Decorrelation Rate Research Articles

Investigation of geodesic acoustic modes and related zonal flows at TEXTOR

This paper attempts to give an overview on the study of the geodesic acoustic mode (GAM) and the related velocity oscillation of the zonal flow (ZF) at TEXTOR. The reported results are obtained from poloidal cross correlation reflectometry. The advantages of the diagnostic combined with a multi-antenna set-up, as it is installed at TEXTOR, are shortly reviewed and compared with other diagnostics used in experiments on GAMs.Furthermore, the GAM properties in ohmic discharges are reported as frequency scaling with local temperature, poloidal structure and radial distribution. GAM induced density fluctuations and related velocity oscillations are measured for a large radial range. In the context of the latter the collisionality on the GAMs at the plasma edge is investigated. The measurement of the GAM related velocity fluctuations shows that the ZF occurs in two rings at least, separated by a rational surface. The velocity oscillation allows us to estimate the effect of GAMs on the shearing rate. The influence on the shearing rate is quantitatively investigated. The GAM induced shearing rate is not able to overcome the decorrelation rate of the ambient turbulence (AT).Also the relation between AT and GAMs is analyzed. Therefore the AT is characterized and the turbulence driving the GAMs is discussed. A relation between the density scale length and the pronounced occurrence of GAMs is obtained. This is related to a narrow region of k⊥ρs values, which is characteristic for drift ballooning modes. The spectrum of the AT is analyzed in both ZF rings. A significant change in the shape of the low frequency turbulence is obtained. This may be connected with a transition from drift ballooning modes to ITG modes. The latter seems to drive the GAMs less effectively.

Shear-Based Model for Electron Transport in Hybrid Hall Thruster Simulations

An electron cross-field transport model based on instantaneous simulated plasma properties is incorporated into a radial-axial hybrid simulation of a Hall plasma thruster. The model is used to capture the reduction of fluctuation-based anomalous transport that is seen experimentally in the region of high axial shear in the electron fluid. Similar transport barriers are observed by the magnetic confinement fusion community due to shear suppression of plasma turbulence through an increase in the decorrelation rate of plasma eddies. The model assumes that the effective Hall parameter can be computed as the sum of the classical term, a near-wall conductivity term, and a fluctuation-based term that includes the effect of shear. A comparison is made between shear-based, experimental, and Bohm-type models for cross-field transport. Although the shear-based model predicts a wider transport barrier than experimentally observed, overall, it better predicts measured plasma properties than the Bohm model, particularly in the case of electron temperature and electric potential. The shear-based transport model also better predicts the breathing-mode oscillations and time-averaged discharge current than both the Bohm and experimental mobility models. The plasma property that is most sensitive to adjustment of the fitting parameters used in the shear-based model is the plasma density. Applications of these fitting parameters in other operating conditions and thruster geometries are examined in order to determine the robustness and portability of the model. Without changing the fitting parameters, the simulation was able to reproduce macroscopic properties, such as thrust and efficiency, of an SPT-100-type thruster within 30% and match qualitative expectations for a bismuth-fueled Hall thruster.

Diagnosing Cysts With Correlation Coefficient Images From 2-Dimensional Freehand Elastography

We compared the diagnostic potential of using correlation coefficient images versus elastograms from 2-dimensional (2D) freehand elastography to characterize breast cysts. In this preliminary study, which was approved by the Institutional Review Board and compliant with the Health Insurance Portability and Accountability Act, we imaged 4 consecutive human subjects (4 cysts, 1 biopsy-verified benign breast parenchyma) with freehand 2D elastography. Data were processed offline with conventional 2D phase-sensitive speckle-tracking algorithms. The correlation coefficient in the cyst and surrounding tissue was calculated, and appearances of the cysts in the correlation coefficient images and elastograms were compared. The correlation coefficient in the cysts was considerably lower (14%-37%) than in the surrounding tissue because of the lack of sufficient speckle in the cysts, as well as the prominence of random noise, reverberations, and clutter, which decorrelated quickly. Thus, the cysts were visible in all correlation coefficient images. In contrast, the elastograms associated with these cysts each had different elastographic patterns. The solid mass in this study did not have the same high decorrelation rate as the cysts, having a correlation coefficient only 2.1% lower than that of surrounding tissue. Correlation coefficient images may produce a more direct, reliable, and consistent method for characterizing cysts than elastograms.

Monitoring of tissue thermal modification with a bundle-based full-field speckle analyzer

Speckle-contrast monitoring of laser-mediated tissue modification is examined for the specific case of delivery of speckle-modulated light from the tissue to detector (CCD camera) with a fiber-optic element (bundle). The influence of the transfer properties of a bundle-based optical system on the decorrelation rate of detected dynamic speckles is analyzed. Compared with the widely used method on the base of speckle-contrast analysis in the image plane, the considered technique is characterized by a more pronounced correlation between variations of the contrast of time-averaged speckle patterns and changes in the temperature of the modified tissue. The possibility of characterization of the modification kinetics (in particular, by the evaluation of the characteristic activation energy) using the developed speckle technique is demonstrated.

Correlation of RF signals during angular compounding

A theoretical analysis of the correlation between radio-frequency (RF) echo signal data acquired from the same location but at different angles is presented. The accuracy of the theoretical results is verified with computer simulations. Refinements to previous analyses of the correlation of RF signals originating from the same spatial location at different angular positions are made. We extend the analysis to study correlation of RF signals coming from different spatial locations and eventually correlation of RF signal segments that intersect at the same spatial location. The theory predicts a faster decorrelation with a change in the insonification angle for longer RF echo signal segments. As the RF signal segment becomes shorter, the decorrelation rate with angle is slower and approaches the limit corresponding to the correlation of RF signals originating from the same spatial location. Theoretical results provide a clear understanding of angular compounding techniques used to improve the signal-to-noise ratio in ultrasonic parametric imaging and in elastography.

Conversion efficiency of ultracold fermionic atoms to bosonic molecules via Feshbach resonance sweep experiments.

We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of 40K and 6Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau-Zener transition but faster than "the collision rate" in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin states, required to enable s-wave scattering. By constructing the many-body state of the system we show that this preparation yields a mixture of even and odd parity pair states, where only even parity can produce molecules. The odd parity spin-symmetric states must decorrelate before the constituent atoms can further Feshbach scatter, thereby increasing the conversion efficiency; "the collision rate" is the pair decorrelation rate.

Liapunov Multipliers and Decay of Correlations in Dynamical Systems

The essential decorrelation rate of a hyperbolic dynamical system is the decay rate of time-correlations one expects to see stably for typical observables once resonances are projected out. We define and illustrate these notions and study the conjecture that for observables in $C^1$, the essential decorrelation rate is never faster than what is dictated by the {\em smallest} unstable Liapunov multiplier.

Observation and characterization of radially sheared zonal flows in DIII-D

Zonal flows, thought crucial to the saturation and self-regulation of turbulence and turbulent transport in magnetically confined plasmas, have been observed and characterized in the edge region of DIII-D plasmas. These flows exhibit temperature scaling characteristics and spatial features predicted for geodesic acoustic modes (GAMs), a class of higher-frequency zonal flows seen in nonlinear simulations of plasma turbulence. The zonal flows (GAMs) have been observed in the turbulence flow-field in the radial region 0.85 ⩽ r/a ⩽ 1.0 via application of time-delay-estimation techniques to two-dimensional measurements of density fluctuations, obtained with beam emission spectroscopy. Spatial and temporal analysis of the resulting flow-field demonstrates the existence of a coherent oscillation (approximately 15 kHz) in the poloidal flow of density fluctuations that has a long poloidal wavelength, possibly m = 0, narrow radial extent (krρi < 0.2), and a frequency that varies monotonically with the local temperature. The approximate effective shearing rate, dvθ/d r, of the flow is of the same order of magnitude as the measured nonlinear decorrelation rate of the turbulence. These characteristics are consistent with predicted features of zonal flows, specifically identified as GAMs, observed in three-dimensional Braginskii simulations of core/edge turbulence.

Direct measurement of poloidal long-wavelength E x B flows in the HT-7 tokamak.

The poloidal long-wavelength E x B time-varying flows were directly measured using a forked Langmuir probe in the HT-7 tokamak. Low-frequency (<10 kHz) E x B flows were observed at the plasma edge, which possess many of the characteristics of zonal flows, including a poloidal long-wavelength (k(theta)rho(i) approximately 0) and narrow radial extent (k(r)rho(i) approximately 0.1). The cross bicoherence of turbulent Reynolds stress indicates the existence of nonlinear three-wave coupling processes and the generation of low-frequency E x B flows. The estimated flow-shearing rate is of the same order of magnitude as the turbulence decorrelation rate and may thus regulate the fluctuation level and thereby the turbulence-driven transport.

Experimental characterization of coherent, radially-sheared zonal flows in the DIII-D tokamak

The application of time-delay-estimation techniques to two-dimensional measurements of density fluctuations, obtained with beam emission spectroscopy in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] plasmas, has provided temporally and spatially resolved measurements of the turbulence flow-field. Features that are characteristic of self-generated zonal flows are observed in the radial region 0.85⩽r/a⩽1.0. These features include a coherent oscillation (approximately 15 kHz) in the poloidal flow of density fluctuations that has a long poloidal wavelength, possibly m=0, narrow radial extent (krρI&amp;lt;0.2), and whose frequency varies monotonically with the local temperature. The approximate effective shearing rate, dvθ/dr, of the flow is of the same order of magnitude as the measured nonlinear decorrelation rate of the turbulence, and the density fluctuation amplitude is modulated at the frequency of the observed flow oscillation. Some phase coherence is observed between the higher wavenumber density fluctuations and low frequency poloidal flow fluctuations, suggesting a Reynolds stress contribution. These characteristics are consistent with predicted features of zonal flows, specifically identified as geodesic acoustic modes, observed in 3-D Braginskii simulations of core/edge turbulence.

Observation of coherent sheared turbulence flows in the DIII-D Tokamak.

Time-resolved measurements of the turbulent density flow field in a tokamak plasma reveal low-frequency ( approximately 15 KHz), coherent oscillations in the poloidal flow, v(theta). These flow oscillations have a long poloidal wavelength (m<3) and narrow radial extent (k(r)rho(i) approximately 0.2). The estimated flow-shearing rate is of the same order of magnitude as the turbulence decorrelation rate and may thus regulate the turbulence amplitude. These features are consistent with theoretically predicted axisymmetric, self-regulating, sheared flows recognized as geodesic acoustic modes.

On the relationship between power mode and pressure amplitude decorrelation

Estimation of mean transit time, along with tissue blood volume, are important factors in determining soft tissue perfusion. Recently, power mode decorrelation techniques have been successfully used to estimate mean transit time of red blood cells or contrast material through a region-of-interest (ROI) both in laminar flow phantoms and in vivo. The previously described theory for power mode decorrelation derives from a phenomenological stochastic differential equation (Langevin equation) based on conservation of matter, relating the detected signal power to the measured rate of decorrelation. Given the experimental support for power mode decorrelation as a method to estimate mean transit time, it becomes important to determine the relationship between the phenomenological parameters that appear in the corresponding stochastic equation and system parameters, such as the transducer point response function. With this equation as a starting point, and using the fact that the pressure amplitude is a Gaussianly distributed random process, the following stochastic differential equation for the pressure amplitude p( t) is derived, a necessary first step in establishing the relationship between the measured decorrelation rate and system parameters ( i.e., point response function): dp(t) /dt=−(v/2+2ik·v)p(t)+f(t),(1) where v/2 represents the rate of decorrelation, 2 k· v is the Doppler shift for an insonating wave vector k and particle velocity v.f( t) is a stationary, white noise Gaussian random process. (E-mail: adlerr@hss.edu)

Decorrelation characteristics of transverse blood flow along an intravascular array catheter: Effects of aggregation of red blood cells

A method to measure transverse blood flow, based on the correlation between consecutive radiofrequency (RF) signals, has been introduced. This method was validated for an intravascular (IVUS) rotating single element catheter. Currently, we are implementing the method for an IVUS array transducer catheter. The decorrelation characteristics during transverse blood flow using the IVUS array catheter were investigated using computer modeling. Before this, blood was simulated as a collection of randomly located point scatterers and, by moving this scattering medium transversely across the acoustical beam, blood flow was simulated. This paper presents a more realistic scattering media by simulating aggregates of red blood cells (RBCs) as strings of point scatterers. Three configurations of aggregates of RBCs were simulated. First, aggregates of RBCs were strings with different lengths and parallel to the catheter axis. Second, the strings were with a fixed length and angles of plus or minus 45° with respect to the catheter axis. Third, the strings were with different lengths and random angles ranging from −45° to + 45°. The decorrelation characteristics for these configurations of aggregates of RBCs were investigated and compared with point scatterers. For the aggregates of RBCs parallel to the catheter axis, the decorrelation rate became slower when the aggregate length was increased. RBC aggregations with fixed and random lengths and angles resulted in a decorrelation rate that approaches the decorrelation pattern from point scatterers. Results suggests that the presence of aggregates of RBCs will probably not affect the measurements of transverse blood flow using a decorrelation-based method and an IVUS array catheter. (E-mail: lupotti@tch.fgg.eur.nl)

Transparency effects on powder speckle decorrelation

Laser speckle decorrelation has previously been applied to measure the mean powder size of bulk powder beds and the roughness of porous rocks. The angular decorrelation rate of laser speckle from bulk powder beds correlates strongly with the mean powder size. However it was found that the angular decorrelation rates of transparent powders were much higher than those of opaque or dyed powders of the same size distribution. The accuracy of size measurements could be severely compromised if transparency effects were not compensated. Monte Carlo modelling of remitted photon path lengths in a powder bed suggests and experimental data supports that diffuse reflectance data may be used to correct for transparency effects on angular decorrelation rate data.

Does flow shear suppress turbulence in nonionized flows?

The suppression of turbulence by mean flow shear is shown to apply to nonionized flows as well as plasmas. However, besides the criterion that the shearing rate exceed the turbulent decorrelation rate, there are three additional conditions. These stipulate that the shear flow must be stable, that turbulence must remain in the domain of flow shear for longer than an eddy turnover time, and that the dynamics should be two dimensional (2D). In nonionized flows, these conditions are not typically satisfied, explaining why shear suppression is not a familiar phenomenon in hydrodynamics. The three conditions are discussed in the context of nonionized and plasma flows. Two examples of suppression in nonionized flows are presented. One involves the formation of coherent structures in 2D Navier–Stokes turbulence and the other involves large-scale turbulence in the stratosphere.

Statistical Theory of Subcritically-Excited Strong Turbulence in Inhomogeneous Plasmas. III

A statistical theory of nonlinear-nonequilibrium plasma state with strongly developed turbulence and with strong inhomogeneity of the system has been developed. A unified theory for both the thermally excited fluctuations and the strongly turbulent fluctuations is presented. With respect to the turbulent fluctuations, the coherent part to a certain test mode is renormalized as the drag to the test mode, and the rest, the incoherent part, is considered to be a random noise. The renormalized operator includes the effect of nonlinear destabilization as well as the decorrelation by turbulent fluctuations. Formulation is presented by deriving an Fokker-Planck equation for the probability distribution function. Equilibrium distribution function of fluctuations is obtained. Transition from the thermal fluctuations, that is governed by the Boltzmann distribution, to the turbulent fluctuation is clarified. The distribution function for the turbulent fluctuation has tail component and the width of which is in the same order as the mean fluctuation level itself. The Lyapunov function is constructed for the strongly turbulent plasma, and it is shown that an approach to a certain equilibrium distribution is assured. The result for the most probable state is expressed in terms of `minimum renormalized dissipation rate', which is given by the ratio of the nonlinear decorrelation rate of fluctuation energy and the random excitation rate which includes both the thermal noise and turbulent self-noise effects. Application is made for example to the current-diffusive interchange mode turbulence in inhomogeneous plasmas. The applicability of this method covers plasma turbulences in much wider circumstance as well as neutral fluid turbulence. This method of analyzing strong turbulence has successfully extended the principles of statistical physics, i.e., Kubo-formula, Prigogine's principle of minimum entropy production rate. The condition for the turbulence transition is analogous to the Maxwell's construction in the phase transition physics in thermodynamical equilibrium. The method provides the extension of the nonequilibrium statistical physics to the far-nonequilibrium states.

Suppression of turbulence and transport by sheared flow

The role of stable shear flow in suppressing turbulence and turbulent transport in plasmas and neutral fluids is reviewed. Localized stable flow shear produces transport barriers whose extensive and highly successful utilization in fusion devices has made them the primary experimental technique for reducing and even eliminating the rapid turbulent losses of heat and particles that characterize fusion-grade plasmas. These transport barriers occur in different plasma regions with disparate physical properties and in a range of confining configurations, indicating a physical process of unusual universality. Flow shear suppresses turbulence by speeding up turbulent decorrelation. This is a robust feature of advection whenever the straining rate of stable mean flow shear exceeds the nonlinear decorrelation rate. Shear straining lowers correlation lengths in the direction of shear and reduces turbulent amplitudes. It also disrupts other processes that feed into or result from turbulence, including the linear instability of important collective modes, the transport-producing correlations between advecting fluid and advectants, and large-scale spatially connected avalanchelike transport events. In plasmas, regions of stable flow shear can be externally driven, but most frequently are created spontaneously in critical transitions between different plasma states. Shear suppression occurs in hydrodynamics and represents an extension of rapid-distortion theory to a long-time-scale nonlinear regime in two-dimensional stable shear flow. Examples from hydrodynamics include the emergence of coherent vortices in decaying two-dimensional Navier-Stokes turbulence and the reduction of turbulent transport in the stratosphere.

Statistical Theory of Subcritically-Excited Strong Turbulence in Inhomogeneous Plasmas. II

A statistical description is developed for a self-sustained subcritical turbulence in inhomogeneous plasmas. Interchange mode in the presence of inhomogeneous magnetic field, which reveals a submarginal strong turbulence, is considered. Nonlinear dispersion relation is extended to a Langevin equation for a dressed test mode, in which nonlinear interactions are kept as renormalized drag and random self noise. Based upon the assumption that the random noise has a faster time scale, the solutions are obtained for the fluctuation level, decorrelation rate, auto- and cross-correlation functions and spectrum. They are expressed as nonlinear functions of non-equilibrium parameters like gradient. Extended fluctuation-dissipation theorem (Einstein relation) is described as statistical relations. Then the Langevin equation is reformulated into a Fokker-Planck equation of the probability distribution function. The steady state probability function is solved. Imposing the constraint of the self-noise, the power-law d...

Statistical Theory of Subcritically-Excited Strong Turbulence in Inhomogeneous Plasmas. I

A statistical description is developed for a self-sustained subcritical turbulence in inhomogeneous plasmas. Interchange mode in the presence of inhomogeneous magnetic field, which reveals a submarginal strong turbulence, is considered. Nonlinear dispersion relation is extended to a Langevin equation for a dressed test mode, in which nonlinear interactions are kept as renormalized drag and random self noise. Based upon the assumption that the random noise has a faster time scale, the solutions are obtained for the fluctuation level, decorrelation rate, auto- and cross-correlation functions and spectrum. They are expressed as nonlinear functions of non-equilibrium parameters like gradient. Extended fluctuation-dissipation theorem (Einstein relation) is described as statistical relations. Then the Langevin equation is reformulated into a Fokker-Planck equation of the probability distribution function. The steady state probability function is solved. Imposing the constraint of the self-noise, the power-law distribution with respect to the fluctuation amplitude is obtained in the tail of the distribution function.

Long-Range Saturation of Spatial Decoherence in Wave-Field Transport in Random Multiple-Scattering Media

The transverse spatial coherence of an optical beam alters as the light traverses a dense, multiple-scattering, random dielectric medium. Results of measurements show the predicted initial increase of the decoherence (or decorrelation) rate with spatial separation, followed by saturation at large separation. This behavior can be modeled by using a Boltzmann-like transport equation for the Wigner function of the wave field, whereas the standard model for decoherence (developed for quantum wave fields), which is based on the Fokker-Planck phase-space diffusion equation, contains no saturation and fails at all separations to describe the observed behavior.