed aims of the Cross-Scale mission, for example, are to determine a complete understanding of each of these themes, which map to a number of related, and overlapping, phenomena which need to be probed both theoretically and by multi-scale measurements. Known phenomena play different roles in each theme. The process of magnetic reconnection has a number of directly associated phenomena: FTEs, accelerated flows, energisation, x-line structure. Shock formation is controlled by entropy and free energy considerations, discontinuity relations and the magnetic geometry. Turbulence operates through a hierarchy of subtle transport mechanisms relating to fundamental scaling relations and requirements on criticality. Investigation of these problems requires analysis techniques which can distinguish and quantify temporal behaviour and multi-scale, spatial behaviour. The analysis of existing, multi-point data sets has lead to a number of data co- ordination methods, such as the four spacecraft analysis tools developed for Cluster. With the addition of theoretical modelling (in the context of particular phenomena, captured by a large number of events) and considerations of measurement quality, advanced analysis concepts may be investigated and we consider examples of these here. A particular issue, is how to resolve temporal behaviour across the spatial regimes, so that the data set is suitably coordinated. Moreover, adequate sampling of phenomena to extract the necessary information on the mechanisms operating requires suitable spacecraft configurations and directly maps into the measurement quality achievable.
NG31B-1199
3D BGK Modes in Finite Magnetic Field as Electrostatic Solitary Waves in Space Plasmas
There has been renewed interest in the theory of Bernstein-Greene-Kruskal (BGK) modes, motivated by recent identifications of electrostatic solitary waves in space plasmas from spacecraft such as Geotail, Fast, Polar, Cassini, and Cluster. To fully account for theses observations, the classical one-dimensional (1D) BGK mode theory is insufficient. While 1D BGK theory is quite mature, there appears to be no exact 3D solutions in the literature, except for the limiting case when the magnetic field is infinitely strong [Chen et al., Phys. Rev. E 69, 055401(R) (2004)], as well as 3D BGK modes with zero magnetic field [Ng & Bhattacharjee, Phys. Rev. Lett., 95, 245004, 2005], and 2D BGK modes with finite magnetic field [Ng, Bhattacharjee & Skiff, Phys. Plasmas 13, 055903 (2006)]. Here we construct approximate 3D BGK modes in finite magnetic field with approximations characterized by explicit parameters so as to show that they tend to the infinite-field solutions. Width-amplitude relation of such BGK modes, as well as the spatial electric field structures, will be compared with observations.
NG31B-1200
Characteristic Parameters of Drift-Vortices Coupled to Alfven Waves in an Inhomogeneous Space Plasma
We present detailed measurements of ion scale vortices of drift-type coupled to Alfven waves in an inhomogeneous and collisionless space magnetoplasma. The two free parameters of a dipolar vortex, intensity and spatial radius, are measured. The vortices are driven by a strong density gradient on a boundary layer with scale size of the same order as the vortex diameter. Observations of vortices off the gradient shows that symmetry-braking conditions in a real inhomogeneous plasma can lead not only to cross-field but also to cross-boundary anomalous transport of particles and energy.
NG31B-1201
ROMA (Rank-Ordered Multifractal Analysis) Spectra for Intermittent Fluctuations with Nonlinear Crossover Behavior --- Electric Field in the Auroral Zone
ROMA (Rank-Ordered Multifractal Analysis) has the capabilities of deciphering the multifractal characteristics of intermittent fluctuations. The method allows one to understand the multifractal properties through global scale invariants. The utilities of ROMA, which combines the ideas of parametric rank ordering and single- parameter scaling of monofractals, were first demonstrated in its application to the results obtained from large-scale 2-D MHD simulations. In this study, we apply ROMA to the electric field fluctuations measured by the SIERRA sounding rocket in the auroral zone. The intermittent fluctuations span across time scales of multiple regimes that presumably reflect a change in the dominant physical processes. We extend the ROMA technique to take into account such nonlinear crossover behavior in the time scales, and obtain global scale invariants associated with the cross-regime multifractal spectra.
NG31B-1202
3D Numerical Simulations of Driven Dissipative Relaxed Plasma Processes
We develop a self-consistent, time-dependent numerical simulations of driven dissipative turbulent plasmas using full three dimensional compressible MHD code with a numerical resolution of 1283. Our simulations follow the time variation of global helicity, magnetic energy, and the dissipation rate and confirm that the global helicity remains approximately constant while magnetic energy is decaying faster and dissipation rate is decaying even faster than the magnetic energy. The underlying driven plasma system is shown to possess finite parallel and perpendicular components of currents. The latter establishes that most driven plasma systems are non force free and that the principle of minimum dissipation rate under the constraint of (approximate) conservation of global helicity is a viable approach for plasma relaxation processes in general in a driven system.
NG31B-1203
Nonlinear dynamics of two-dimensional electron plasma
The turbulent relaxation of a magnetized two dimensional (2D) electron plasma experiment has been investigated. The nonlinear dynamics of this kind of plasma can be approximated in leading order as a 2D guiding center fluid, which behaves in complete analogy to the 2D Euler equations. Departures form this analogy include dissipative and three dimensional effects. Here we examine the characteristics of the experimental data and compare these to solutions of 2D dissipative Navier Stokes equations. We find, perhaps remarkably, that the two systems show similar time histories, including increase of entropy and decrease of the ratio of enstrophy-to-energy. Attempts to re-examine the theories of selective decay and maximum entropy are reviewed, including difficulties that are peculiar to the one species case. Distinguishing between these possibilities has potentially important implications for self organizing systems in space and astrophysical plasmas, including the ionosphere and solar corona. Research supported by DOE grant DE- FG02-06ER54853.
NG31B-1204
Nonlinear electrostatic instabilities in a multi-ion plasma with two drifting ion- species
It is shown that the presence of a finite amplitude Alfvén-cyclotron in a solar wind-like plasma with two drifting ion-components relative to the background plasma, leads to electrostatic ion-acoustic-like waves triggered by the interaction of a forward propagating linear ion-acoustic wave supported by one species, and an ion-acoustic backward propagating ion-acoustic waves supported by a different ion-species. This is shown to occur in fast solar wind streams with drifting protons and alpha-particles. Linear ion-acoustic instabilities of this kind are known to occur when the phase velocity of an ion-acoustic wave moving forward and supported by one species, overlaps with the phase velocity of a backward propagating ion-acoustic wave supported by another ion-species. However, not only their properties are completely different, but also, while the latter are linear instabilities -they do not require the presence of a large amplitude Alfvén-cyclotron wave- the former are nonlinear instabilities and require at least two different drifting ion species relative to the core protons. It has been recently shown that the electrostatic turbulence in space plasmas consists of longitudinal waves with acoustic-like dispersion relation [Valentini et al., Phys. Rev. Lett. 100, 125003, 2008], so that these type of waves might also play an important role in several ion-component plasmas such as the solar wind and the magnetosphere.
NG31B-1205
Quantitative Measures of Chaos in the Magnetotail
In this paper we re-examine the nature of charged particle motion in the magnetotail focusing on objective, quantitative measures of chaotic nature of the orbits. In particular, we focus on three quantities as a function of the particle energy:1) the Lyapunov exponent (λ) 2) the fraction of the orbits that enter into the chaotic region of phase space and 3) the average trapping time of the orbits. We calculate the Lyapunov exponent by finding the time asymptotic value of λ for a uniform source distribution of 500,000 particles. We find that at particular resonance energies the number of particles entering into the chaotic region of phase space experiences a minimum and that both the Lyapunov exponent and the time that the particles are trapped have maxima. It is shown that the longest lived orbits at the resonance energies tend to uniformly sample the chaotic region of phase space, whereas the longest lived orbits between the resonance energies tend to get trapped for long periods of time near the integrable regions of phase space and only sparsely sample the chaotic regions. As a general trend, the value of λ tends to increase for increasing values of the energy. It has been conjectured that the "chaos" should be a maximum when the ion gyroradius is equal to the maximum curvature of the magnetic field. We find that in this regime, whereas all of the particles enter into the chaotic region the Lyapunov exponent is not near a maximum value.