Statistical analysis of Hasegawa - Wakatani turbulence

Resistive drift wave turbulence is a multipurpose paradigm that can be used to understand transport at the edge of fusion devices. The Hasegawa-Wakatani model captures the essential physics of drift turbulence while retaining the simplicity needed to gain a qualitative understanding of this process. We provide a theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent events in Hasegawa-Wakatani turbulence with enforced equipartition of energy in large scale zonal flows and small scale drift turbulence. We find that for a wide range of adiabatic index values the stochastic component representing the small scale turbulent eddies of the flow, obtained from the ARIMA model, exhibits super-diffusive statistics, consistent with intermittent transport. The PDFs of large events (above one standard deviation) are well approximated by the Laplace distribution, while small events often exhibit a Gaussian character. Furthermore there exist a strong influence of zonal flows for example, via shearing and then viscous dissipation maintaining a sub-diffusive character of the fluxes

Intermittency, scaling and the Fokker-Planck approach to fluctuations of the solar wind bulk plasma parameters as seen by the WIND spacecraft

The solar wind provides a natural laboratory for observations of MHD turbulence over extended temporal scales. Here, we apply a model independent method of differencing and rescaling to identify self-similarity in the Probability Density Functions (PDF) of fluctuations in solar wind bulk plasma parameters as seen by the WIND spacecraft. Whereas the fluctuations of speed v and IMF magnitude B are multi-fractal, we find that the fluctuations in the ion density rho, energy densities B^2 and rho v^2 as well as MHD-approximated Poynting flux vB^2 are mono-scaling on the timescales up to ~26 hours. The single curve, which we find to describe the fluctuations PDF of all these quantities up to this timescale, is non-Gaussian. We model this PDF with two approaches-- Fokker-Planck, for which we derive the transport coefficients and associated Langevin equation, and the Castaing distribution that arises from a model for the intermittent turbulent cascade.Comment: 8 pages, 11 figures. APS format accepted to be published at PRE. Changes include the discussion of the functional form of tails for rescaled PDFs. Introductions has been modified as well. New figure 7 has been adde

Approaches to scaling phenomena in space and laboratory plasma

Many laboratory and space plasma phenomena exhibit scaling, i.e., no characteristic spatial and/or temporal scale can be identified in their dynamics. This lack of a characteristic scale makes the dynamics of these systems extremely complex and intractable to analytical approaches. Their statistical features, however, appear to be simple and exhibit a degree of universality. We will explore two approaches to scaling in plasma systems, one based on avalanching sandpile model and the second one based on turbulence. The avalanching model developed here exhibits a wide range of dynamic behavior and incorporates other established models as limiting cases. A single control parameter that specifies the length scale over which the redistribution rule operates compared to the finite system size, allows us to explore different regimes of the model's dynamics close to and away from the existing fixed points. An advanced Virtual Reality visualization technique was employed to gain a better qualitative understanding of the sandpile behavior in the parameter space. This sandpile model was used to simulate features found in the fusion plasma in both low and high confinement modes. Because of the simplicity of this model, it was possible to formally characterize and explain the mechanisms underlying steep gradients formation and appearance of internal transport barriers, and to identify links to tokamak plasma behavior. The solar wind is a supersonic, super-Alfvenic flow of compressible and inhomogeneous plasma from the Sun. The solar wind provides a natural laboratory for observations of MHD turbulence over extended temporal scales. In this case a generic and model independent method of differencing and rescaling was applied to identify self-similarity in the Probability Density Functions (PDF) of fluctuations in solar wind bulk plasma parameters as seen by the WIND spacecraft. The single curve, which we found to describe the fluctuations PDF of some quantities, is non-Gaussian. We model this PDF with two approaches-Fokker-Planck, for which we derived the transport coefficients and associated Langevin equation, and the Castaing distribution that arises from a model for the intermittent turbulent cascade. The technique was also used to quantify the statistical properties of fluctuations in the coupled solar wind-magnetosphere system. These quantitative and model-independent results place important constraints on models for the coupled solar wind-magnetosphere system

Elucidating plasma dynamics in Hasegawa-Wakatani turbulence by information geometry

The impact of adiabatic electrons on drift-wave turbulence, modeled by the Hasegawa-Wakatani equations, is studied using information length. Information length is a novel theoretical method for measuring distances between statistical states represented by different probability distribution functions (PDFs) along the path of a system and represents the total number of statistically different states that a system evolves through in time. Specifically, the time-dependent PDFs of turbulent fluctuations for a given adiabatic index A are computed. The changes in fluctuation statistics are then quantified in time by using information length. The numerical results provide time traces exhibiting intermittent plasma dynamics, and such behavior is identified by a rapid change in the information length. The effects of A are discussed.</p

Statistically determined dispersion relations of magnetic field fluctuations in the terrestrial foreshock

We obtain dispersion relations of magnetic field fluctuations for two crossings of the terrestrial foreshock by Cluster spacecraft. These crossings cover plasma conditions that differ significantly in their plasma β and in the density of the reflected ion beam, but not in the properties of the encountered ion population, both showing shell-like distribution function. Dispersion relations are reconstructed using two-point instantaneous wave number estimations from pairs of Cluster spacecraft. The accessible range of wave vectors, limited by the available spacecraft separations, extends to ≈2 × 104 km. Results show multiple branches of dispersion relations, associated with different powers of magnetic field fluctuations. We find that sunward propagating fast magnetosonic waves and beam resonant modes are dominant for the high plasma β interval with a dense beam, while the dispersions of the interval with low beam density include Alfvén and fast magnetosonic modes propagating sunward and anti-sunward

Wave pressure and energy cascade rate of kink waves computed with Elsasser variables

Numerical simulations have revealed a new type of turbulence of unidirectional waves in a plasma that is perpendicularly structured (Magyar et al. 2017), named uniturbulence. For this new type of turbulence, the transverse structuring modifies the upward propagating wave to have both Elsasser variables, leading to the well-known perpendicular cascade. In this paper, we study an analytical description of the non-linear evolution of kink waves in a cylindrical flux tube, which are prone to uniturbulence. We show that they lead to a non-linear cascade for both propagating and standing waves. We calculate explicit expressions for the wave pressure and energy cascade rate. The computed damping rate {\tau}/P depends on the density contrast of the flux tube and the background plasma and is inversely proportional to the amplitude of the kink wave. The dependence on the density contrast shows that it plays a role especially in the lower solar corona. These expressions may be added in Alfven wave driven models of the solar atmosphere (such as AWSOM, van der Holst et al. 2014), modifying it to UAWSOM (Uniturbulence and Alfven Wave Solar Model)

Topology of turbulence within collisionless plasma reconnection

In near-collisionless plasmas, which are ubiquitous in astrophysics, entropy production relies on fully-nonlinear processes such as turbulence and reconnection, which lead to particle acceleration. Mechanisms for turbulent reconnection include multiple magnetic flux ropes interacting to generate thin current sheets which undergo reconnection, leading to mixing and magnetic merging and growth of coherent structures, unstable reconnection current layers that fragment and turbulent reconnection outflows. All of these processes act across, and encompass, multiple reconnection sites. We use Magnetospheric Multi Scale four-point satellite observations to characterize the magnetic field line topology within a single reconnection current layer. We examine magnetopause reconnection where the spacecraft encounter the Electron Diffusion Region (EDR). We find fluctuating magnetic field with topology identical to that found for dynamically evolving vortices in hydrodynamic turbulence. The turbulence is supported by an electron-magnetohydrodynamic (EMHD) flow in which the magnetic field is effectively frozen into the electron fluid. Accelerated electrons are found in the EDR edge where we identify a departure from this turbulent topology, towards two-dimensional sheet-like structures. This is consistent with a scenario in which sub-ion scale turbulence can suppress electron acceleration within the EDR which would otherwise be possible in the electric field at the X-line

Wavelet determination of magnetohydrodynamic range power spectral exponents in solar wind turbulence seen by Parker Solar Probe

Context. The high Reynolds number solar wind flow provides a natural laboratory for the study of turbulence in situ. Parker Solar Probe samples the solar wind between 0.17 AU and 1 AU, providing an opportunity to study how turbulence evolves in the expanding solar wind. Aims. We aim to obtain estimates of the scaling exponents and scale breaks of the power spectra of magnetohydrodynamic (MHD) turbulence at sufficient precision to discriminate between Kolmogorov and Iroshnikov-Kraichnan (IK) turbulence, both within each spectrum and across multiple samples at different distances from the Sun and at different plasma β. Methods. We identified multiple long-duration intervals of uniform solar wind turbulence, sampled by PSP/FIELDS and selected to exclude coherent structures, such as pressure pulses and current sheets, and in which the primary proton population velocity varies by less than 20% of its mean value. The local value of the plasma β for these datasets spans the range 0.14  Results. Within 0.3 AU of the Sun, the IR exhibits two distinct ranges of scaling. The inner, high-frequency range has an exponent consistent with that of IK turbulence within uncertainties. The outer, low-frequency range is shallower, with exponents in the range from –1.44 to –1.23. Between 0.3 and 0.5 AU, the IR exponents are closer to, but steeper than, that of IK turbulence and do not coincide with the value –3/2 within uncertainties. At distances beyond 0.5 AU from the Sun, the exponents are close to, but mostly steeper than, that of Kolmogorov turbulence, –5/3: uncertainties inherent in the observed exponents exclude the value –5/3. Between these groups of spectra we find examples, at 0.26 AU and 0.61 AU, of two distinct ranges of scaling within the IR with an inner, high-frequency range with exponents ∼ − 1.4, and a low-frequency range with exponents close to the Kolmogorov value of –5/3. Conclusions. Since the PSD-estimated scaling exponents are a central predictor in turbulence theories, these results provide new insights into our understanding of the evolution of turbulence in the solar wind

The role of compressibility in solar wind plasma turbulence

Incompressible Magnetohydrodynamics is often assumed to describe solar wind turbulence. We use extended self similarity to reveal scaling in structure functions of density fluctuations in the solar wind. Obtained scaling is then compared with that found in the inertial range of quantities identified as passive scalars in other turbulent systems. We find that these are not coincident. This implies that either solar wind turbulence is compressible, or that straightforward comparison of structure functions does not adequately capture its inertial range properties.Comment: 4 pages, 7 figure

Approaches to scaling phenomena in space and laboratory plasma

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