Radial Correlation Research Articles

Studying the local structure of liquid in chloro- and alkyl-substituted benzene derivatives via the molecular scattering of light

The coefficients of scattering and the depolarization of scattered light are measured in liquid benzene, chlorobenzene, o-dichlorobenzene, o-chlorotoluene, toluene, and o-xylene in the temperature range of 293‒368 K at a wavelength of 546 nm. Isothermic compressibility, internal pressure, and the functions of radial and orientational correlation are calculated for these liquids in the indicated temperature range, using the classical theory of molecular light scattering. We show that the local structure of these liquids is determined by orthogonal contacts between benzene rings (the T-configuration) and stacked (S-type) configurations. T-configurations predominate in benzene, chlorobenzene, and o-chlorotoluene, while toluene, o-xylene, and o-dichlorobenzene are characterized by S-configurations. It is also shown that the local structures of these liquids are reorganized in a certain temperature range.

Radial correlation length across magnetic islands: Simulations and experiments

The turbulence radial correlation length Lr of density fluctuations is studied across magnetic islands both numerically and experimentally. The numerical study has been carried out by a resistive MHD code (called FAR). It shows asymmetric Lr profiles when measured across magnetic islands. Subsequent simulations using a synthetic Doppler reflectometer suggest that this diagnostic has the capability to capture the effect observed in the results provided by FAR. Finally, experimental studies performed using the Doppler reflectometer installed at the TJ-II stellarator show asymmetries in the coherence profiles matching the radial position of magnetic islands. The similarities found between simulations and experiments indicate that radial correlation length measurements could be used to detect magnetic islands in fusion plasmas.

Recovery of the characteristics of plasma turbulence from the radial correlation backscattering diagnostics

Signals of the backscattering radial correlation Doppler diagnostics of plasma density fluctuations in the presence of the cutoff of the probing wave are analyzed theoretically with allowance for the curvature of magnetic surfaces. The scattering of the probing electromagnetic wave is considered in the linear (Born) approximation with respect to the amplitude of fluctuations. Using the Wentzel−Kramers−Brillouin approach, analytical expressions for the scattered signal and the correlation function of two scattered signals corresponding to oblique probing at different frequencies are derived. A criterion is obtained for the tilt angle of the antenna pattern at which the two-point turbulence correlation function can be measured directly. A method is proposed to recover the spectrum of plasma density fluctuations from the data on the radial wavenumbers even if this criterion is violated.

Poloidal asymmetry in the narrow heat flux feature in the TCV scrape-off layer

Heat flux profiles inferred from a reciprocating probe at the outer midplane of the TCV tokamak during inner wall limited discharges feature radial fall-off lengths that shorten near the last closed flux surface (LCFS) consistent with the so-called narrow feature. The narrow feature is significantly wider on the outboard side compared with that measured on the inner wall by infrared thermography, so it is difficult to discern from the main scrape-off layer feature. After small shifts were applied for alignment, the fraction of the power contained in the narrow feature matches between inboard and outboard measurements, and they scale together with plasma current Ip, suggesting that we are observing the same phenomenon. The outboard side fall-off length within the narrow feature is found to scale closely with the radial correlation length of the edge turbulence as expected if the narrow feature arises due to radially sheared E × B flows. This is found to hold true even for cases where the narrow feature is weak and the fall-off lengths are approaching that of the far scrape-off layer. After the small shifts for alignment, non-zero floating potential profiles were found to match between inboard and outboard sides. A simple model of polarization and diamagnetic cross-field currents is described, which is consistent with the shape of these floating potential profiles. The model predicts that the floating potential at the LCFS must be negative, which supports the argument to shift the upstream measurements. The predicted currents are also consistent with the E × B flows believed to cause the narrow feature. The model is used to predict the magnitude of the floating potential of the LCFS, and the results are found to match measurements for all values of Ip. This paper therefore demonstrates consistency between the measurements of the narrow feature on the inboard and outboard sides of the plasma, as well as consistency between the measurements, non-linear turbulence simulations, and analytical models of the narrow feature arising from sheared E × B flows.

Energy exchange dynamics across L–H transitions in NSTX

We studied the energy exchange dynamics across the low-to-high-confinement (L–H) transition in NSTX discharges using the gas-puff imaging (GPI) diagnostic. The investigation focused on the energy exchange between flows and turbulence to help clarify the mechanism of the L–H transition. We applied this study to three types of heating schemes, including a total of 17 shots from the NSTX 2010 campaign run. Results show that the edge fluctuation characteristics (fluctuation levels, radial and poloidal correlation lengths) measured using GPI do not vary just prior to the H-mode transition, but change after the transition. Using a velocimetry approach (orthogonal-dynamics programming), velocity fields of a cm GPI view during the L–H transition were obtained with good spatial (∼1 cm) and temporal (∼2.5 μs) resolutions. Analysis using these velocity fields shows that the production term is systematically negative just prior to the L–H transition, indicating a transfer from mean flows to turbulence, which is inconsistent with the predator–prey paradigm. Moreover, the inferred absolute value of the production term is two orders of magnitude too small to explain the observed rapid L–H transition. These discrepancies are further reinforced by consideration of the ratio between the kinetic energy in the mean flow to the thermal free energy, which is estimated to be much less than 1, suggesting again that the turbulence depletion mechanism may not play an important role in the transition to the H-mode. Although the Reynolds work therefore appears to be too small to directly deplete the turbulent free energy reservoir, order-of-magnitude analysis shows that the Reynolds stress may still make a non-negligible contribution to the observed poloidal flows.

Effective model of QCD magnetic monopoles from numerical study of one- and two-component Coulomb quantum Bose gases

Magnetic monopoles are suggested to play an important role in strongly coupled quark-gluon plasma (sQGP) near the deconfinement temperature. So far, their many-body treatment has only been done classically, with just binary scattering solved in quantum mechanics. In this paper we start quantum many-body studies of the monopole ensembles. Specifically, we carry out numerical simulations of the path integral for one- and two-component Coulomb Bose systems. We determine the relation between the critical temperature for the Bose-Einstein condensation phase transition $T_\text{c}$ and the Coulomb coupling strength using two methods, the classic finite-size scaling of the condensate and a lattice-tested method based on permutation cycles. For a one-component Coulomb Bose gas, we observe the same behavior of the critical temperature -- initially rising slightly then falling as interaction strength is increased -- as seen in the case of hard spheres; we also observe the same behavior for a two-component Coulomb Bose gas. We then calculate sets of radial correlation functions between the like and unlike charged particles. By matching those with the correlation functions previously calculated on the lattice, we derive an effective quantum model of color magnetic monopoles in QCD. From this matched model, we are able to extract the monopole contribution to QCD equation of state near $T_\text{c}$.

Determination of the structural properties of the aqueous electrolyte LiCl6H2O at the supercooled state using the Reverse Monte Carlo (RMC) simulation

A structural study of an aqueous electrolyte whose experimental results are available. It is a solution of A structural study of an aqueous electrolyte whose experimental results are available. It is a solution LiCl6H2O type at supercooled state (162K) contrasted with pure water at room temperature by means of Partial Distribution Functions (PDF) issue from neutron scattering technique. The aqueous electrolyte solution of the chloride lithium LiCl presents interesting properties which is studied by different methods at different concentration and thermodynamical states: This system possesses the property to become a glass through a metastable supercooled state when the temperature decreases. Based on these partial functions, the Reverse Monte Carlo method (RMC) computes radial correlation functions which allow exploring a number of structural features of the system. The purpose of the RMC is to produce a consistent configuration with the experimental data. They are usually the most important in the limit of systematic errors (of unknown distribution).

A comparison of the correlation functions of the Lennard–Jones fluid for the first-order Duh–Haymet–Henderson closure with molecular simulations

ABSTRACTFirst-order integral equation theories are much more computationally efficient than second-order theories, but the latter are usually much more accurate for computing correlation functions of fluids. We here test the accuracy of the Duh–Haymet–Henderson (DHH) integral equation theory by comparing radial distribution, cavity correlation and bridge functions computed from DHH, first-order and second-order Percus–Yevick theories, with molecular dynamics calculations for the Lennard–Jones fluid. We find that the DHH theory is almost as accurate as the second-order Percus–Yevick theory at liquid-like densities for both sub- and super-critical temperatures. However, the accuracy of the DHH theory decreases with decreasing density. The correlation functions computed from DHH theory are very similar to those computed from first-order Percus–Yevick theory at low densities. The cavity correlation and bridge functions at low densities computed from these two theories are qualitatively different from results computed from molecular simulations. However, the radial distribution functions computed from all three methods are essentially identical at low densities, indicating that errors in the cavity correlation and bridge functions at low densities cancel out to give high accuracy in the radial distribution function.

Experimental determination of the correlation properties of plasma turbulence using 2D BES systems

A procedure is presented to map from the spatial correlation parameters of a turbulent density field (the radial and binormal correlation lengths and wavenumbers, and the fluctuation amplitude) to correlation parameters that would be measured by a beam emission spectroscopy (BES) diagnostic. The inverse mapping is also derived, which results in resolution criteria for recovering correct correlation parameters, depending on the spatial response of the instrument quantified in terms of point-spread functions (PSFs). Thus, a procedure is presented that allows for a systematic comparison between theoretical predictions and experimental observations. This procedure is illustrated using the Mega-Ampere Spherical Tokamak BES system and the validity of the underlying assumptions is tested on fluctuating density fields generated by direct numerical simulations using the gyrokinetic code GS2. The measurement of the correlation time, by means of the cross-correlation time-delay method, is also investigated and is shown to be sensitive to the fluctuating radial component of velocity, as well as to small variations in the spatial properties of the PSFs.

Reconstruction of turbulence radial wave number spectra based on the multi-frequency microwave Doppler backscattering data

An analytical treatment of radial correlation Doppler reflectometry (RCDR) within the framework of a model taking into account the two-dimensional probing wave propagation and scattering is performed. A procedure for the reconstruction of the turbulence radial wavenumber spectra from RCDR data is proposed and numerically justified for the real geometry of reflectometry experiments in large and modest-scale fusion plasmas.

Path-integral and Ornstein-Zernike computations of quantum fluid structures under strong fluctuations

This work deals with the computation of the structure factors of quantum fluids under complex conditions involving substantial density fluctuations and/or large particle delocalization effects. The method is based on the combination of path-integral Monte Carlo (PIMC) simulations and the pair Ornstein-Zernike framework (OZ2). PIMC provides the radial correlation functions (centroid, instantaneous, and thermalized-continuous total linear response), which are used as data input to the OZ2 calculations that lead to their associated structure factors. To undertake this project normal liquid 4He and supercritical 3He are selected, studying conditions in the range (T = 4.2 K; 0.01886 <ρN/Å-3 < 0.02687). Full inter-comparison between the structure factors determined via both OZ2 and direct PIMC calculations is made. In addition, comparison with experimental data, including thermodynamic properties, is made wherever possible. The results establish that, even under severe thermodynamic and/or quantum fluctuation conditions, OZ2 remains in the quantum domain as a highly reliable and cost-effective framework to determine accurate structure factors, also allowing one to understand the related isotopic shifts in fluid He.

Specific properties of argon-like liquids near their spinodals

The work is devoted to the computer simulation study of the spinodal position for argon and low-molecular liquids having the averaged interparticle potentials similar to that for argon. For this purpose several new methods are developed: the study of the intersection points for pressure curves on pairs of two close isochors, specific changes for the isochoric behavior of the radial correlation functions near the spinodal, non-trivial changes of the temperature dependencies for isochoric values of the self-diffusion coefficient, kinematic shear viscosity and Maxwell relaxation time of argon at the intersection of its spinodal. The three last characteristics are determined with the help of analysis of long time tails for the velocity auto-correlation function. Obtained in such a way the position of spinodal is compared with that following from the experimental study and computer simulations of the isothermal compressibility.

The role of turbulence–flow interactions in L- to H-mode transition dynamics: recent progress

Recent experimental and simulation work has substantially advanced the understanding of L-mode plasma edge turbulence and plasma flows and their mutual interaction across the L–H transition. Flow acceleration and E × B shear flow amplification via the turbulent Reynolds stress have been directly observed in multiple devices, using multi-tip probe arrays, Doppler backscattering, beam emission spectroscopy, and gas puff imaging diagnostics. L–H transitions characterized by limit-cycle oscillations (LCO) allow probing of the trigger dynamics and the synergy of turbulence-driven and pressure-gradient-driven flows with high spatio-temporal resolution. L-mode turbulent structures exhibit characteristic changes in topology (tilting) and temporal and radial correlation preceding the L–H transition. Long-range toroidal flow correlations increase preceding edge-transport-barrier formation. The energy transfer from the turbulence spectrum to large-scale axisymmetric flows has been quantified in L-LCO and fast L–H transitions in several devices. After formation of a transient barrier, the increasing ion pressure gradient (via the E × B flow shear associated with diamagnetic flow) sustains fluctuation suppression and secures the transition to H-mode. Heuristic models of the L–H trigger dynamics have progressed from 0D predator–prey models to 1D extended models, including neoclassical ion flow-damping and pressure-gradient evolution. Initial results from 2D and 3D reduced fluid models have been obtained for high-collisionality regimes.

Sturmian bases for two-electron systems in hyperspherical coordinates

We give a detailed account of an ab initio spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular Sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron–electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb–Sturmian functions of half integer angular momentum. We show that, in the case of H−, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for transitions in helium are obtained thereby confirming the accuracy of the bound state wave functions generated with the present method.

In-out asymmetry of zonal flow shear and turbulence reduction

In-out asymmetry of ion temperature gradient turbulence in toroidal geometry is studied by performing nonlinear gyrokinetic simulation using the GyroKinetic Plasma Simulation Program code [Kwon et al., Nucl. Fusion 52, 013004 (2012)]. Effects of self-generated zonal flow shear on the in-out asymmetry of radial correlation length and amplitude of turbulence are addressed by varying collisionality. Both quantities exhibit strong in-out asymmetry (longer and higher, respectively, at the low field side) in the absence of zonal flows. When the zonal flow shear (which is higher at the low field side) gets stronger, the radial correlation length decreases with its in-out asymmetry also getting reduced as expected from E×B shear decorrelation theory. On the other hand, in-out asymmetry of turbulence amplitude behaves differently from that of the radial correlation length.

Quantifying Drop Size Distribution Variability over Areas: Some Implications for Ground Validation Experiments

Abstract In previous work it was found that over a small network of disdrometers, the variability of probability size distributions (PSDs) expressed using the relative dispersion (RD; the ratio of the standard deviation to the mean) increased with the expansion of the network size. The explanation is that the network acts to integrate the Fourier transform of the spatial correlation function from smallest wavelengths to those comparable to the network size . Consequently, as increases, so do the variances at the different drop sizes. Thus, RD and PSD variability grow as increases. The limits to this growth, however, were not determined quantitatively. This finding is given fuller theoretical quantitative meaning over much larger dimensions by explicitly deriving the variance contributions at all the different drop sizes as well as for a variety of moments of the PSD by using spatial radial correlation functions estimated from temporal correlations. This is justifiable when the time for each observation is short. One example is provided. The relative dispersion of the PSD is dominated by fluctuations in the occurrences of the larger drops. The RDs of the raw moments are only a few percent of the PSD. Thus, approaches attempting to estimate radial correlation functions using, say, radar measurements of moments are of limited utility, a usefulness further compromised by the distortion of the correlation function by filtering over the beam dimension. These findings present a challenge for efforts to validate remote sensing measurements by ground truth experiments using networks.

Poloidal inhomogeneity of turbulence in the FT-2 tokamak by radial correlation Doppler reflectometry and gyrokinetic modelling

The poloidal dependence of the drift-wave turbulence characteristics is investigated at the FT-2 tokamak by radial correlation Doppler reflectometry (RCDR) technique and using the full distribution function global gyrokinetic modelling by ELMFIRE code. The poloidal variation of the turbulence radial correlation length from 0.2–0.55 cm is demonstrated both by measurement and computation. The turbulence correlation length rapidly decreases from the top of the poloidal cross-section to the high field side and then steadily grows in the poloidal direction. A well-pronounced excess of the turbulence radial correlation length in deuterium over its value in hydrogen discharges is demonstrated.

Influence of long-scale length radial electric field components on zonal flow-like structures in the TJ-II stellarator

The influence of long-scale length radial electric fields on zonal flows-like structures has been studied in the TJ-II stellarator. This relation has been investigated in the edge plasma using two electrical rake probes. The results presented here show an empirical correlation between the properties of long-range correlations (LRCs) with zonal flow-like structures and the magnitude of radial (neoclassical, NC) electric fields in TJ-II neutral beam heated plasmas. These experimental findings show that the enhancement of the NC radial electric field increases the magnitude of LRCs, considered as a proxy of zonal flows, while the radial correlation length of the plasma potential fluctuations was found to decrease by about 40%. A strong relation between the magnitude of electric field structures with long and short radial scales was found. The calculated shearing rate corresponding to the short scale length structures of the radial electric field may be sufficient to regulate turbulence.

Quasi-long-range order in trapped two-dimensional Bose gases

We study the fate of algebraic decay of correlations in a harmonically trapped two-dimensional degenerate Bose gas. The analysis is inspired by recent experiments on ultracold atoms where power-law correlations have been observed despite the presence of the external potential. We generalize the spin wave description of phase fluctuations to the trapped case and obtain an analytical expression for the one-body density matrix within this approximation. We show that algebraic decay of the central correlation function persists to lengths of about 20% of the Thomas--Fermi radius. We establish that the trap-averaged correlation function decays algebraically with a strictly larger exponent weakly changing with trap size and find indications that the recently observed enhanced scaling exponents receive significant contributions from the normal component of the gas. We discuss radial and angular correlations and propose a local correlation approximation which captures the correlations very well. Our analysis goes beyond the usual local density approximation and the developed summation techniques constitute a powerful tool to investigate correlations in inhomogeneous systems.

Fatigue hot spot simulation for two Widmanstätten titanium microstructures

A simulated microstructure-sensitive fatigue study has been performed for two titanium alloy microstructures. The investigated materials exhibit a Widmanstätten structure and include the α–β alloy Ti–6Al–4V and the near β alloy Ti-18 in a β-annealed, slow-cooled, and aged condition (BASCA). In other work [1], crystal plasticity models implemented into ABAQUS (2011) [2] UserMATerial subroutines have been calibrated to experimental cyclic deformation data for both materials. The current study utilizes calibrated crystal plasticity models to simulate fatigue loading of varying microstructures for each material to study the influence of key morphological and crystallographic aspects on the fatigue performance, e.g., the mean colony size, phase volume fraction, and crystallographic texture. Localized stress and plastic strain are studied via computation of fatigue indicator parameters (FIPs), which represent the driving force for fatigue crack formation and early propagation in the microstructure. The maximum FIP values are sampled over several stochastic simulations and are utilized to determine extreme value statistical distributions which demonstrate the trends in the microstructural influence on fatigue performance. Marked radial correlation functions developed by Przybyla and McDowell [3] have also been employed to study the correlation between favorably oriented slip systems and the extreme value FIP locations within the instantiated microstructures. The simulation results suggest that reduced lamellar colony sizes, reduced α-phase, and a transverse texture within a reference plane normal to the applied uniaxial loading direction can enhance resistance to formation and early growth of fatigue cracks.