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At least 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Imaging electron-density fluctuations by multidimensional X-ray photon-coincidence diffraction

The ultrafast spontaneous electron-density fluctuation dynamics in molecules is studied theoretically by off-resonant multiple X-ray diffraction events. The time- and wavevector-resolved photon-coincidence signals give an image of electron-density fluctuations expressed through the four-point correlation function of the charge density in momentum space. A Fourier transform of the signal provides a real-space image of the multipoint charge-density correlation functions, which reveal snapshots of the evolving electron density in between the diffraction events. The proposed technique is illustrated by ab initio simulations of the momentum- and real-space inelastic scattering signals from a linear cyanotetracetylene molecule.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Is it possible to deduce the ground state OH density from relative optical emission intensities of the OH(A 2 Σ + -X 2 Π i ) transition in atmospheric pressure non-equilibrium plasmas?—An analysis of self-absorption

The measurement of absolute densities of reactive species and radicals such as OH is of growing interest for many plasma applications. Here, we extend the use of a self-absorption model for atomic emission spectroscopy to molecular emission spectroscopy. The proposed analysis of self-absorbed molecular emission spectra is a simple and inexpensive method to determine OH(X) densities and rotational temperatures compared to laser induced fluorescence. We compare the recorded absolute OH density in a non-equilibrium diffuse atmospheric-pressure RF glow discharge by this method with broadband UV absorption considering a number of rotational lines with J' ≤ 6.5, the detection limit of the line integrated OH(X) density with this method is of the order of 2 × 10 19 m –2 . The accuracy of the density is sensitive to the rotational temperature of the OH(A) state and the non-equilibrium rotational population distribution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Atomic oxygen density determination in the effluent of the COST reference source using in situ effective lifetime measurements in the presence of a liquid interface

Abstract Spatially resolved, absolute densities of atomic oxygen are measured for several helium-based admixtures in the effluent of the COST Reference Microplasma Jet using two-photon absorption laser induced fluorescence (TALIF). Admixtures investigated include a helium-only admixture, four helium/oxygen admixtures (0.1 % , 0.5 % , 0.6 % , and 1.0 % oxygen), and a helium/water admixture (2500 ppm water), chosen to coincide with previously published characterizations of plasma-treated liquid. The atomic oxygen TALIF signal is calibrated for density using the noble gas xenon, which possesses a very similar two-photon excitation and fluorescence scheme. Measurements are conducted for the jet operating in ambient air with both an open effluent and a liquid surface present, allowing for comparison with liquid phase measurements conducted under similar conditions. The presence of a water surface does not appear to alter the background chemistry in the effluent but reduces O densities close to the liquid interface when compared to a similar distance from the nozzle in an open effluent case. This may be the result of a reduction in flow velocity caused by the liquid obstructing the gas flow. Additionally, measurements near the liquid surface revealed a region of atomic oxygen well outside of where the core of the effluent impinges on the liquid. This is likely relevant for applications as it considerably expands the surface area subject to O absorption. Critically, in situ measurements of the effective lifetimes of the laser-excited 3p 3 P J state of atomic oxygen were recorded in the effluent by employing a picosecond (ps) laser and a nanosecond (ns) ICCD. By experimentally determining the contribution from collisional quenching via the in situ effective lifetime measurements, significant improvements in the accuracy of the atomic oxygen density calibration were made, with differences of approximately 30 % from existing methods of estimating quenching rates at atmospheric pressure. Finally, spatially resolved atomic oxygen densities allow for an investigation of O formation and extinction pathways in the effluent and a comparison between admixtures.

laser diagnostics↗
DOE OSTI2024

Phase-field modeling of stored-energy-driven grain growth with intra-granular variation in dislocation density

Abstract We present a phase-field (PF) model to simulate the microstructure evolution occurring in polycrystalline materials with a variation in the intra-granular dislocation density. The model accounts for two mechanisms that lead to the grain boundary migration: the driving force due to capillarity and that due to the stored energy arising from a spatially varying dislocation density. In addition to the order parameters that distinguish regions occupied by different grains, we introduce dislocation density fields that describe spatial variation of the dislocation density. We assume that the dislocation density decays as a function of the distance the grain boundary has migrated. To demonstrate and parameterize the model, we simulate microstructure evolution in two dimensions, for which the initial microstructure is based on real-time experimental data. Additionally, we applied the model to study the effect of a cyclic heat treatment (CHT) on the microstructure evolution. Specifically, we simulated stored-energy-driven grain growth during three thermal cycles, as well as grain growth without stored energy that serves as a baseline for comparison. We showed that the microstructure evolution proceeded much faster when the stored energy was considered. A non-self-similar evolution was observed in this case, while a nearly self-similar evolution was found when the microstructure evolution is driven solely by capillarity. These results suggest a possible mechanism for the initiation of abnormal grain growth during CHT. Finally, we demonstrate an integrated experimental-computational workflow that utilizes the experimental measurements to inform the PF model and its parameterization, which provides a foundation for the development of future simulation tools capable of quantitative prediction of microstructure evolution during non-isothermal heat treatment.

Materials Science↗
DOE OSTI2021

Observation of quasi-coherent density fluctuation in scrape-off layer enhancing boundary transport in high-βN hybrid plasmas on DIII-D

In this work, we report the observation of a quasi-coherent density fluctuation (QCF) by the Doppler backscattering system in the scrape-off layer (SOL) region of the DIII-D tokamak. This QCF is observed in high power, high performance hybrid plasmas with near double-null divertor (DND) shape during the electron cyclotron heating period. This mode is correlated with a steepened SOL density profile, and leads to significantly elevated particle and heat fluxes between ELMs. The SOL QCF is a long-wavelength ion-scale fluctuation (k θ ρ s ≈0.2-0.4 and k r ρ s ≈0.03), and propagates in the ion diamagnetic direction in the plasma frame. Its radial expanse is about 1.5–2 cm, well beyond the typical width of heat flux λ q on DIII-D. Also, the SOL QCF does not show any clear dependence on the effective SOL collisionality, and thus may raise issues on the control of plasma-material interactions in low collisionality plasmas in which the blob-induced transport is reduced. A linear simulation using BOUT++ with a 5-field reduced model is performed and compared with experimental observations. In simulation results, an interchange-like density perturbation can be driven by the SOL density gradient, and its peak location and the radial width of the density perturbation are in agreement with the experimental observations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Strongly intermittent far scrape-off layer fluctuations in Alcator C-Mod plasmas close to the empirical discharge density limit

Abstract Intermittent plasma fluctuations in the boundary region of the Alcator C-Mod device were comprehensively investigated using data time-series from gas puff imaging and mirror Langmuir probe diagnostics. Fluctuations were sampled during stationary plasma conditions in ohmically heated, lower single null diverted configurations with scans in both line-averaged density and plasma current, with Greenwald density fractions up to 0.85. Utilizing a stochastic model, we describe the plasma fluctuations as a super-position of uncorrelated pulses, with large-amplitude events corresponding to blob-like filaments moving through the scrape-off layer (SOL). A deconvolution method is used to estimate the pulse arrival times and amplitudes. The analysis reveals a significant increase of pulse amplitudes and waiting times as the line-averaged density approaches the empirical discharge density limit. Broadened and flattened average radial profiles are thus accompanied by strongly intermittent and large-amplitude fluctuations. Although these filaments are arriving less frequently at high line-averaged densities, we show that there are significant increases in radial far-SOL particle and heat fluxes which will further enhance plasma–wall interactions. The stochastic model has been used as a framework for study of the scalings in the intermittency parameter, flux and mean amplitude and waiting times, and is being used to inform predictive capability for the effects of filamentary transport as a function of Greenwald fraction.

Physics↗
DOE OSTI2025

Investigation of divertor detachment induced through neon seeding and density ramp on HL-3

A new self-consistent 1D scrape-off layer model has been recently developed in BOUT++ framework, named SD1D, which includes equations for various particle species (e.g. main plasma, neutrals and impurities) and couples open databases like ADAS and AMJUEL. It is able to quickly and effectively simulate divertor detachment experiments. In this work, a typical detachment experiment (shot #6270) on HL-3 with neon seeding is simulated using the SD1D code. It is found that the target electron temperature and the target ion saturation current in the simulations are consistent with experimental results measured by Langmuir probes on the target plate. The variation of D α radiation intensity in the divertor is qualitatively similar to the measured D α signal. Following the experimental validations, different upstream densities are set in the simulations to study the impurity distribution under different plasma density conditions. It is found that increasing upstream density can be helpful for the control of the neon radiation front (closer to the target). In this work we also compare two detachment regimes in simulations. Based on the same initial experimental parameters (shot #6270) on HL-3, a scan of upstream density and a scan of neon seeding rate are carried out respectively. It is found that the role of atomic and molecular processes is different in the two detachment regimes. The current density roll-over is ascribed to a drop in the divertor ion source, and the variation of D α radiation intensity via different excitation channels is associated with the relevant collisional reaction sources.

BOUT++↗
DOE OSTI2025

Development of a wide bandwidth heterodyne dispersion interferometer for electron density measurement of atmospheric pressure plasmas

One of the challenges of electron density measurements of an atmospheric pressure plasma (APP) with a laser interferometer is the significant and unwanted phase shift caused by changes in the neutral gas density. These unwanted phase shifts can be mitigated and plasma density measured using an interferometer architecture called a dispersion interferometer (DI). A DI is composed of two nonlinear orientation patterned GaAs crystals for frequency doubling and measures the phase shift induced by a plasma in the interference signal between two second-harmonic beams. Measurement of plasma dynamics or a short plasma pulse in less than a millisecond is enabled with heterodyne detection in a DI using an acousto-optic cell with a frequency of 40 MHz. This heterodyne DI (HDI) is targeted to measure APPs in an electron density range of 10 20 –10 24 m −3 . Finally, the HDI achieves a line-integrated density resolution of 2 × 10 15 m −2 (a phase resolution of 0.005°) with a time constant of 1 μs using ensemble averaging techniques.

atmospheric pressure plasma↗
DOE OSTI2026

Fluid-kinetic modeling of a high power density radio frequency inductively coupled positive hydrogen ion source

High power density radio-frequency (RF) inductively coupled positive ion sources are attractive candidates for next-generation neutral beam injection (NBI) systems, where higher injected power and longer pulse lengths are desired without sacrificing source reliability. Operating at absorbed power densities of order $\gt 1~\mathrm{W\,cm}^{-3}$ places these sources in a regime with stronger gas heating, higher dissociation, and non-Maxwellian electron energy distributions. The Large Uniform Plasma for Ionizing Neutrals (LUPIN) is an RF inductively coupled plasma source designed to explore this high power density regime and to provide guidance for a positive ion source upgrade for the DIII-D NBI system. LUPIN is designed to operate at up to 20 kW of RF power at 2 MHz, coupling energy through a cylindrical quartz vessel to achieve target ion current densities of $2100\,\mathrm{A\,m}^{-2}$ . This paper presents fluid-kinetic modeling of LUPIN using the hybrid plasma equipment model where electrons are treated kinetically, and the simulations reveal that electron energy distribution function transitions from nearly Maxwellian in the core to bi-Maxwellian towards the edge. Parametric simulations investigate the effects of RF power, gas pressure, and frequency on plasma density, ion flux, and uniformity. Parametric sweeps reveal that increasing power shifts the primary ionization channel from molecular to atomic with diminishing flux gains due to skin-depth contraction and gas rarefaction. Higher frequency localizes heating and increases $\mathrm{H}_2^+$ and $\mathrm{H}_3^+$ delivery to the grid, while elevated pressure boosts ionization yet hinders ion transport due to increase in collisionality.

inductively coupled plasma↗
DOE OSTI2018

Simulation of density fluctuations before the L-H transition for Hydrogen and Deuterium plasmas in the DIII-D tokamak using the BOUT++ code

A six-field two-fluid model has been used to simulate density fluctuations. The equilibrium is generated by experimental measurements for both Deuterium (D) and Hydrogen (H) plasmas at the lowest densities of DIII-D low to high confinement (L-H) transition experiments. In linear simulations, the unstable modes are found to be resistive ballooning modes with the most unstable mode number n=30 or $k_\theta\rho_i\sim0.12$ . The ion diamagnetic drift and $E\times B$ convection flow are balanced when the radial electric field (E r ) is calculated from the pressure profile without net flow. The curvature drift plays an important role in this stage. Two poloidally counter propagating modes are found in the nonlinear simulation of the D plasma at electron density $n_e\sim1.5\times10^{19}$ m -3 near the separatrix while a single ion mode is found in the H plasma at the similar lower density, which are consistent with the experimental results measured by the beam emission spectroscopy (BES) diagnostic on the DIII-D tokamak. The frequency of the electron modes and the ion modes are about 40kHz and 10 kHz respectively. The poloidal wave number $k_\theta$ is about 0.2 cm -1 ($k_\theta\rho_i\sim0.05$ ) for both ion and electron modes. The particle flux, ion and electron heat fluxes are~3.5–6 times larger for the H plasma than the D plasma, which makes it harder to achieve H-mode for the same heating power. The change of the atomic mass number A from 2 to 1 using D plasma equilibrium make little difference on the flux. Increase the electric field will suppress the density fluctuation. In conclusion, the electric field scan and ion mass scan results show that the dual-mode results primarily from differences in the profiles rather than the ion mass.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Investigation into the formation of the scrape-off layer density shoulder in JET ITER-like wall L-mode and H-mode plasmas

The low temperature boundary layer plasma (scrape-off layer or SOL) between the hot core and the surrounding vessel determines the level of power loading, erosion and implantation of material surfaces, and thus the viability of tokamak-based fusion as an energy source. Here, this study explores mechanisms affecting the formation of flattened density profiles, so-called 'density shoulders', in the low-field side (LFS) SOL, which modify ion and neutral fluxes to surfaces—and subsequent erosion. There is evidence against local enhancement of ionization inducing shoulder formation. We find that increases in SOL parallel resistivity, Λ div (=[ L || ν ei Ω i ]/ c s Ω e ), postulated to lead to shoulder growth through changes in SOL turbulence characteristics, correlates with increases in SOL shoulder amplitude, A s , but only under a subset of conditions (D 2 -fuelled L-mode density scans with outer strike point on the horizontal target). Λ div fails to correlate with A s for cases of N 2 seeding or during sweeping of the strike point across the horizontal target. The limited correlation of Λ div and A s is also found for H-mode discharges. Thus, while it may be necessary for Λ div to be above a threshold of ~1 for shoulder formation and/or growth, another mechanism is required. More significantly, we find that in contrast to parallel resistivity, outer divertor recycling, as quantified by the total outer divertor Balmer D α emission, I – D α , does scale with A s where Λ div does and even where Λ div does not. Divertor recycling could lead to SOL density shoulder formation through: (a) reducing the parallel to the field flow (loss) of ions out of the SOL to the divertor; and (b) changes in radial electric fields which lead to E × B poloidal flows as well as potentially affecting SOL turbulence birth characteristics. Therefore, changes in divertor recycling may be the sole process involved in bringing about SOL density shoulders or it may be that it acts in tandem with parallel resistivity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Experimental evidence of lower hybrid wave scattering in Alcator C-Mod due to scrape off layer density fluctuations

Novel experimental measurements of the lower hybrid (LH) wave electric field vector, E LH , obtained in Alcator C-Mod using dynamic Stark spectroscopy are presented. Three key results were obtained by comparison with 3D full-wave COMSOL simulations using the cold plasma dielectric tensor and reflectometry-measured density profiles. (1) As a function of space and LH power, the magnitude of E LH was found to agree with the full-wave simulation result. (2) The direction of E LH was found to have a substantial poloidal component and is in strong disagreement with the nearly radial full-wave simulation result. (3) The addition of scrape off layer density fluctuations to the density profile implemented in the full-wave simulations can be used to explain the E LH direction discrepancy. It is concluded that diffraction and scattering by turbulence-driven scrape off layer density fluctuations is the responsible mechanism behind the modification in the direction of E LH . Furthermore, these results further support the previously reported proposition that edge turbulence is an important mechanism behind the strong anomalous drop in LH current drive efficiency for diverted plasmas in the high-density regime.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Disentanglement of density and rotation dependences of the field penetration threshold on the J-TEXT tokamak

The field penetration threshold of magnetic perturbations has been observed to vary non-monotonically with an increase of density in ohmic plasmas on the J-TEXT tokamak. This observation appears contradicting the previous empirical density scaling law. Disentanglement of plasma density and rotation dependences of the field penetration threshold has been carried out. It shows that the field penetration threshold depends only weakly on the density but linearly on the plasma rotation. This result is not only important for the prediction of error field tolerance in fusion devices, but also opens a question on the role of density in the forced magnetic reconnection process in magnetized plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Overview of density pedestal structure: Role fueling versus transport

How much of the density pedestal structure profile is determined by fueling versus transport is still a valid question. In most current tokamaks, the Scrape-Off Layer is not opaque enough to screen the neutrals and limit their penetration past the separatrix. As such recycled neutrals as well as additional gas puffing can directly affect the pedestal structure through ionization. Yet, in ITER and other future burning plasma magnetic confinement devices, this ionization source will be pushed further out into the Scrape-Off Layer. This poses the question, how much of the pedestal density structure is governed by this edge ionization source versus plasma transport effects. Theoretically, several turbulent modes have been identified which could provide a 'pinch' like up-gradient transport mechanism. Up-gradient transport is necessary in a source-free region to obtain a peaked density profile, which is often observed in the core of tokamaks. In an opaque Scrape-Off Layer, without the existence of such a pinch, the pedestal density structure would eventually disappear. Not only would this limit our ability to fuel a fusion reactor, it would also affect the pedestal stability. In this paper we will give an overview of the state of the art on what sets the pedestal density structure based on experimental observations as well as theoretical models. We will complement these studies with new results from Alcator C-Mod and DIII-D where the opaqueness is increased to reach values similar to those in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Density and temperature profiles after low-Z and high-Z shattered pellet injections on DIII-D

Abstract In this work we utilize the recently upgraded Thomson scattering diagnostic to resolve density and temperature plasma profiles after pure deuterium and mixed neon/deuterium shattered pellet injections (SPIs) on DIII-D. This allows us to study individual components of the staggered scheme proposed for disruption mitigation on ITER, consisting of a low-Z material SPI followed by a delayed high-Z SPI. Obtained spatio-temporal density profiles exhibit very different dynamics after dominantly neon and pure deuterium SPIs. The neon SPI causes a fast radiative plasma collapse in a few milliseconds and results in almost flat density profile once the impurity mixes with the plasma during and after the thermal quench (TQ). The deuterium SPI leads to a disruption delayed by ten and more milliseconds, but very limited core fueling can be observed before the disruption. Even during and after the TQ, the edge deuterium density significantly exceeds the core density. 1D transport modeling suggests that this poor core fueling can be explained by strong outward grad-B-induced drift of the injected deuterium. Preliminary simulations show that larger pellet shards and greater injected quantity can be used to improve the penetration of the low-Z material into the core. These results call for optimization and further evaluation of the staggered SPI on ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Achievement of a high-density, high-confinement, and high-beta tokamak plasma regime in DIII-D, and implications for a lower-current path for ITER and FPP

Experiments on DIII-D have demonstrated a density-confinement synergy that enables sustainment of high performance in a previously unattained parameter regime of simultaneous very high energy confinement quality (H 98y2 ≥ 1.5), very high line-average density Greenwald fraction (ƒ Gr = πa 2 < n >/I P ≥ 1.4), and high toroidal beta (β T ≥ 3%). Tokamak operation in this regime is essential for a compact steady-state FPP, as well as for Q=10 with 500 MW of fusion power in ITER at I P << 15 MA. These experiments leveraged the knowledge that, in the high-poloidal-beta (β P ) regime, impurity and density gradients can enhance turbulence stabilization caused by high α MHD (α MHD ~(dβ P )⁄dr). This was described by theoretical predictions and gyrokinetic transport simulations [M.T. Kotschenreuther et al, 2024 Nucl. Fusion, 64 076033], and later confirmed by experiments on DIII-D [S. Ding et al, 2024 Nature 629 555]. To increase both β P and β T , the new experiments increased the ideal-wall stability β N -limit by using a smaller plasma-outer wall distance and higher triangularity in the plasma cross section (top/bottom average δ~0.9), enabled by the recent “shape & volume rise” (SVR) modification to the DIII-D divertor. The higher triangularity also contributed to achieving higher ƒ Gr by enabling higher pedestal density. At high density, the pedestal is ballooning limited and exhibits small and frequent ELMs, while the divertor is near detachment even without any impurity seeding. High plasma performance was attained and sustained reproducibly, with the eventual terminations brought about by an MHD mode destabilized as the current profile slowly continued to evolve. A path to stationary fully noninductive operation might include ECH injection to reduce both core impurity accumulation and the electron collisionality, thus increasing the bootstrap current. These experiments provide the first experimental demonstration of the ƒ Gr , H 98y2 , and β T values required simultaneously for ITER Q = 10 at I P < 10 MA, pointing to practical ways to improve the energy confinement in a fusion reactor.

Garofalo, Andrea M. [General Atomics, San Diego, C↗
DOE OSTI2022

Fast wave interferometer for ion density measurement on DIII-D

=A fast wave interferometer (FWI), which can measure ion mass density, has been developed on DIII-D for its use on future fusion reactors, as well as for the study of ion behavior in current plasma devices. The frequency of the fast waves used for the FWI is around 60 MHz, and require antennas and coaxial cables or waveguides, which, unlike traditional mirror-based optical interferometers, are less susceptible to neutron/gamma-ray radiation and are relatively immune to impurity deposition and erosion as well as alignment issues. The bulk ion density evaluated using FWI show good agreement with that derived from CO 2 interferometry within about 15%. When the ion mass density measurement by FWI is combined with an electron density measurement from CO 2 interferometry, Z eff measurements are also enabled and are in agreement with those from visible Bremsstrahlung measurements. Additionally, large-bandwidth FWI measurements clearly resolve 10–100 kHz coherent modes and demonstrate its potential as a core fluctuation diagnostic, sensitive to both magnetic and ion density perturbations.

Instruments & Instrumentation↗
DOE OSTI2021

A multishock model for the density variance of anisotropic, highly magnetized, supersonic turbulence

ABSTRACT Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $\sigma ^2_{\rho /\rho _0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parametrizes the star formation (SF) rate of a cloud. However, models for $\sigma ^2_{\rho /\rho _0}$ all share a common feature – the variance is assumed to be isotropic. This assumption does not hold when a trans-/sub-Alfvénic mean magnetic field, ${B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $\sigma _{\rho /\rho _0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $\sigma _{\rho /\rho _0}^2$ in the high Mach number $(\mathcal {M})$ limit as small-scale density fluctuations become suppressed by the strong ${B}_0$. The model reduces to the isotropic $\sigma _{\rho /\rho _0}^2\!-\!\mathcal {M}$ relation in the hydrodynamical limit. To validate our model, we calculate $\sigma _{\rho /\rho _0}^2$ from 12 high-resolution, three-dimensional, supersonic, sub-Alfvénic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented overdensities observed in some MCs and the implications for SF theory in the presence of a sub-Alfvénic ${B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.

Beattie, James R.↗