Density Fluctuation Level Research Articles

First determination of the angular dependence of rise and decay times of solar radio bursts using multi-spacecraft observations

A large arsenal of space-based and ground-based instruments is dedicated to the observation of radio emissions, whether they originate within our solar system or not. Radio photons interact with anisotropic density fluctuations in the heliosphere which can alter their trajectory and influence the properties that are deduced from observations. This is particularly evident in solar radio observations, where anisotropic scattering leads to highly directional radio emissions. Consequently, observers at varying locations will measure different properties, including different source sizes, source positions, and intensities. However, it is not known whether the measurements of the decay time of solar radio bursts are also affected by the observer’s position. Decay times are dominated by scattering effects, and so are frequently used as proxies of the level of density fluctuations in the heliosphere, making the identification of any location-related dependence crucial. We combine multi-vantage observations of interplanetary Type III bursts from four non-collinear, angularly separated spacecraft with simulations to investigate the dependence of the decay- and rise-time measurements on the separation of the observer from the source. We propose a function to characterise the entire time profile of radio signals, allowing for the simultaneous estimation of the peak flux, decay time, and rise time, while demonstrating that the rise phase of radio bursts is non-exponential, having a non-constant growth rate. We determine that the decay and rise times are independent of the observer’s position, identifying them as the only properties that remain unaffected and thus do not require corrections for the observer’s location. Moreover, we examine the ratio between the rise and decay times and find that it does not depend on the frequency. Therefore, we provide the first evidence that the rise phase is also significantly impacted by scattering effects, adding to our understanding of the plasma emission process.

Electrostatic Wave Decay in the Randomly Inhomogeneous Solar Wind

Despite a few space observations where Langmuir and ion acoustic waves are expected to participate in the mechanism of electrostatic decay, this is to date believed to be the main and fastest nonlinear wave process in the solar wind. However, in such a plasma where random density fluctuations are ubiquitous, the question of whether nonlinear wave processes play a significant role in Langmuir wave turbulence generated by electron beams associated with type III solar radio bursts remains still open. This paper provides several answers by studying, owing to two-dimensional challenging particle-in-cell simulations, the dynamics and the properties of the ion acoustic waves excited by such Langmuir wave turbulence and the role they play in the electrostatic decay. The impact on this process of plasma background density fluctuations and electron-to-ion temperature ratio is studied. Moreover, it is shown that, for a typical solar wind plasma with an average level of density fluctuations of a few percent of the ambient density and a temperature ratio of the order of 1, nonlinear induced scattering off ions occurs, with small intensity low-frequency quasi-modes and only in localized plasma regions where density is depleted or weakly perturbed by low-frequency turbulence.

Second Harmonic Electromagnetic Wave Emissions from a Turbulent Plasma with Random Density Fluctuations

In the solar wind, electromagnetic waves at the harmonic plasma frequency 2ω p can be generated as a result of coalescence between forward- and backward-propagating Langmuir waves. A new approach to calculate their radiation efficiency in plasmas with external background density fluctuations is developed. The evolution of Langmuir wave turbulence is studied by solving numerically the Zakharov equations in a two-dimensional randomly inhomogeneous plasma. Then, the dynamics of the nonlinear electric currents modulated at frequencies close to 2ω p are calculated, as well as their radiation into harmonic electromagnetic waves. In the frame of this non-self-consistent approach where all transformations of Langmuir waves on density inhomogeneities are taken into account, the electromagnetic wave radiation rate (emissivity) is determined numerically as well as analytically, providing in both cases similar results. Moreover, scaling laws of the harmonic wave emissivity as a function of the ratio of the light velocity to the electron plasma thermal velocity are found. It is also shown how the emissivity depends on the average level of density fluctuations and on the isotropic/anisotropic character of the Langmuir waves’ and density fluctuations’ spectra.

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.

Experimental and numerical investigations of electron transport enhancement by electron-cyclotron plasma-wave interaction in tokamaks

Energy transfer from electron-cyclotron (EC) waves to the plasma is being routinely used in tokamaks to heat and drive current through the electron channel. Technical applications such as magnetohydrodynamic mode mitigation require power deposition with a high degree of localization. However, observations made in tokamaks show a broader distribution of suprathermal electrons than predicted by standard drift-kinetic codes. The present paper explores a possible wave-induced increase of electron turbulent transport that may explain the experimental data, using power-modulated EC waves in the Tokamak à Configuration Variable (TCV). In particular, an indirect measurement of the suprathermal electron population via hard x-rays exhibits an enhanced radial transport with increased wave power. This correlates well with the measured increase of the density fluctuation level during the power pulses, associated with the destabilization of ion temperature gradient modes and trapped electron modes and with stiff electron profiles. Forward bounce-averaged drift-kinetic simulations show that a radial diffusion model directly proportional to the wave power deposition is required to match the experimental data. The power dependency is confirmed by global flux-driven gyro-kinetic simulations using a realistic EC power source, computing turbulent transport from first principles and showing a radial increase of electron transport with increased wave power.

Application of the 2D Code Tamic Analyzer Based on the Method of Impedance Analog of the Sestroretskii Electromagnetic Space for Problems of Plasma Diagnostics in Tokamak Fusion Facilities

Applications of the two-dimensional full-wave electromagnetic code Tamic Analyzer, developed by B.V. Sestroretskii to study the limiting possibilities of diagnostics of reflectometry in tokamak plasma. It is shown that by comparing experimental reflectometry data with calculations using this code, it is possible to determine the structure of density fluctuations in a tokamak, but the experimental radial correlation lengths can be significantly overestimated. Simulation using the Taimic Anylyser code made it possible to determine the limiting level of density fluctuations at which it is possible to measure the plasma density profile and observe Alfven fluctuations in the International Experimental Thermonuclear Reactor of the tokamak type (ITER) under construction. Possible ways to increase the speed and counting field of the code are considered.

Probing sub-galactic mass structure with the power spectrum of surface-brightness anomalies in high-resolution observations of galaxy–galaxy strong gravitational lenses. II. Observational constraints on the subgalactic matter power spectrum

ABSTRACT Stringent observational constraints on the subgalactic matter power spectrum would allow one to distinguish between the concordance ΛCDM and the various alternative dark-matter models that predict significantly different properties of mass structure in galactic haloes. Galaxy–galaxy strong gravitational lensing provides a unique opportunity to probe the subgalactic mass structure in lens galaxies beyond the Local Group. Here, we demonstrate the first application of a novel methodology to observationally constrain the subgalactic matter power spectrum in the inner regions of massive elliptical lens galaxies on 1–10 kpc scales from the power spectrum of surface-brightness anomalies in highly magnified galaxy-scale Einstein rings and gravitational arcs. The pilot application of our approach to Hubble Space Telescope (HST/WFC3/F390W) observations of the SLACS lens system SDSS J0252+0039 allows us to place the following observational constraints (at the 99 per cent confidence level) on the dimensionless convergence power spectrum $\Delta ^{2}_{\delta \kappa }$ and the standard deviation in the aperture mass σAM: $\Delta ^{2}_{\delta \kappa }\lt 1$ (σAM < 0.8 × 108 M⊙) on 0.5-kpc scale, $\Delta ^{2}_{\delta \kappa }\lt 0.1$ (σAM < 1 × 108 M⊙) on 1-kpc scale and $\Delta ^{2}_{\delta \kappa }\lt 0.01$ (σAM < 3 × 108 M⊙) on 3-kpc scale. These first upper-limit constraints still considerably exceed the estimated effect of CDM subhaloes. However, future analysis of a larger sample of galaxy–galaxy strong lens systems can substantially narrow down these limits and possibly rule out dark-matter models that predict a significantly higher level of density fluctuations on the critical subgalactic scales.

Effect of Symmetry/Asymmetry of Shear Rotation of a Plasma Column in a Radial Electric Field on the Level of Turbulent Density Fluctuations

The influence of the properties of the profile of a radial static electric field E(r) on the evolution of an unstable ion temperature–gradient (ITG) drift wave in a nonuniformly rotating plasma column in a magnetic field is studied. The effect of symmetry on the decrease in the level of turbulent fluctuations, which are associated with the limiting state of the ITG wave during its destruction, is discussed. The level of turbulence is estimated in the framework of approximation of finite amplitudes depending on the electric field structure. It is shown that the maximum decrease in the level of fluctuations occurs with a symmetrical configuration of the radial electric field.

Observation of Turbulent Magnetohydrodynamic Cascade in the Jovian Magnetosheath

We present the first estimation of the energy cascade rate in Jupiter’s magnetosheath (MS). We use in situ observations from the Jovian Auroral Distributions Experiment and the magnetometer investigation instruments on board the Juno spacecraft, in concert with two recent compressible models, to investigate the cascade rate in the magnetohydrodynamic (MHD) scales. While a high level of compressible density fluctuations is observed in the Jovian MS, a constant energy flux exists in the MHD inertial range. The compressible isothermal and polytropic energy cascade rates increase in the MHD range when density fluctuations are present. We find that the energy cascade rate in Jupiter’s magnetosheath is at least 2 orders of magnitude (100 times) smaller than the corresponding typical value in the Earth’s magnetosheath.

The frequency ratio and time delay of solar radio emissions with fundamental and harmonic components

ABSTRACT Solar radio bursts generated through the plasma emission mechanism produce radiation near the local plasma frequency (fundamental emission) and double the plasma frequency (harmonic). While the theoretical ratio of these two frequencies is close to 2, simultaneous observations give ratios ranging from 1.6 to 2, suggesting either a ratio different from 2, a delay of the fundamental emission, or both. To address this long-standing question, we conducted high-frequency, high-time resolution imaging spectroscopy of type III and type J bursts with fine structures for both the fundamental and harmonic components with LOFAR between 30 and 80 MHz. The short-lived and narrow frequency-band fine structures observed simultaneously at fundamental and harmonic frequencies give a frequency ratio of 1.66 and 1.73, similar to previous observations. However, frequency-time cross-correlations suggest a frequency ratio of 1.99 and 1.95 with a time delay between the F and H emissions of 1.00 and 1.67 s, respectively for each event. Hence, simultaneous frequency ratio measurements different from 2 are caused by the delay of the fundamental emission. Among the processes causing fundamental emission delays, anisotropic radio-wave scattering is dominant. Moreover, the levels of anisotropy and density fluctuations reproducing the delay of fundamental emissions are consistent with those required to simulate the source size and duration of fundamental emissions. Using these simulations we are able to, for the first time, provide quantitative estimates of the delay time of the fundamental emissions caused by radio-wave propagation effects at multiple frequencies, which can be used in future studies.

Structured type III radio bursts observed in interplanetary space

Context. The last few decades have seen numerous studies dedicated to fine structures of type III radio bursts observed in the meter–decameter wavelengths. Most of the explanations of the structured radio emission involve the propagation of electron beams through the strongly inhomogeneous plasma in the low corona. To date, only a few type III bursts with fine structures, observed at hecto–kilometric wavelengths, have been reported. Aims. We report here the existence of numerous structured type III radio bursts observed during the STEREO era by all three WAVES instruments on board STEREO A, B, and Wind. The aim of the study is to report and classify structured type III bursts, and to present the characteristics of their fine structures. The final goal is to try to understand the physical mechanism responsible for the generation of structured radio emission. Methods. In this study we used data from all available spacecraft, specifically STEREO and Wind. We employed 1D density models to obtain the speed of the source of type III radio emission, the electron beam. We also performed a spectral analysis of the fine structures in order to compare their characteristics with the metric–decametric fine structures. Results. The presented similarities of the type III fine structures in the metric to decametric and interplanetary wavelengths indicate that the physical processes responsible for the generation of structured type III radio bursts could be the same, at heights from the low corona to the interplanetary range. We show that the observed structuring and intermittent nature of the type III bursts can be explained by the variation in the level of density fluctuations, at different distances from the Sun.

Experimental study of the core instability before and after internal transport barrier formation in EAST

In a reversed shear discharge in the Experimental Advanced Superconducting Tokamak (EAST), an internal transport barrier (ITB) was formed. For the first time, the turbulence in the plasma core before and after the formation of the ITB in EAST was investigated by microwave reflectometry. It was found that during the formation of the ITB, the turbulence inside the barrier was not completely suppressed. The density fluctuation level decreased in the early phase of ITB and significantly increased later. It was found that the density fluctuation level increased with the density gradient after the appearance of reversed shear Alfvén eigenmodes (RSAEs). The change in turbulence, measurable by the reflectometer, did not affect the rate of increase in core density. Through the measurement of RSAEs, it was found that the formation of this ITB may be related to the minimum q (q min). q min was close to 2.

Effect of the divertor configuration on the JET edge radial electric field

The role of the divertor configuration and divertor plasma physics on the L–H transition is poorly understood, leading to large uncertainties in predicting the L–H power threshold in future devices. This contribution reports on edge perpendicular plasma flow measurements by Doppler backscattering in JET L–H transition experiments with the outer divertor strike-point at different positions: horizontal target (HT), vertical target (VT), and in the corner configuration (between the HT and VTs). The edge perpendicular flow was found to be significantly affected by changes in the divertor configuration in the region inside the separatrix. Our results do not show evidence for the existence of a critical edge flow shear needed to achieve H-mode for different divertor configurations, with a larger shear observed for the VT configuration. No significant change in the shear flow and in the density fluctuation level is measured preceding the L–H transition in the region just inside the separatrix. The dynamics of the L–H transitions are also influenced by the divertor configuration with divertor oscillations (DOs) observed only in the HT configuration. Interestingly, DOs are associated with marked changes in the edge perpendicular flow around the separatrix.

Kinetic modeling of neutral transport for a continuum gyrokinetic code

We present the first-of-its-kind coupling of a continuum full-f gyrokinetic turbulence model with a 6D continuum model for kinetic neutrals, carried out using the Gkeyll code. Our objective is to improve the first-principle understanding of the role of neutrals in plasma fueling, detachment, and their interaction with edge plasma profiles and turbulence statistics. Our model includes only atomic hydrogen and incorporates electron-impact ionization, charge exchange, and wall recycling. These features have been successfully verified with analytical predictions and benchmarked with the DEGAS2 Monte Carlo neutral code. We carry out simulations for a scrape-off layer (SOL) with simplified geometry and National Spherical Torus Experiment parameters. We compare these results to a baseline simulation without neutrals and find that neutral interactions reduce the normalized density fluctuation levels and associated skewness and kurtosis, while increasing auto-correlation times. A flatter density profile is also observed, similar to the SOL density shoulder formation in experimental scenarios with high fueling.

Dynamics of Langmuir Wave Spectra in Randomly Inhomogeneous Solar Wind Plasmas

Abstract Solar coronal and wind plasmas often contain density fluctuations of various scales and amplitudes. The scattering of Langmuir wave turbulence on these inhomogeneities modifies the properties of the radiated electromagnetic emissions traveling from the Sun to the Earth. This paper shows the similarities between the physical results obtained by (i) a model based on the Zakharov equations, describing the self-consistent dynamics of Langmuir wave turbulence spectra in a plasma with external density fluctuations, and (ii) a modeling, within the framework of geometric optics approximation, of quasi-particles (representing plasmon quanta) moving in a fluctuating potential. It is shown that the dynamics of the Langmuir spectra is governed by anomalous diffusion processes, as a result of multiple scattering of waves on the density fluctuations; the same dynamics are observed in the momenta distributions of quasi-particles moving in potential structures with random inhomogeneities. These spectra and distributions are both characterized by a fast broadening during which energy is transported to larger wavevectors and momenta, exhibiting nonlinear time dependence of the average squares of wavevectors and quasi-particle momenta as well as non-Gaussian tails in the asymptotic stage. The corresponding diffusion coefficients depend on the time and are proportional to the square of the average level of density (or potential) fluctuations. It appears that anomalous transport and superdiffusion phenomena are responsible for the spectral broadening.

Impact of magnetic islands on plasma flow and turbulence in W7-X

The effect of magnetic islands on plasma flow and turbulence has been experimentally investigated in the stellarator W7-X. Magnetic configurations with the 5/5 magnetic island positioned at the plasma edge, inside the last closed flux surface, are studied. The main diagnostic used in the present work is a V-band Doppler reflectometer that allows the measurement of the perpendicular plasma flow and density fluctuations with good spatial resolution. A characteristic signature of the 5/5 magnetic island is clearly detected in the perpendicular flow profile. The comparison of the experimental flow and the neoclassically driven E × B flow indicates that the island contribution to the flow is maximum at the island boundaries and close to zero at the island O-point. Besides, a reduction in the density fluctuation level is found nearby the island O-point. The similarities between these observations and those found in other devices and in gyrokinetic simulations are discussed.

Radial electric field and density fluctuations measured by Doppler reflectometry during the post-pellet enhanced confinement phase in W7-X

Radial profiles of density fluctuations and the radial electric field, E r, have been measured using Doppler reflectometry during the post-pellet enhanced confinement phase achieved, under different heating power levels and magnetic configurations, during the 2018 W7-X experimental campaign. A pronounced E r-well is measured with local values as high as −40 kV m−1 in the radial range ρ ∼ 0.7–0.8 during the post-pellet enhanced confinement phase. The maximum E r intensity scales with both the plasma density and electron cyclotron heating power level, following a similar trend to the plasma energy content. A good agreement is found when the experimental E r profiles are compared to simulations carried out using the neoclassical codes, the drift kinetic equation solver (DKES) and kinetic orbit-averaging solver for stellarators (KNOSOS). The density fluctuation level decreases from the plasma edge toward the plasma core and the drop is more pronounced in the post-pellet enhanced confinement phase than in reference gas-fuelled plasmas. Besides, in the post-pellet phase, the density fluctuation level is lower in the high iota magnetic configuration than in the standard one. To determine whether this difference is related to the differences in the plasma profiles or to the stability properties of the two configurations, gyrokinetic simulations have been carried out using the codes stella and EUTERPE. The simulation results point to the plasma profile evolution after the pellet injection and the stabilization effect of the radial electric field profile as the dominant players in the stabilization of the plasma turbulence.

Parametric Simulation Studies on the Wave Propagation of Solar Radio Emission: The Source Size, Duration, and Position

Abstract The observed features of the radio source indicate that the waves of solar radio bursts are convoluted with complex propagation effects. In this work, we perform ray-tracing simulations on radio wave transport in the corona and interplanetary region with anisotropic electron density fluctuations. For the first time, the variation of the apparent source size, burst duration, and source position for the fundamental emission and harmonic emission at the frequency of 35 MHz are simulated as a function of the anisotropic parameter α and the angular scattering rate coefficient η = ϵ 2/h 0, where ϵ 2 = 〈δ n 2〉/n 2 is the density fluctuation level and h 0 is its correlation length near the wave excitation site. It is found that isotropic fluctuations produce a much larger decay time than a highly anisotropic fluctuation for fundamental emission. By comparing the observed duration and source size with the simulation results in the parameter space, we can estimate the scattering coefficient and the anisotropic parameter η = 8.9 × 10−5 km−1 and α = 0.719 with a point pulse source assumption. Position offsets due to wave scattering and refraction can produce the co-spatial of the fundamental and harmonic waves in the observation of some type III radio bursts. The visual speed due to the wave propagation effect can reach 1.5c for η = 2.4 × 10−4 km−1 and α = 0.2 for the fundamental emission in the sky plane, accompanied with large expansion rate of the source size. The direction of the visual speed is mostly identical to the direction of the offset, thus, for the observation aimed at obtaining the source position, the source centroid at the starting time is closer to the wave excitation site.

Effect of edge turbulent transport on scrape-off layer width on HL-2A tokamak

Effect of edge turbulent transport on scrape-off layer (SOL) width has been investigated in Ohmically heated L-mode plasma under limiter configurations on HL-2A tokamak. It has been found that SOL width is doubled when plasma current decreases about 20%. With larger plasma current, E × B shear is stronger and has greater suppression effect on edge turbulent transport. SOL width is larger when power of relative density fluctuation level in the edge region is larger. It is concluded that edge turbulent transport plays a significant role on SOL width. These experimental findings may provide a better understanding and controlling of power exhaust for present and future fusion devices.

LOFAR observations of radio burst source sizes and scattering in the solar corona

Low frequency radio wave scattering and refraction can have a dramatic effect on the observed size and position of radio sources in the solar corona. The scattering and refraction is thought to be due to fluctuations in electron density caused by turbulence. Hence, determining the true radio source size can provide information on the turbulence in coronal plasma. However, the lack of high spatial resolution radio interferometric observations at low frequencies, such as with the LOw Frequency ARray (LOFAR), has made it difficult to determine the true radio source size and level of radio wave scattering. Here we directly fit the visibilities of a LOFAR observation of a Type IIIb radio burst with an elliptical Gaussian to determine its source size and position. This circumvents the need to image the source and then de-convolve LOFAR’s point spread function, which can introduce spurious effects to the source size and shape. For a burst at 34.76 MHz, we find full width at half maximum (FWHM) heights along the major and minor axes to be 18.8′ ± 0.1′ and 10.2′ ± 0.1′, respectively, at a plane of sky heliocentric distance of 1.75 R⊙. Our results suggest that the level of density fluctuations in the solar corona is the main cause of the scattering of radio waves, resulting in large source sizes. However, the magnitude of ε may be smaller than what has been previously derived in observations of radio wave scattering in tied-array images.