Measurements Of Density Fluctuations Research Articles

Integration of fixed-frequency and FM-CW (frequency-modulated continuous-wave) reflectometers for coincident turbulence measurements on LTX-β (Lithium Tokamak eXperiment-β).

The fixed-frequency and frequency-modulated continuous-wave (FM-CW) reflectometers on LTX-β (Lithium Tokamak eXperiment-β) have been configured to use the same transmission lines and antenna arrays for coincident views of the core and edge plasma. The fixed-frequency channels (13.1-20.5 and 20-40GHz, tunable between discharges) provide time-resolved measurements of density fluctuations, while the FM-CW channels (13.1-20.2 and 19.5-33.5GHz) measure the density profile and fluctuations, with high spatial resolution and a sampling rate determined by the frequency sweep interval (5 μs). Data from both reflectometers are synchronously acquired to simultaneously leverage the wide bandwidth and high spatial resolution of the respective systems. Experiments showed that mutual crosstalk interference is momentary and does not diminish the capability of either system. Spectral analysis indicated broad power spectra (several hundreds of kHz) and suggests that the signals from the FM-CW system are consistent with under-sampled fixed-frequency signals. Radial correlations were explored using data from the two reflectometers, as well as from the FM-CW system alone. The core channels showed high levels of agreement between these two comparisons, suggesting that the data from the reflectometers are interchangeable for statistical estimates. For the edge channels, comparisons using data from the FM-CW reflectometer alone showed significant decorrelation due to time lag caused by the finite frequency up-sweep duration. Alternatively, this effect is eliminated when cross-correlating data from the different reflectometers. These results highlight the advantages of operating the fixed-frequency and FM-CW reflectometers in this manner, where the combined system can overcome the limitations of each separate system.

Origin of the type III radiation observed near the Sun

Aims. We investigate processes associated with the generation of type III radiation using Parker Solar Probe measurements. Methods. We measured the amplitudes and phase velocities of electric and magnetic fields and their associated plasma density fluctuations. Results. 1. There are slow electrostatic waves near the Langmuir frequency and at as many as six harmonics, the number of which increases with the amplitude of the Langmuir wave. Their electrostatic nature is shown by measurements of the plasma density fluctuations. From these density fluctuations and the electric field magnitude, the k-value of the Langmuir wave is estimated to be 0.14 and kλd = 0.4. Even with the large uncertainty in this quantity (more than a factor of two), the phase velocity of the Langmuir wave was < 10 000 km/s. 2. The electromagnetic wave near the Langmuir frequency has a phase velocity lower than 50 000 km/s. 3. We cannot determine whether there are electromagnetic waves at the harmonics of the Langmuir frequency. If they existed, their magnetic field components would be below the noise level of the measurement. 4. The rapid (less than one millisecond) amplitude variations typical of the Langmuir wave and its harmonics are artifacts resulting from the addition of two waves, one of which has small frequency variations that arise because the wave travels through density irregularities. None of these results are expected in or consistent with the conventional model of the three-wave interaction of two counter-streaming Langmuir waves that coalesce to produce the type III wave. They are consistent with a new model in which electrostatic antenna waves are produced at the harmonics by radiation of the Langmuir wave, after which at least the first harmonic wave evolved through density irregularities such that its wave number decreased and it became the type III radiation.

Applicability of alkali beam emission spectroscopy on NSTX-U.

Understanding fast pedestal dynamics and turbulent transport in the edge and scrape-off layer (SOL) plasma of spherical tokamaks is crucial for the design and operation of future fusion reactors. The alkali beam emission spectroscopy diagnostic technique offers a means to measure the absolute electron density radial profile and fluctuation amplitude in these regions. In this study, we demonstrate that injecting a sodium neutral beam radially into the plasma and analyzing the light emission from its 3p-3s atomic transition using near-orthogonal viewing angles allows for accurate measurement of the electron density profile and fluctuations in the National Spherical Torus Experiment (NSTX) Upgrade spherical tokamak. Our findings indicate a peak signal-to-noise ratio of 118 in the pedestal and 12 in the SOL under typical NSTX plasma conditions. The spatial resolution for the electron density profile is estimated to be between 2 and 8mm, while for fluctuation measurements, it ranges from 12 to 15mm.

Design of radial interferometer-polarimeter for internal magnetic and density fluctuation measurements at multiple space-time scales in the National Spherical Torus Experiment-Upgrade (NSTX-U).

A Faraday-effect radial interferometer-polarimeter is designed for the National Spherical Torus Experiment-Upgrade (NSTX-U) to measure multiscale magnetic and density fluctuations critical to understanding fusion plasma confinement and stability, including those originating from magnetohydrodynamic instabilities, energetic particle-driven modes, and turbulence. The diagnostic will utilize the three-wave technique with 5MHz bandwidth to simultaneously measure line-integrated magnetic and density fluctuations up to the ion-cyclotron frequency. Probe beams will be launched radially from the low-field side at the NSTX-U midplane, where the measured Faraday fluctuations mainly correspond to radial magnetic fluctuations that directly link to magnetic transport. A correlation technique will be employed to reduce the measurement noise to below 0.01° enabling detection of small amplitude fluctuations. Two toroidally displaced chords with 7° separation will be installed to measure toroidal mode numbers up to n = 25 for mode identification. Solid-state microwave sources operating at 321μm (935GHz) will be used to minimize the impact of the Cotton-Mouton effect.

A Q-band frequency tunable Doppler backscattering (DBS) system for pedestal and scrape-off layer density fluctuation and flow measurements in the DIII-D tokamak.

We present the design and laboratory tests for a new Q-band frequency tunable Doppler backscattering (DBS) system suitable for probing poloidal wavenumber kñ = 6-8cm-1 density fluctuations and their flow velocities in the pedestal and scape-off layer (SOL) of the DIII-D tokamak. This system will provide new measurements in the increasingly important and under-diagnosed far pedestal and SOL plasma regions. These results are important for experimental transport studies and necessary for the validation of transport models, both of which are important to fusion energy research. The use of a single tunable frequency reduces the complexity and potential failure points as compared to a multichannel system. This new system utilizes a 33-50GHz tunable source and will be integrated into the current V-band DBS in DIII-D using a broadband Q- and V-band multiplexer. A full-scale mockup of the quasi-optical system was used to test and optimize the performance. These tests include beam profile measurements at different distances (and angles) from a paraboloidal focusing and steering mirror. The measurements cover the full frequency range 33-75GHz of the integrated/combined Q-V band DBS system and target a large radial coverage of the low-field side of the plasma from ρ = 1.1 to ρ = 0.5, where ρ is the normalized flux surface radial coordinate.

Millimeter-wave high-wavenumber scattering diagnostic developments on EAST and NSTX-U.

A pioneering 4-channel, high-k poloidal, millimeter-wave collective scattering system has been successfully developed for the Experimental Advanced Superconducting Tokamak (EAST). Engineered to explore high-k electron density fluctuations, this innovative system deploys a 270GHz mm-wave probe beam launched from Port K and directed toward Port P (both ports lie on the midplane and are 110° part), where large aperture optics capture radiation across four simultaneous scattering angles. Tailored to measure density fluctuations with a poloidal wavenumber of up to 20cm-1, this high-k scattering system underwent rigorous laboratory testing in 2023, and the installation is currently being carried out on EAST. Its primary purpose lies in scrutinizing ion and electron-scale instabilities, such as the electron temperature gradient (ETG) mode, by furnishing measurements of the kθ (poloidal wavenumber) spectrum. This advancement significantly bolsters the capacity to probe high-k electron density fluctuations within the framework of EAST. Beam tracing and data interpretation modules developed for both EAST and NSTX-U high-k scattering diagnostics are described.

Inter-ELM pedestal turbulence dynamics dependence on q95 and temperature gradient

A series of dedicated experiments from the DIII-D tokamak provide spatially and temporally resolved measurements of electron density and temperature, and multiscale and multichannel fluctuations over a wide range of conditions. Measurements of long wavelength density fluctuations in the type-I ELMing H-mode pedestals routinely reveal a coexistence of multiple instabilities that exhibit dramatic different dynamic behaviors as q95 and temperature gradients are varied, apparently responsible for limiting pedestal temperature profiles. Two distinct frequency bands of density fluctuations are modulated by an ELM cycle with frequency above 200 kHz propagating in the electron diamagnetic direction in the lab frame (electron mode) and below 200 kHz propagating in the ion diamagnetic direction (ion mode). The electron mode amplitude peaks near the electron temperature gradient region and increases with q95 which seems to be correlated with the increased χe at higher q95, similar to the characteristics expected for the micro-tearing mode (MTM). At higher q95, during the inter-ELM period, the ion mode decays at the later phase of the ELM cycle. Consistently, the poloidal correlation length of the ion mode is also found to reduce, which suggests the possible E × B flow shear suppression of the ion mode at the later phase of the ELM cycle as the Er well recovers. In contrast, the electron mode grows during the ELM cycle and reaches saturation at around 50%–60% of the ELM period. Linear gyrokinetic simulations find the MTMs to be the most unstable mode in the pedestal electron temperature gradient region. The higher q95 and lower magnetic shear destabilize the MTMs. These observations provide key insights into the underlying physics of multifield properties and a rich dataset of experimental ‘fingerprints’ that enable new tests of theoretical pedestal models and lead to the development of a predictive model for pedestal formation on the ITER and future burning plasma experiments.

Multi-Perspective Heterodyne Digital Holography For High-Speed Imaging Of Density Fluctuations In Supersonic Flow

Density fluctuation measurements with high spatio-temporal resolution provide meaningful insights into the dynamics of turbulent structures in shear layers, boundary layers, and disturbances that influence the transition to turbulence. The current contribution presents a new multiple perspective digital holographic imaging technique that aims to resolve high-frequency density fluctuations with spatial discrimination along the line of sight. A key element of the proposed method is the generation of a beamlet array of varying view angles that is spatially overlapped within the measurement zone. We present the first experimental realization of this approach using a 7-element hexagonally packed fly’s eye lens array and analyze results for a pair of mutually perpendicular and axially offset sonic jets. The experimental apparatus also incorporates heterodyne detection with a heterodyne frequency set to 1/4 of the imaging frame rate. The optical system performance is evaluated for a crossing jet flow and key design considerations for the multi-perspective optical system are discussed.

A methodology for estimating spectral indices to fluctuation measurements of ionospheric parameters

Spectral analysis is a technique largely used to study scale size regime of ionospheric plasma irregularities based on in situ measurements, notwithstanding the visual representation of power spectral density (PSD) of a signal is often a source of ambiguity during fitting routines and identification of breakpoints. In this work, a method is proposed in order to mitigate the uncertainties inherent to this process. Here, the spectral behavior of time series fluctuations is alternatively investigated using Detrended Fluctuation Analysis (DFA). The DFA algorithm is a scaling analysis procedure widely applied to estimate the detection of long-range correlation without considering apparent short-range ones. Furthermore, the DFA technique is able to remove trends implicit to the signal and to be applied to non-stationary time series. Using in situ measurements of both ionospheric electron density and electric field fluctuations, it was able to analyze plasma bubbles with scales ranging from 1.66 km to 12.4 m. The results show that DFA and PSD routines provide quite similar spectra, but different spectral indices. On the other hand, the spectra revealed steep slopes wrapping the medium scales, a characteristic also detected in other studies. Besides that, the DFA is less noisy than Fourier spectra, which allows a more precise identification of spectral breakpoints.

Localized phase contrast imaging at the Wendelstein 7-X stellarator

In its basic form, phase contrast imaging (PCI) provides line-integrated measurements of electron density fluctuations in plasmas. As turbulent fluctuations in magnetically confined plasmas have wave vectors almost perpendicular to the background magnetic field, the signals scattered by fluctuations from different parts of the PCI line-of-sight (LoS) are spatially separated in focal planes of the plasma. This allows localized PCI measurements by placing a mask in such a plane, to only permit signals from specific parts of the LoS to reach the PCI detectors. The present paper describes modeling and design of localization masks for the PCI system at the Wendelstein 7-X (W7-X) stellarator as well as the first results obtained using the masks in the recent long-pulse W7-X experimental campaign. During this project, we have extended the theory describing the mask response within the Fraunhofer diffraction model. As a novel development, we show from first principles that the mask response is determined by the fraction of power of the scattered beam spots that passes the mask. These insights have been used to select the W7-X mask design, consisting of a circular cutout, allowing the unscattered beam spot to pass the mask, with wedges covering a fixed angular range outside the central cutout. In the recent W7-X experimental campaign, the masks have verified the location of the main turbulence features observed by the PCI system and provided new information about the location of short-wavelength magnetohydrodynamic modes.

Quasi-optical design for the cross-polarization scattering diagnostic on the HL-3 tokamak.

As the plasma beta (β) increases in high-performance tokamaks, electromagnetic turbulence becomes more significant, potentially constraining their operational range. To investigate this turbulence, a cross-polarization scattering (CPS) diagnostic system is being developed on the HL-3 tokamak for simultaneous measurements of density and magnetic fluctuations. In this work, a quasi-optical system has been designed and analyzed for the Q-band CPS diagnostic. The system includes a lens group for beam waist size optimization, a rotatable wire-grid polarizer for polarization adjustment, and a reflector group for measurement range regulation and system response enhancement. Laboratory tests demonstrated a beam radius of order 4cm at the target measurement location (near the plasma pedestal), cross-polarization isolation exceeding 30 dB, and poloidal and toroidal angle adjustment ranges of ±40° and ±15°, respectively. These results verify the system's feasibility through laboratory evaluations. The quasi-optical system has been installed on the HL-3 tokamak during the 2023 experimental campaign to support the development of CPS diagnostics.

What is the best simulation approach for measuring local density fluctuations near solvo-/hydrophobes?

Measurements of local density fluctuations are crucial to characterizing the interfacial properties of equilibrium fluids. A specific case that has been well-explored involves the heightened compressibility of water near hydrophobic entities. Commonly, a spatial profile of local fluctuation strength is constructed from the measurements of the mean and variance of solvent particle number fluctuations in a set of contiguous subvolumes of the system adjacent to the solvo-/hydrophobe. An alternative measure proposed by Evans and Stewart [J. Phys.: Condens. Matter 27, 194111 (2015)] defines a local compressibility profile in terms of the chemical potential derivative of the spatial number density profile. Using Grand canonical Monte Carlo simulation, we compare and contrast the efficacy of these two approaches for a Lennard-Jones solvent at spherical and planar solvophobic interfaces and SPC/E water at a hydrophobic spherical solute. Our principal findings are as follows: (i) the local compressibility profile χ(r) of Evans and Stewart is considerably more sensitive to variations in the strength of local density fluctuations than the spatial fluctuation profile F(r) and can resolve much more detailed structure; and (ii) while the local compressibility profile is essentially independent of the choice of spatial discretization used to construct the profile, the spatial fluctuation profile exhibits a strong systematic dependence on the size of the subvolumes on which the profile is defined. We clarify the origin and nature of this finite-size effect.

Imaging focused laser differential interferometry.

Focused laser differential interferometry (FLDI) is an important diagnostic for measuring density fluctuations in high-speed flows. Currently, however, high dynamic range FLDI is limited to photodiode measurements. In order to spatially resolve multiple locations within complex flows, we present a novel, to the best of our knowledge, refractive-optic imaging FLDI concept that not only produces two-dimensional images without scanning but also reduces the measurement noise floor of those images. To demonstrate this concept, a 33 × 33 grid of FLDI points is first generated using a microlens array. Then, the beams are split and recombined using two polarized Mach-Zehnder interferometers to maximize flexibility in beam separation and optimize signal sensitivity. Next, the FLDI points are collected slightly out of focus on a high-speed camera in order to increase the number of pixels n per FLDI point, thereby reducing noise floor by n. Finally, an under-expanded jet with a characteristic screech at 14.1 kHz is tested with the imaging FLDI setup, showing clear barrel and reflected shock features as well as spatially varying turbulence densities. Overall, this unique concept enables the creation of reduced-noise-floor, two-dimensional FLDI datasets for the study of supersonic and hypersonic flows.

Time-resolved measurement of acoustic density fluctuations using a phase-shifting Mach-Zehnder interferometer.

Phase-shifting interferometry is one of the optical measurement techniques that improves accuracy and resolution by incorporating a controlled phase shift into conventional optical interferometry. In this study, a four-step phase-shifting interferometer is developed to measure the spatiotemporal distribution of acoustic density oscillations of the gas next to a rigid plate. The experimental apparatus consists of a polarizing Mach-Zehnder interferometer with a polarization camera capable of capturing four polarization directions in one shot image and it is used to measure the magnitude and the phase of density fluctuations through a duct of rectangular cross section connected to a loudspeaker. The results are compared with the well-established thermoacoustic theory describing the thermal coupling between acoustic oscillations and rigid boundaries, and the results show a very good agreement for various ratios of the (frequency-dependent) thermal boundary layer thickness to the plate spacing. This measurement technique could be advantageously employed to analyze more complex heat transfer processes involving the coupling of acoustic oscillations with rigid boundaries.

Merger-driven multiscale ICM density perturbations: testing cosmological simulations and constraining plasma physics

ABSTRACT The hot intracluster medium (ICM) provides a unique laboratory to test multiscale physics in numerical simulations and probe plasma physics. Utilizing archival Chandra observations, we measure density fluctuations in the ICM in a sample of 80 nearby (z ≲ 1) galaxy clusters and infer scale-dependent velocities within regions affected by mergers (r < R2500c), excluding cool-cores. Systematic uncertainties (e.g. substructures, cluster asymmetries) are carefully explored to ensure robust measurements within the bulk ICM. We find typical velocities ∼220 (300) km s−1 in relaxed (unrelaxed) clusters, which translate to non-thermal pressure fractions ∼4 (8) per cent, and clumping factors ∼1.03 (1.06). We show that density fluctuation amplitudes could distinguish relaxed from unrelaxed clusters in these regions. Comparison with density fluctuations in cosmological simulations shows good agreement in merging clusters. Simulations underpredict the amplitude of fluctuations in relaxed clusters on length scales <0.75 R2500c, suggesting these systems are most sensitive to ‘missing’ physics in the simulations. In clusters hosting radio haloes, we examine correlations between gas velocities, turbulent dissipation rate, and radio emission strength/efficiency to test turbulent re-acceleration of cosmic ray electrons. We measure a weak correlation, driven by a few outlier clusters, in contrast to some previous studies. Finally, we present upper limits on effective viscosity in the bulk ICM of 16 clusters, showing it is systematically suppressed by at least a factor of 8, and the suppression is a general property of the ICM. Confirmation of our results with direct velocity measurements will be possible soon with XRISM.

Probing the nature of the QCD phase transition with higher-order net-proton number fluctuation and local parton density fluctuation measurements at RHIC-STAR

The moments of proton and net-proton multiplicity distributions are observables expected to be sensitive to the QCD critical point and the nature of the QCD phase transition from QGP to hadron gas. Hyper-order cumulants are measured in wide centrality bins in STAR BES-I data and found to be qualitatively consistent with trends predicted by lattice QCD which finds a cross-over phase transition at low μB. Data collected at √SNN = 3 GeV in BES-II exhibit trends opposite of those observed in higher energy collisions which may suggest the dominance of hadronic interactions at this energy. The variance of proton multiplicity distributions in azimuthal partitions is measured to search for signals of clustering indicative of a first-order phase transition. A strong dependence on the event multiplicity is observed. This dependence is independent of energy in AMPT while in STAR data a significant trend with energy is observed.

Tangentially viewing phase contrast imaging for turbulence measurementsin toroidal fusion devices

Phase contrast imaging (PCI) is an established and powerful techniquefor measuring density fluctuations in plasmas and has been successfullyapplied to several fusion devices. Rooted in a concept first developed formicroscopy, PCI belongs to the category of internal-reference interferometersand has been shown to possess superior qualities among such techniques,particularly in terms of spatial linearity. In essence, it produces a true imageof fluctuations in the plane perpendicular to the propagation direction of theprobing laser beam, provided their characteristic spatial scale is smaller thanthe beam width. The measurement in itself is line-integrated and thus notspatially resolved longitudinally to the beam. However, the properties of theturbulence itself can be exploited to achieve longitudinal resolution,particularly when the beam propagates nearly tangentially to the magnetic field.This assertion has been recently rigorously tested through numericalmodeling, which has revealed significant additional complexity while confirmingthe general principle. Tangential PCI has been employed extensively in the TCVtokamak and has resulted in a rich body of work on broadband microturbulence inthe ion-temperature-gradient/trapped-electron-moderange and on geodesic acoustic modes. A similar diagnosticarrangement is also at an advanced planning stage for the new superconductingtokamak JT-60SA.

Estimation of 2D profile dynamics of electrostatic potential fluctuations using multi-scale deep learning

Abstract Dynamics in magnetically confined plasmas are dominated by turbulence driven by spatial inhomogeneities in density and temperature. Simultaneous measurement of velocity field and density fluctuations is necessary to observe the particle transport, but the measurement of the velocity field fluctuations is often challenging. Here, we propose a method to estimation velocity field fluctuations from density fluctuations by using plasma turbulence simulations and a deep technique learning. In order to take multi-scale characteristics into account, the several number of spatial filters are used in the convolutional neural network. The velocity field fluctuations are successfully predicted, and the particle transport estimated from the predicted velocity field fluctuations is within 93.1% accuracy. The deep learning could be used for the prediction of physical variables which are difficult to be measured.

An Anisotropic Density Turbulence Model from the Sun to 1 au Derived from Radio Observations

Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, changing their observed time characteristics, sizes, and positions. The same turbulence causes angular broadening and scintillation of galactic and extragalactic compact radio sources observed through the solar atmosphere. Using large-scale simulations of radio-wave transport, the characteristics of anisotropic density turbulence from 0.1 R ⊙ to 1 au are explored. For the first time, a profile of heliospheric density fluctuations is deduced that accounts for the properties of extrasolar radio sources, solar radio bursts, and in situ density fluctuation measurements in the solar wind at 1 au. The radial profile of the spectrum-weighted mean wavenumber of density fluctuations (a quantity proportional to the scattering rate of radio waves) is found to have a broad maximum at around (4–7) R ⊙, where the slow solar wind becomes supersonic. The level of density fluctuations at the inner scale (which is consistent with the proton resonance scale) decreases with heliocentric distance as cm−6. Due to scattering, the apparent positions of solar burst sources observed at frequencies between 0.1 and 300 MHz are computed to be essentially cospatial and to have comparable sizes, for both fundamental and harmonic emission. Anisotropic scattering is found to account for the shortest solar radio burst decay times observed, and the required wavenumber anisotropy is q ∥/q ⊥ = 0.25–0.4, depending on whether fundamental or harmonic emission is involved. The deduced radio-wave scattering rate paves the way to quantify intrinsic solar radio burst characteristics.

Preparation of a beam emission spectroscopy diagnostic based on a Lyman-alpha line to diagnose core and edge-plasma density fluctuation on the HL-2A tokamak

In this article, the design of a Lyman-alpha-based beam emission spectroscopy (LAB) diagnostic on the HL-2A tokamak has been proposed for the first time. The purpose of this novel diagnostic is to measure density fluctuations of tokamak plasma. The light-collection system of LAB, which consists of the first mirror and two groups of coaxial double-mirror telescopes, can realize a two-segmented viewing field of ρ = 0‒0.2 and ρ = 0.75‒1, which is optimized to measure plasma density fluctuation, not only in the edge transport barrier region but also in the internal transport barrier region, to investigate the underlying physics of turbulence in tokamaks. Spectrometers are developed to separate out the Doppler-shifted target line (122.03 and 122.17 nm) from the background Lyman-alpha line (121.53 nm). Here, 30 Core-LAB channels and 30 Edge-LAB channels are under development on the HL-2A tokamak. It has high radial spatial resolutions of about 2.7 mm and 3.3 mm for the core and edge channels, respectively. Taking the high light intensity of this Lyman-alpha line into account, temporal resolution of 200 kHz can be ensured by broad bandwidth amplifiers. This high spatio-temporal resolution makes LAB a potential keen tool to experimentally investigate tokamak plasma physics.