Particle Density Fluctuations Research Articles

Plasma fluctuation spectra as a diagnostic tool for submicron dust

It is shown that the measurements of density fluctuation spectra in dusty plasmas can constitute a basis for in situ diagnostic of invisible submicron dust. The self-consistent kinetic theory that includes the charging processes and the natural density fluctuations of the dust particles predicts modifications of the spectra due to the presence of dust. A laboratory experiment was carried out where submicron dust was produced in a gas phase and diagnosed by surface analysis of samples and by measurements of its influence on the plasma density fluctuation spectra. Quantitative comparison of the latter with the theory yields information on dust density, size, and distribution in agreement with the results of the surface analysis. The method can be applied to various plasma environments in laboratory and space.

Equilibrium Fluctuations for a Model of Coagulating-Fragmenting Planar Brownian Particles

We study a model of mass-bearing coagulating-fragmenting planar Brownian particles. Coagulation occurs when two particles are within a distance of order ε. Our model is macroscopically described by an inhomogeneous Smoluchowski’s equation in the low ε limit provided that the initial number of particles N is of order |log ε|. When a detailed balance condition is satisfied, we establish a central limit theorem by showing that in the low ε limit, the particle density fluctuation fields obey an Ornstein-Uhlenbeck stochastic differential equation.

Size scaling effects on the particle density fluctuations in confined plasmas

In this paper, memory and nonlocal effects on fluctuating mass diffusion are addressed in the context of fusion plasmas. Nonlocal effects are included by considering a diffusivity coefficient depending on the size of the container in the transverse direction to the applied magnetic field. It is obtained by resorting to the general formulation of the extended version of irreversible thermodynamics in terms of the higher order dissipative fluxes. The developed model describes two different types of the particle density time correlation function. Both have been observed in tokamak and nontokamak devices. These two kinds of time correlation function characterize the wave and the diffusive transport mechanisms of particle density perturbations. A transition between them is found, which is controlled by the size of the container. A phase diagram in the {L,2π/k} space describes the relation between the dynamics of particle density fluctuations and the size L of the system together with the oscillating mode k of the correlation function.

Characterization of Phase Transition in Heisenberg Fluids from Density Functional Theory

The phase transition of Heisenberg fluid has been investigated with the density functional theory in mean-field approximation (MF). The matrix of the second derivatives of the grand canonical potential Ω with respect to the particle density fluctuations and the magnetization fluctuations has been investigated and diagonalized. The smallest eigenvalue being 0 signalizes the phase instability and the related eigenvector characterizes this phase transition. We find a Curie line where the order parameter is pure magnetization and a spinodal where the order parameter is a mixture of particle density and magnetization. Along the spinodal, the character of phase instability changes continuously from predominant condensation to predominant ferromagnetic phase transition with the decrease of total density. The spinodal meets the Curie line at the critical endpoint with the reduced density ρ* = ρσ3 = 0.224 and the reduced temperature T* = kT/∊ = 1.87 (σ is the diameter of Heisenberg hard sphere and ∊ is the coupling constant).

Turbulence measurements in fusion plasmas

Turbulence measurements in magnetically confined toroidal plasmas have a long history and relevance due to the detrimental role of turbulence induced transport on particle, energy, impurity and momentum confinement. The turbulence—the microscopic random fluctuations in particle density, temperature, potential and magnetic field—is generally driven by radial gradients in the plasma density and temperature. The correlation between the turbulence properties and global confinement, via enhanced diffusion, convection and direct conduction, is now well documented. Theory, together with recent measurements, also indicates that non-linear interactions within the turbulence generate large scale zonal flows and geodesic oscillations, which can feed back onto the turbulence and equilibrium profiles creating a complex interdependence. An overview of the current status and understanding of plasma turbulence measurements in the closed flux surface region of magnetic confinement fusion devices is presented, highlighting some recent developments and outstanding problems.

Nonequilibrium Phase Transition in the Sedimentation of Reproducing Particles

We study numerically and analytically the dynamics of a sedimenting suspension of active, reproducing particles, such as growing bacteria in a gravitational field. In steady state we find a nonequilibrium phase transition between a "sedimentation" regime, analogous to the sedimentation equilibrium of passive colloids, and a "uniform" regime, in which the particle density is constant in all but the top and bottom of the sample. We discuss the importance of fluctuations in particle density in locating the phase-transition point, and report the kinetics of sedimentation at early times.

Relationship of electric field and charged particle density fluctuations to air turbulence in the mesosphere

A theoretical model is developed that is applicable to the electric field fluctuations that arise in the polar summer mesosphere as a result of the coupling of the charged species to the neutral air turbulence. The motions of electrons, ions, and charged aerosol particles are described as harmonic oscillators both driven and damped by the drag force exerted by the neutral air. The relative fluctuations in the ion density are found to be nearly the same as those in the neutral air as a consequence of the ions' high‐momentum transfer relaxation frequency. The aerosol density fluctuations follow those of the neutral air at frequencies below their relaxation frequency, which is in the acoustic range. The electrons move primarily in response to the electric force to partially cancel the net charge density of ions and aerosol particles except at wavelengths shorter than the Debye length. Electric field and charge density fluctuations are calculated for several sets of conditions. In “bite‐out” regions in which the electron density is reduced as a consequence of attachment to the aerosol particles the electric field fluctuations are found to be enhanced, which is consistent with observations.

Cavity thermodynamics in the Gaussian model of particle density fluctuations

The thermodynamics of cavity creation emerging from the Gaussian model of particle density fluctuations are investigated. The analysis shows that the reversible work of cavity creation is dominated by entropy due to the exclusion of liquid particles from the cavity volume. The enthalpy change is due to a structural reorganization of liquid particles that is distinct from the excluded volume effect and proves to be entirely compensated for by a corresponding entropy term. These results are in line with a previous general analysis [B. Lee, J. Chem. Phys. 83 (1985) 2421].

Effect of Magnetic Configuration on Particle Transport and Density Fluctuation in LHD

The characteristics of particle transport in three different magnetic configurations are studied from density modulation experiments in the Large Helical Device (LHD). These three configurations are represented as different magnetic axis positions (Rax) of the vacuum field. Experiments were carried out in a range of different heating powers for each configuration with almost constant density. The experimental values of particle diffusion coefficients (D) and particle convection velocities (V) are compared with neoclassical estimates. The value of D is found to be anomalously large compared to neoclassical values in both the core and edge in all configurations. At low collisionality, this anomaly tends downward. The core convection velocities are comparable with neoclassical estimates. In more-outward-shifted configurations, particle transport is enhanced. The electron temperature and electron temperature gradient are the determinate parameters for D and V, respectively, in each configuration. The effective helical ripple is one of the important parameters for particle transport in the LHD; however, other hidden parameters exist. The role of fluctuations in particle transport is investigated from turbulence measurements using a two-dimensional phase contrast interferometer. Three kinds of fluctuation having different locations, propagation direction, and peak wave number are observed. One of these, which exists in the outermost edge region and propagates in the ion diamagnetic direction in the laboratory frame, plays a possible role in edge anomalous diffusion. The amplitudes of ion diamagnetic fluctuation components are compared with the linear growth rate of the ion temperature gradient mode.

Turbulence simulations of blob formation and radial propagation in toroidally magnetized plasmas

Two-dimensional numerical fluid turbulence simulations demonstrating the formation and radial propagation of blob structures in toroidally magnetized plasmas are presented and analysed in detail. A salient feature of the model is a linearly unstable edge plasma region with localized sources of particles and heat, which is coupled to a scrape-off layer with linear damping terms for all dependent variables corresponding to transport along open magnetic field lines. The formation of blob structures is related to profile variations caused by bursting in the global turbulence level, which is due to a dynamical regulation by self-sustained differential rotation of the plasma layer. Radial propagation of the blob structures follows from a vertical charge polarization due to magnetic guiding centre drifts in the toroidally magnetized plasma. Statistical analysis of the particle density, radial electric drift and the radial turbulent particle flux reveals asymmetric conditional waveforms with a steep front and a trailing wake and positively skewed and flattened probability distributions, in agreement with recent experimental investigations. Coarse graining and spectral analysis further indicate the presence of long-range correlations in the particle density fluctuations. Finally, conditional statistics of the particle flux demonstrates the intermittency of the turbulent plasma transport and the quasi-periodic apparency of blob structures due to bursting in the global turbulence level.

Experimental study of particle transport and density fluctuations in LHD

A variety of electron density (ne) profiles have been observed in the Large Helical Device (LHD). The density profiles change dramatically with heating power and toroidal magnetic field (Bt). The particle transport coefficients, i.e. diffusion coefficient (D) and convection velocity (V) are experimentally obtained in the standard configuration from density modulation experiments. The values of D and V are estimated separately in the core and edge. The diffusion coefficients are found to be a function of electron temperature (Te), and vary with Bt. Edge diffusion coefficients are proportional to . Non-zero V is observed, and it is found that the electron temperature gradient can drive particle convection, particularly in the core region. The convection velocity both in the core and edge reverses direction from inward to outward as the Te gradient increases. However, the toroidal magnetic field also significantly affects the value and direction of V. The density fluctuation profiles are measured by a two-dimensional phase contrast interferometer. It was found that fluctuations which are localized in the edge propagate towards the ion diamagnetic direction in the laboratory frame, while the phase velocity of fluctuations around mid-radius is close to the plasma poloidal Er × Bt rotation velocity. The fluctuation level becomes larger as particle flux becomes larger in the edge region.

Thermodynamic instabilities of a binary mixture of sticky hard spheres

The thermodynamic instabilities of a binary mixture of sticky hard spheres (SHS) in the modified mean spherical approximation (mMSA) and the Percus-Yevick (PY) approximation are investigated using an approach devised by Chen and Forstmann [corrected] [J. Chem. Phys. [corrected] 97, 3696 (1992)]. This scheme hinges on a diagonalization of the matrix of second functional derivatives of the grand canonical potential with respect to the particle density fluctuations. The zeroes of the smallest eigenvalue and the direction of the relative eigenvector characterize the instability uniquely. We explicitly compute three different classes of examples. For a symmetrical binary mixture, analytical calculations, both for mMSA and for PY, predict that when the strength of adhesiveness between like particles is smaller than the one between unlike particles, only a pure condensation spinodal exists; in the opposite regime, a pure demixing spinodal appears at high densities. We then compare the mMSA and PY results for a mixture where like particles interact as hard spheres (HS) and unlike particles as SHS, and for a mixture of HS in a SHS fluid. In these cases, even though the mMSA and PY spinodals are quantitatively and qualitatively very different from each other, we prove that they have the same kind of instabilities. Finally, we study the mMSA solution for five different mixtures obtained by setting the stickiness parameters equal to five different functions of the hard sphere diameters. We find that four of the five mixtures exhibit very different type of instabilities. Our results are expected to provide a further step toward a more thoughtful application of SHS models to colloidal fluids.

Sedimentation of hard-sphere suspensions at low Reynolds number

Lattice-Boltzmann simulations have been used to investigate low-Reynolds-number settling of monodisperse and polydisperse suspensions. We confirm the discovery that particle velocity fluctuations are strongly suppressed by no-slip walls at the top and bottom of the system, even in regions distant from the boundaries. We also show that a monodisperse suspension develops a strongly anisotropic long-range microstructure during the settling process, with vanishing density fluctuations in the horizontal plane. We find no numerical evidence that the particle concentration in the bulk is stratified; diffusive spreading of the suspension–supernatant interface is suppressed by hindered settling, as would be expected in moderately concentrated suspensions.Long-range correlations in particle density fluctuations are destroyed by polydispersity in particle size, and in this case density fluctuations are finite at all length scales and in all directions. However, in polydisperse suspensions there is significant stratification, due to differential settling rather than interface diffusion, which provides an alternative mechanism for screening the hydrodynamic interactions. It is possible that this is the dominant mechanism for hydrodynamic screening in several laboratory experiments.

Stochastic models of edge turbulent transport in the thermonuclear reactors

Two-dimensional stochastic model of turbulent transport in the scrape-off layer (SOL) of thermonuclear reactors is considered. Convective instability arisen in the system with respect to perturbations reveals itself in the strong outward bursts of particle density propagating ballistically across the SOL. The criterion of stability for the fluctuations of particle density is formulated. A possibility to stabilize the system depends upon the certain type of plasma waves interactions and the certain scenario of turbulence. A bias of limiter surface would provide a fairly good insulation of chamber walls excepting for the resonant cases. Pdf of the particle flux for the large magnitudes of flux events is modeled with a simple discrete time toy model of I-dimensional random walks concluding at the boundary. The spectra of wandering times feature the pdf of particle flux in the model and qualitatively reproduce the experimental statistics of transport events.

Principal Components Analysis of Extensive Air Showers Applied to the Identification of Cosmic TeV Gamma‐Rays

We apply a principal components analysis (PCA) to the secondary particle density distributions at ground level produced by cosmic gamma-rays and protons. For this purpose, high-energy interactions of cosmic rays with Earth's atmosphere and the resulting extensive air showers have been simulated by means of the CORSIKA Monte Carlo code. We show that a PCA of the two-dimensional particle density fluctuations provides a decreasing sequence of covariance matrix eigenvalues that have typical features of a polynomial law, which are different for different primary cosmic rays. This property is applied to the separation of electromagnetic showers from proton simulated extensive air showers, and it is proposed as a new discrimination method that can be used experimentally for gamma-proton separation. A cutting parameter related to the polynomial behavior of the decreasing sequence of covariance matrix eigenvalues is calculated, and the efficiency of the cutting procedure for gamma-proton separation is evaluated.

Activated Hopping, Barrier Fluctuations, and Heterogeneity in Glassy Suspensions and Liquids

Our entropic barrier hopping theory of glassy hard sphere colloidal suspensions is extended to include heterogeneity within a simple trap model framework. The origin of local domains, their size, and the corresponding static barrier fluctuations are attributed to mesoscopic density fluctuations of an amplitude controlled by the bulk compressibility. Based on typical values of the density fluctuation correlation length in dense liquids, the domain size on which correlated hopping occurs is estimated to be 3−4 particle or molecular diameters. Consequences of barrier fluctuations include an increased average relaxation time, faster diffusion, stretched exponential relaxation, diffusion-viscosity decoupling, and a fractional Stokes−Einstein relation. The common origin of the fluctuation effects is the heterogeneity-induced component of the barrier. For colloidal suspensions in the typically studied volume fraction regime the barrier fluctuations have modest consequences, but significantly larger effects are predicted in the putative glassy regime. A statistical dynamical analysis of domain lifetime suggests that for suspensions the relaxation time of mesoscopic collective density fluctuations is at least as long as the single particle hopping time. A general, model-independent analysis of the single molecule incoherent dynamic structure factor for suspensions and thermal liquids has also been performed in the long time and intermediate wavevector regime. The coupling of single particle density and longitudinal stress fluctuations results in a wavevector-dependent apparent diffusion constant and a dynamic correlation length scale which is strongly temperature dependent and directly related to the translation-rotation decoupling factor. This dynamic length is estimated to be 10 times larger than a molecular diameter for tris-naphthyl benzene near the glass transition temperature but shrinks to a molecular size above the crossover temperature that signals the emergence of collective barriers.

Complexity in high-energy physics

In addition to its importance in describing high-energy processes themselves, the dynamics of multiparticle production has become part of the general field of non-linear phenomena and complex systems. Multiparticle dynamics is one of the rare fields of physics where higher-order correlations are directly accessible in their full multi-dimensional characteristics under well-controlled experimental conditions. Multi-particle dynamics, therefore, is an ideal testing ground for the development of advanced statistical methods. Higher-order correlations have, indeed, been observed as particle-density fluctuations. Approximate scaling with improving resolution provides evidence for a self-similar correlation effect. Quantum-Chromodynamics branching is a good candidate for a dynamical explanation of these correlations in e +e − collisions at CERN/LEP and, as expected, also of those in pp collisions at future CERN/LHC energies. However, also other sources such as identical-particle Bose–Einstein interference effects contribute.

Application of bidimensional power spectrum properties of extensive air shower particle distributions to γ–proton discrimination

High-energy interactions of cosmic γ rays and protons with the earth atmosphere have been simulated by means of the CORSIKA Monte Carlo code, and the secondary particle density distributions at ground level in the resulting extensive air showers have been studied. It is shown that the power spectrum of the bidimensional particle density fluctuations have features typical of a 1/ f noise in the bidimensional frequency domain, and is found to have different features for different primary cosmic rays. This property is applied to the separation of electromagnetic from proton simulated extensive air showers and it is proposed as a new discrimination method that can be used experimentally for real-time γ–proton separation. A cutting parameter related to the bidimensional power spectrum is calculated and the efficiency of the cutting procedure for γ–proton separation is evaluated.

Energy loss of a fast-electron beam due to the excitation of collective oscillation in hot plasma

Energy loss due to a fast-electron beam interacting with the hot plasma at a high density is analysed theoretically. By splitting the particle density fluctuations into the individual part due to the random thermal motion of the individual electrons and the collective part due to plasma–wave excitation, we are concerned with the collective interaction of the relativistic plasma electrons resulting from the Coulomb interactions. Consequently, we derive the frequency of the hot plasma and the ``Debye length'' with the modification of the relativistic effect. And finally we calculate the energy loss of a fast-electron beam due to the excitation of collective oscillation in the hot plasma.

Propagating particle density fluctuations in molten NaCl

In this paper we present the observation of acoustic modes in the spectra of molten NaCl measured over a large momentum transfer range using synchrotron radiation. A surprisingly large positive dispersion was deduced witha mode velocity exceeding the adiabatic value by nearly 70%. The large effect seems to be describable as a viscoelastic reaction of the liquid. Additionally, the derived dispersion resembles the Q-ω relation of the acoustic modes in liquid sodium. As an explanation for the large positive dispersion we propose that the density fluctuations in molten NaCI can be interpreted as a decoupled motion of the lighter and smaller cations on a nearly resting anionic background. These molten alkali halide measurements are the first experimental evidences for the so-called fast sound in a binary ionic liquid.