Probability Distribution Function Of Fluctuations Research Articles

Magnetic field fluctuation properties of coronal mass ejection-driven sheath regions in the near-Earth solar wind

Abstract. In this work, we investigate magnetic field fluctuations in three coronal mass ejection (CME)-driven sheath regions at 1 AU, with their speeds ranging from slow to fast. The data set we use consists primarily of high-resolution (0.092 s) magnetic field measurements from the Wind spacecraft. We analyse magnetic field fluctuation amplitudes, compressibility, and spectral properties of fluctuations. We also analyse intermittency using various approaches; we apply the partial variance of increments (PVIs) method, investigate probability distribution functions of fluctuations, including their skewness and kurtosis, and perform a structure function analysis. Our analysis is conducted separately for three different subregions within the sheath and one in the solar wind ahead of it, each 1 h in duration. We find that, for all cases, the transition from the solar wind ahead to the sheath generates new fluctuations, and the intermittency and compressibility increase, while the region closest to the ejecta leading edge resembled the solar wind ahead. The spectral indices exhibit large variability in different parts of the sheath but are typically steeper than Kolmogorov's in the inertial range. The structure function analysis produced generally the best fit with the extended p model, suggesting that turbulence is not fully developed in CME sheaths near Earth's orbit. Both Kraichnan–Iroshinikov and Kolmogorov's forms yielded high intermittency but different spectral slopes, thus questioning how well these models can describe turbulence in sheaths. At the smallest timescales investigated, the spectral indices indicate shallower than expected slopes in the dissipation range (between −2 and −2.5), suggesting that, in CME-driven sheaths at 1 AU, the energy cascade from larger to smaller scales could still be ongoing through the ion scale. Many turbulent properties of sheaths (e.g. spectral indices and compressibility) resemble those of the slow wind rather than the fast. They are also partly similar to properties reported in the terrestrial magnetosheath, in particular regarding their intermittency, compressibility, and absence of Kolmogorov's type turbulence. Our study also reveals that turbulent properties can vary considerably within the sheath. This was particularly the case for the fast sheath behind the strong and quasi-parallel shock, including a small, coherent structure embedded close to its midpoint. Our results support the view of the complex formation of the sheath and different physical mechanisms playing a role in generating fluctuations in them.

Robust statistics towards detection of the 21 cm signal from the Epoch of Reionization

We explore methods for robust estimation of the 21 cm signal from the Epoch of Reionisation (EoR). A Kernel Density Estimator (KDE) is introduced for measuring the spatial temperature fluctuation power spectrum from the EoR. The KDE estimates the underlying probability distribution function of fluctuations as a function of spatial scale, and contains different systematic biases and errors to the typical approach to estimating the fluctuation power spectrum. Extraction of histograms of visibilities allows moments analysis to be used to discriminate foregrounds from 21 cm signal and thermal noise. We use the information available in the histograms, along with the statistical dis-similarity of foregrounds from two independent observing fields, to robustly separate foregrounds from cosmological signal, while making no assumptions about the Gaussianity of the signal. Using two independent observing fields to robustly discriminate signal from foregrounds is crucial for the analysis presented in this paper. We apply the techniques to 13 hours of Murchison Widefield Array (MWA) EoR data over two observing fields. We compare the output to that obtained with a comparative power spectrum estimation method, and demonstrate the reduced foreground contamination using this approach. Using the second moment obtained directly from the KDE distribution functions yields a factor of 2-3 improvement in power for k < 0.3hMpc^{-1} compared with a matched delay space power estimator, while weighting data by additional statistics does not offer significant improvement beyond that available for thermal noise-only weights.

Edge computing for space applications: Field programmable gate array-based implementation of multiscale probability distribution functions.

Data processing is a challenging problem in space applications. The limited bandwidth available for communication between satellites and the ground and the increasing resolution of scientific instruments make it virtually impossible to transfer all the data recorded on board. Although various mitigation strategies were developed, large amounts of on-board data are still lost. This paper presents a Field Programmable Gate Array (FPGA)-based architecture which is able to perform on-board nonlinear analysis of data and compute probability distribution functions of fluctuations. We propose two implementations for our solution, which can be used for space applications and also other computational contexts. On a spacecraft, the logic resources of the FPGA will typically be shared by several designs running various digital signal processing algorithms. That is why each algorithm should be designed in variants, optimized for different criteria, so that the entire group of algorithms makes an efficient usage of the FPGA resources. The proposed solution focuses on two major optimization criteria, area and speed, such that the FPGA resources are efficiently used. Also, the power consumption is at least two orders of magnitude less in comparison with classical software implementations. The solution was tested with both synthetic and real data and shows excellent results paving the way towards an application that can be ported on a space-grade FPGA.

Comparison of beam emission spectroscopy and gas puff imaging edge fluctuation measurements in National Spherical Torus Experiment

In this study, the close physical proximity of the Gas Puff Imaging (GPI) and Beam Emission Spectroscopy (BES) diagnostics on the National Spherical torus Experiment (NSTX) is leveraged to directly compare fluctuation measurements, and to study the local effects of the GPI neutral deuterium puff during H-mode plasmas without large Edge Localized Modes. The GPI and BES views on NSTX provide partially overlapping coverage of the edge and scrape-off layer (SOL) regions above the outboard midplane. The separation in the toroidal direction is 16 °, and field lines passing through diagnostic views are separated by ∼ 20 cm in the direction perpendicular to the magnetic field. Strong cross-correlation is observed, and strong cross-coherence is seen for frequencies between 5 and 15 kHz. Also, probability distribution functions of fluctuations measured ∼ 3 cm inside the separatrix exhibit only minor deviations from a normal distribution for both diagnostics, and good agreement between correlation length estimates, decorrelation times, and structure velocities is found at the ±40% level. While the two instruments agree closely in many respects, some discrepancies are observed. Most notably, GPI normalized fluctuation levels exceed BES fluctuations by a factor of ∼ 9. BES mean intensity is found to be sensitive to the GPI neutral gas puff, and BES normalized fluctuation levels for frequencies between 1 and 10 kHz are observed to increase during the GPI puff.

Multiparticle statistical model of the solar wind

A multiparticle statistical approach to plasma (gas) modeling is presented, in which the fact that the macroscopic parameters are measured with finite resolution scales is taken into account [Minkova, 2004; 2005; 2007]. This approach is based on the Liouville theorem formulated for a stationary open system in the approximation of detailed dynamic balance with its surroundings. When the finite resolution scales of measuring instruments are taken into account, the plasma (gas) is described by multiparticle distribution functions. The latter are used to derive the probability distribution functions of fluctuations and the average values of macroscopic parameters. The multiparticle statistical approach allows a stationary solar wind model to be constructed under a number of simplifying assumptions. Its results for the average values of macroscopic parameters coincide with those of the two-particle kinetic model [Vasenin et al., 2003] and agree with inecliptic observational data.

The trispectrum of the cosmic microwave background on subdegree angular scales: an analysis of the BOOMERanG data

The trispectrum of the cosmic microwave background can be used to assess the level of non-Gaussianity on cosmological scales. It probes the fourth-order moment, as a function of angular scale, of the probability distribution function of fluctuations and has been shown to be sensitive to primordial non-Gaussianity, secondary anisotropies (such as the Ostriker–Vishniac effect) and systematic effects (such as astrophysical foregrounds). In this paper we develop a formalism for estimating the trispectrum from high-resolution sky maps that incorporates the impact of finite sky coverage. This leads to a series of operations applied to the data set to minimize the effects of contamination due to the Gaussian component and correlations between estimates at different scales. To illustrate the effect of the estimation process, we apply our procedure to the BOOMERanG data set and show that it is consistent with Gaussianity. This work presents the first estimation of the cosmic microwave background trispectrum on subdegree scales.

A Simple Model of Intermittency in Drift Wave-Zonal Flow Turbulence

An analogy between sandpile relaxation and the evolution of the drift wave spectrum by zonal flow induced shearing is used to characterize the probability distribution function of fluctuations in the drift wave population density Ñ, and thus address the predictability of intermittency in drift wave-zonal flow turbulence. Basic conservation and symmetry properties are used to derive a generalized Burgers equation for Ñ in the radial wave number kr. Shocks are symptomatic of shearing events, which are analogous to avalanches in the sandpile. The pdf P(ΔÑ) is shown to be intrinsically asymmetric in kr and the asymptotic behaviors of both left and right tails are determined. The implications of these results for transport are discussed.

E×B Velocity Shear and Intermittent Structures in RFX

Electrostatic turbulence in the edge region of the RFX device has been shown to be intermittent, i.e. not self-similar. In fact the probability distribution function of fluctuations at large scales is Gaussian in shape, whereas it displays strong tails for small scale fluctuations. The events responsible for these heavy tails are associated with turbulent structures with well defined density and floating potential spatial profiles, which have been characterised using arrays of probes. These structures tend to occur preferentially in correspondence to large scale magnetic relaxation events driven by core-resonant tearing modes. They also display an inclination related to the average velocity shear.

Intermittency and self-similarity in plasma edge fluctuations

The intermittency of the floating potential fluctuations as measured at the edge of a plasma of interest for controlled thermonuclear fusion research is investigated. The probability distribution functions of fluctuations are not scale invariant, that is the wings of these functions are more important at the smallest scales, a classical signature of intermittency. Self-similarity is recovered at scales greater than about 20 μs.

Intermittency in the solar wind turbulence through probability distribution functions of fluctuations

Intermittency in fluid turbulence can be emphasized through the analysis of Probability Distribution Functions (PDF) for velocity fluctuations, which display a strong non‐gaussian behavior at small scales. Castaing et al. (1990) have introduced the idea that this behavior can be represented, in the framework of a multiplicative cascade model, by a convolution of gaussians whose variances is distributed according to a log‐normal distribution. In this letter we have tried to test this conjecture on the MHD solar wind turbulence by performing a fit of the PDF of the bulk speed and magnetic field intensity fluctuations calculated in the solar wind, with the model. This fit allows us to calculate a parameter λ² depending on the scale, which represents the width of the log‐normal distribution of the variances of the gaussians. The physical implications of the obtained values of the parameter as well as of its scaling law are finally discussed.

Statistical properties of interplanetary fluctuations behind the bow shock

Snell's transmission model can determine all modes of refracted waves if the incident angle is between the two critical angles. However, the model cannot be used to study transmission of waves at all incident angles. Assuming that interplanetary fluctuations impinge on the bow shock from all directions, an alternative model is introduced in this paper to simulate their interaction. The results show that the state of fluctuations undergoes a significant jump across Earth's bow shock. Both the amplitude of fluctuations and the degree of fluctuation anisotropy increase across the Earth's bow shock. The calculated probability distribution functions of fluctuations immediately behind the bow shock resemble those reconstructed from observed magnetosheath data. Simulations are carried out to study the spatial variation for the state of fluctuations behind the bow shock under typical interplanetary conditions. We have found that the dawn-dusk (or South-North) asymmetry of the state of fluctuations is present in the magnetosheath when the background magnetic field is in the ecliptic (or meridian). A numerical experiment for MHD waves with incident angles within the limits of the two critical incident angles is also carried out to compare the result calculated from this proposed model with those from the well-developed Snell's transmission model.

A method for identification of linear or nonlinear systems with the use of externally applied random force

A response function method using externally applied random force is developed to identify linear or nonlinear systems. The probability distribution function of fluctuations and probability flow in phase space are used as the means for these identifications. It is also demonstrated that anomalous behavior of these quantities can be utilized as the forerunner phenomenon of the catastrophe of unstable systems.

Contribution to Statistical Mechanics far from Equilibrium. II: Extension to Non-Steady States and to General Stochastic Models

The new approach to non-equilibrium statistical mechanics initiated in Part I of this series is extended to cover non-steady states as well as more general stochastic models. The logarithm of the solution to the stochastic equation for the probability distribution function of gross variables is obtained as a systematic perturbation series starting from the logarithm of the suitably defined Gaussian part of the local equilibrium distribution function, which is best expressed in terms of the characteristic function of the probability distribution function. Again the effects of heat baths which surround the system enter only on the level of fully renormalized macroscopic equations of motion. A self-consistent scheme was derived which determines the macroscopic law of evolution and the probability distribution function of fluctuations.