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At least 1,747 records · Page 97
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Asymmetric explosion of clusters in intense laser fields

We examine asymmetric expansion of argon clusters illuminated by 800 nm laser pulses of duration Almost-Equal-To 23fs, using three-dimensional particle-in-cell (PIC) simulation. For this short pulse duration, laser energy absorption by cluster electrons is dominated by the nonlinear resonance (NLR) absorption process [Phys. Rev. Lett. 96, 123401 (2006)]. In this work, we concentrate, particularly, on the ionic outcome in the NLR regime and show that higher charge states of argon ions are produced along the laser polarization than in the transverse directions leading to the anisotropy (asymmetry) in the ion energy distribution. This anisotropy already established during the short pulse duration (or in the early duration of a long pulse) may contribute to the anisotropic ion emission reported in cluster experiments with pulse duration longer than 100 fs. Our PIC results are compared with a charged-sphere model showing that cluster explosion is mainly due to Coulomb repulsion between the cluster ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A divergence-free constrained magnetic field interpolation method for scattered data

An interpolation method to evaluate magnetic fields, given its unstructured and scattered magnetic data, is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The coefficients of the expansion are obtained by minimizing a cost function defined as the L2 norm of the difference between the ground truth and the reconstructed magnetic field evaluated on the training data. The divergence-free condition is incorporated as a constraint in the cost function, allowing the method to achieve arbitrarily small errors in the magnetic field divergence. An exponential decay of the approximation error is observed and compared with the less favorable algebraic decay of local splines. Compared to local methods involving computationally expensive search algorithms, the proposed method exhibits a significant reduction of the computational complexity of the field evaluation, while maintaining a small error in the divergence even in the presence of magnetic islands and stochasticity. Finally, applications to the computation of Poincaré sections using data obtained from numerical solutions of the magnetohydrodynamic equations in toroidal geometry are presented and compared with local methods currently in use.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Monte Carlo Perturbation Theory Estimates of Sensitivities to System Dimensions

Here, Monte Carlo methods are developed using adjoint-based perturbation theory and the differential operator method to compute the sensitivities of the k-eigenvalue, linear functions of the flux (reaction rates), and bilinear functions of the forward and adjoint flux (kinetics parameters) to system dimensions for uniform expansions or contractions. The calculation of sensitivities to system dimensions requires computing scattering and fission sources at material interfaces using collisions occurring at the interface—which is a set of events with infinitesimal probability. Kernel density estimators are used to estimate the source at interfaces using collisions occurring near the interface. The methods for computing sensitivities of linear and bilinear ratios are derived using the differential operator method and adjoint-based perturbation theory and are shown to be equivalent to methods previously developed using a collision history–based approach. The methods for determining sensitivities to system dimensions are tested on a series of fast, intermediate, and thermal critical benchmarks as well as a pressurized water reactor benchmark problem with iterated fission probability used for adjoint-weighting. The estimators are shown to agree within 5% and 3σ of reference solutions obtained using direct perturbations with central differences for the majority of test problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

The QCD Equation of state and critical end-point estimates at O ( μ B 6 )

Here, we present results for the QCD Equation of State at non-zero chemical potentials corresponding to the conserved charges in QCD using Taylor expansion upto sixth order in the baryon number, electric charge and strangeness chemical potentials. The latter two are constrained by the strangeness neutrality and a fixed electric charge to baryon number ratio. In our calculations, we use the Highly Improved Staggered Quarks (HISQ) discretization scheme at physical quark masses and at different values of the lattice spacings to control lattice cut-off effects. Furthermore we calculate the pressure along lines of constant energy density, which serve as proxies for the freeze-out conditions and discuss their dependence on μ Β , which is necessary for hydrodynamic modelling near freezeout. We also provide an estimate of the radius of convergence of the Taylor series from the 6th order coefficients which provides a new constraint on the location of the critical end-point in the T-μ Β plane of the QCD phase diagram.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Precision Plasmonics with Monomers and Dimers of Spherical Gold Nanoparticles: Nonequilibrium Dynamics at the Time and Space Limits

Monomers and dimers of spherical gold nanoparticles (NPs) exhibit highly uniform plasmonic properties at the single-particle level due to their high structural homogeneity (precision plasmonics). Recent investigations in precision plasmonics have largely focused on static properties using conventional techniques such as transmission electron microscopy and optical dark-field microscopy. Here in this Feature Article, we first highlight the application of femtosecond time-resolved electron diffraction for monitoring the nonequilibrium dynamics of spherical gold NPs after ultrafast optical excitation. The analysis of the transient diffraction patterns allows us to directly obtain quantitative information on the incoherent excitation of the lattice, that is, heating upon electron–lattice equilibration, as well as on the development of strain due to lattice expansion on picosecond time scales. The controlled assembly of two spherical gold NPs into a dimer with a few nanometers gap leads to unique optical properties. Specifically, extremely high electric fields (hot spot) in the gap are generated upon resonant optical excitation. Conventional optical microscopy cannot spatially resolve this unique hot spot due to the optical diffraction limit. We therefore employed nonlinear photoemission electron microscopy to visualize hot spots in single dimers of spherical gold NPs. A quantitative comparison of different single dimers confirms the homogeneity of the hot spots on the single-particle level. Finally, overall, these initial results are highly encouraging because they pave the way to investigate nonequilibrium dynamics in highly uniform plasmonic nanostructures at the time and space limits.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2012

The First in situ Observation of Kelvin-Helmholtz Waves at High-Latitude Magnetopause during Strongly Dawnward Interplanetary Magnetic Field Conditions

We report the first in situ observation of high-latitude magnetopause (near the northern duskward cusp) Kelvin-Helmholtz waves (KHW) by Cluster on January 12, 2003, under strongly dawnward interplanetary magnetic field (IMF) conditions. The fluctuations unstable to Kelvin-Helmholtz instability (KHI) are found to propagate mostly tailward, i.e., along the direction almost 90 deg. to both the magnetosheath and geomagnetic fields, which lowers the threshold of the KHI. The magnetic configuration across the boundary layer near the northern duskward cusp region during dawnward IMF is similar to that in the low-latitude boundary layer under northward IMF, in that (1) both magnetosheath and magnetospheric fields across the local boundary layer constitute the lowest magnetic shear and (2) the tailward propagation of the KHW is perpendicular to both fields. Approximately 3-hour-long periods of the KHW during dawnward IMF are followed by the rapid expansion of the dayside magnetosphere associated with the passage of an IMF discontinuity that characterizes an abrupt change in IMF cone angle, Phi = acos (B(sub x) / absolute value of Beta), from approx. 90 to approx. 10. Cluster, which was on its outbound trajectory, continued observing the boundary waves at the northern evening-side magnetopause during sunward IMF conditions following the passage of the IMF discontinuity. By comparing the signatures of boundary fluctuations before and after the IMF discontinuity, we report that the frequencies of the most unstable KH modes increased after the discontinuity passed. This result demonstrates that differences in IMF orientations (especially in f) are associated with the properties of KHW at the high-latitude magnetopause due to variations in thickness of the boundary layer, and/or width of the KH-unstable band on the surface of the dayside magnetopause.

solar wind↗
DOE OSTI2016

Recombination-enhanced surface expansion of clusters in intense soft x-ray laser pulses

Here, we studied the nanoplasma formation and explosion dynamics of single large xenon clusters in ultrashort, intense x-ray free-electron laser pulses via ion spectroscopy. The simultaneous measurement of single-shot diffraction images enabled a single-cluster analysis that is free from any averaging over the cluster size and laser intensity distributions. The measured charge state-resolved ion energy spectra show narrow distributions with peak positions that scale linearly with final ion charge state. These two distinct signatures are attributed to highly efficient recombination that eventually leads to the dominant formation of neutral atoms in the cluster. The measured mean ion energies exceed the value expected without recombination by more than an order of magnitude, indicating that the energy release resulting from electron-ion recombination constitutes a previously unnoticed nanoplasma heating process. This conclusion is supported by results from semiclassical molecular dynamics simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Broadband coherent XUV light from e − / e + microbunching in an intense laser pulse

Attosecond pulses of coherent extreme ultraviolet (XUV) light are instrumental for investigating subatomic dynamics and can be produced using a free-electron laser (FEL). It has been suggested that an optical FEL, which employs a laser pulse in place of a conventional undulator, could enable a dramatically more compact implementation of such a light source. Yet, the high electron density and subsequent high emittance implied by an optical FEL makes this concept challenging to realize with an electron beam. There has been impressive progress in recent years producing collimated dense and relativistic beams of electrons and positrons in the laboratory. As we demonstrate here, the inherent stability of a quasi-neutral electron-positron beam mitigates Coulomb expansion, and renders it a promising alternative source of coherent light. Specifically, we show via computer simulations that broadband coherent light in the XUV domain, which takes the form of 8-as pulses at 92-as intervals, can be generated by microbunching of relativistic electrons and positrons in a laser pulse. This process occurs over a sub-millimeter length scale, enabling the development of light sources which are orders-of-magnitude more compact than existing sources, with potential applications in physics, chemistry, biology, and industry.

47 OTHER INSTRUMENTATION↗
DOE OSTI2017

The effects of convergence ratio on the implosion behavior of DT layered inertial confinement fusion capsules

The wetted foam capsule design for inertial confinement fusion capsules, which includes a foam layer wetted with deuterium-tritium liquid, enables layered capsule implosions with a wide range of hot-spot convergence ratios (CR) on the National Ignition Facility. In this paper, we present a full-scale wetted foam capsule design that demonstrates high gain in one-dimensional simulations. In these simulations, increasing the convergence ratio leads to an improved capsule yield due to higher hot-spot temperatures and increased fuel areal density. High-resolution two-dimensional simulations of this design are presented with detailed and well resolved models for the capsule fill tube, support tent, surface roughness, and predicted asymmetries in the x-ray drive. Our modeling of these asymmetries is validated by comparisons with available experimental data. In 2D simulations of the full-scale wetted foam capsule design, jetting caused by the fill tube is prevented by the expansion of the tungsten-doped shell layer due to preheat. While the impacts of surface roughness and predicted asymmetries in the x-ray drive are enhanced by convergence effects, likely underpredicted in 2D at high CR, simulations predict that the capsule is robust to these features. Nevertheless, the design is highly susceptible to the effects of the capsule support tent, which negates all of the one-dimensional benefits of increasing the convergence ratio. Indeed, when the support tent is included in simulations, the yield decreases as the convergence ratio is increased for CR > 20. Finally and nevertheless, the results suggest that the full-scale wetted foam design has the potential to outperform ice layer capsules given currently achievable levels of asymmetries when fielded at low convergence ratios (CR < 20).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Viscous anisotropic hydrodynamics for the Gubser flow

In this work we describe the dynamics of a highly anisotropic system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion (Gubser flow) for arbitrary shear viscosity to entropy density ratio. We derive the equations of motion of dissipative anisotropic hydrodynamics by applying to this situation the moments method recently derived by Moln´ar et al. (MNR) [1, 2], based on an expansion around an arbitrary anisotropic one-particle distribution function. One requires an additional evolution equation in order to close the conservation laws. This is achieved by selecting the relaxation equation for the longitudinal pressure with a suitable Landau matching condition. As a result one obtains two coupled differential equations for the energy density and the longitudinal pressure which respect the SO (3)q Ⓧ SO (1, 1) Ⓧ Z 2 symmetry of the Gubser flow in the deSitter space. These equations are solved numerically and compared with the predictions of the recently found exact solution of the relaxation-time-approximation Boltzmann equation subject to the same flow. We also compare our numerical results with other fluid dynamical models. As a result we observe that the MNR description of anisotropic fluid dynamics reproduces the space-time evolution of the system than all other currently known hydrodynamical approaches.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Analysis of the dispersion relation for resistive wall modes in tokamaks with account of the skin effect

The accuracy of the dispersion relations derived earlier analytically for the resistive wall modes (RWMs) in tokamaks is evaluated. Existing models use the expansions in the ratio of the wall thickness d{sub w} to the skin depth s. This parameter is small in the standard theory of 'slow' RWMs, but it is large in the recently developed approach for the 'fast' RWMs. Here, a dispersion relation applicable not only to these extreme cases, but also to the intermediate range is derived in the single-mode cylindrical approximation without restrictions on s/d{sub w}. The derived equation is solved numerically, the result is compared with the predictions of the earlier analytical models with either s Much-Greater-Than d{sub w} or s Much-Less-Than d{sub w}. The applicability limits of the asymptotic expressions for the RWM growth rate are clarified. In particular, the limits are specified in which their error does not exceed 10%. It is shown that these expressions always underestimate the growth rate. The study confirms the necessity of the skin effect incorporation in the description of RWM dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

A GLOBAL GALACTIC DYNAMO WITH A CORONA CONSTRAINED BY RELATIVE HELICITY

We present a model for a global axisymmetric turbulent dynamo operating in a galaxy with a corona that treats the parameters of turbulence driven by supernovae and by magneto-rotational instability under a common formalism. The nonlinear quenching of the dynamo is alleviated by the inclusion of small-scale advective and diffusive magnetic helicity fluxes, which allow the gauge-invariant magnetic helicity to be transferred outside the disk and consequently to build up a corona during the course of dynamo action. The time-dependent dynamo equations are expressed in a separable form and solved through an eigenvector expansion constructed using the steady-state solutions of the dynamo equation. The parametric evolution of the dynamo solution allows us to estimate the final structure of the global magnetic field and the saturated value of the turbulence parameter α{sub m}, even before solving the dynamical equations for evolution of magnetic fields in the disk and the corona, along with α-quenching. We then solve these equations simultaneously to study the saturation of the large-scale magnetic field, its dependence on the small-scale magnetic helicity fluxes, and the corresponding evolution of the force-free field in the corona. The quadrupolar large-scale magnetic field in the disk is found to reach equipartition strength within a timescale of 1 Gyr. The large-scale magnetic field in the corona obtained is much weaker than the field inside the disk and has only a weak impact on the dynamo operation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Examining Graphite Degradation in Molten Salt Environments: A Chemical, Physical, and Material Analysis

Molten-salt reactors (MSRs) are Generation IV nuclear reactors that use liquid salt as a coolant and/or fuel. In several MSR designs, graphite serves as a moderator and/or reflector. However, due to limited experimental data and operational experience, our understanding of graphite behavior in molten salt environments remains incomplete. This report aims to identify the degradation mechanisms of nuclear graphite in MSRs, detail the mechanisms of each factor, and provide an initial assessment of their impact on the structural integrity of graphite components. This assessment is based on an extensive literature review and insights from subject matter experts. Furthermore, given the limited data, a modeling strategy using existing Grizzly software is proposed for a more thorough analysis where appropriate. Additionally, it presents mitigation strategies where applicable. The report covers physical degradation mechanisms such as infiltration, erosion, and abrasion, as well as chemical degradation mechanisms including fluorination, intercalation, corrosion, and oxidation. Molten salt can infiltrate the porous structure of graphite, leading to several detrimental effects. Entrapment of fissile products within the graphite pores can cause radiation damage and could pose challenges in the handling and disposal of contaminated components. The differential thermal expansion between the infiltrated salt and graphite, along with internal stress from pressurized molten salt and volumetric heating, can compromise the structural integrity of graphite. To mitigate these effects, employing ultra-fine graphite grades and applying sealants and coatings are effective strategies. A computational model based on coupled solid mechanics and heat transfer phenomena could be used to predict the internal stresses using Grizzly software. In pebble-bed MSRs, graphite fuel pebbles can cause abrasion against reactor components due to friction and wear. The severity of wear is influenced by various factors such as temperature, environment, and the presence of lubricants. Tribological studies reveal that higher temperatures and molten salt environments, such as FLiBe, significantly reduce wear rates compared to dry conditions. Additionally, the chemical composition of the salt can further optimize graphite's tribological performance. Long-term wear effects can be modeled by incorporating surface defects into the geometry and predict stresses under thermal and radiation effects using Grizzly software. Chemical degradation of graphite in a molten salt environment can occur through fluorination and intercalation. Fluorination can occur via replacement of hydrogen or oxygen atoms, or at the active sites, but does not cause structural degradation. Intercalation, on the other hand, can lead to exfoliation, where layers of graphite separate and peel away, damaging the graphite. Protective coatings can enhance graphite's resistance to intercalation. Graphite generally exhibits good chemical stability in molten salt environments, though it can corrode under specific conditions, particularly in the presence of impurities or oxidants. Studies have shown that protective coatings, such as plasma-sprayed partially stabilized zirconia (PSZ), can effectively prevent such degradation. Corrosion behavior varies significantly with different graphite grades and coating applications, underscoring the need for detailed studies on uncoated and coated graphite to understand and mitigate corrosion mechanisms in MSRs. Research indicates that the presence of oxidants and impurities can accelerate graphite degradation in molten salts, making it essential to explore acceptable impurity limits. Oxidation is another critical degradation mechanism, leading to weight loss and structural damage due to the formation of CO and CO 2 from the reaction of carbon atoms with oxygen. This process creates new porosity and compromises graphite's integrity. While extensive research on graphite oxidation has been conducted for gas-cooled reactors, studies specific to MSRs are limited. Findings from the coal industry suggest that molten alkali metal salts can significantly accelerate graphite oxidation, a hypothesis worth exploring for fluoride salts in MSRs. Understanding oxidation behavior in MSRs is vital for developing protective measures. The analysis of post-irradiated graphite from the MSRE experiment demonstrated exceptional chemical compatibility with molten fluoride salt, suggesting that the extent of chemical attack on graphite largely depends on the salt's infiltration capability. Therefore, the use of ultra-fine grade graphite could help mitigate chemical degradation effects. Existing oxidation modeling capabilities in Grizzly, which use reaction-diffusion equations to model graphite-air interactions, could be adapted to simulate the chemical degradation effects of graphite in molten salt environments.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1999

Some Peculiar Properties of Magnetic Clouds as Observed by the WIND Spacecraft

We aimed at understanding the common characteristics of magnetic clouds, relevant to solar-interplanetary connections, but exceptional ones were noted and are stressed here through a short compendium. The study is based on analyses of 28 good or better events (Out of 33 candidates) as identified in WIND magnetic field and plasma data. These cloud intervals are provided by WIND-MFI's Website under the URL (http://lepmfi.gsfc.nasa.gov/mfi/mag_cloud_publ.html#table). The period covered is from early 1995 to November 1998. A force free, cylindrically symmetric, magnetic field model has been applied to the field data in usually 1-hour averaged form for the cloud analyses. Some of the findings are: (1) one small duration event turned out to have an approximately normal size which was due to a distant almost "skimming" passage by the spacecraft; (2) One truly small event was observed, where 10 min averages had to be used in the model fitting; it had an excellent model fit and the usual properties of a magnetic cloud, except it possessed a small axial magnetic flux; (3) One cloud ha a dual axial-field-polarity, in the sense that the "core" had one polarity and the annular region around it had an opposite polarity. This event also satisfied the model and with a ve3ry good chi-squared value. Some others show a hint of this dual polarity; (4) The temporal distribution of occurrence clouds over the 4 years show a dip in 1996; (5) About 50 % of the clouds had upstream shocks; any others had upstream pressure pulses; (6) The overall average speed (390 km/s) of the best 28 events is less than the normally quoted for the average solar wind speed (420 km/s) The average of central cloud speed to the upstream solar wind speed was not much greater than one (1.08), even though many of these clouds were drivers of interplanetary shocks. Cloud expansion is partly the reason for the existence of upstream shocks; (7) The cloud axes often (about 50 % of the time) revealed reasonable attitudes with respect to the interpreted solar source, from simple geometry, but many bore no relationship, suggesting that their observations at 1 AU were probably those of the legs of the global cloud often having near-radial axes; (8) many clouds appear to have magnetic holes at or their their boundaries.

Berdichevsky, D.↗
NASA NTRS2026

Advances in Entry Systems Modeling: Modeling Summer Visit 2025 Technical Reports

This NASA Technical Memorandum presents the collective work carried out during the Modeling Summer Visit (MSV) 2025, a collaborative research program between NASA Ames Research Center and three leading European research institutions: the University of Bordeaux, the von Karman Institute (VKI), and Ecole Polytechnique. Held from July 7th to August 1st, 2025, the NASA ARC MSV program brought together 42 researchers from Europe to work alongside NASA staff on 22 projects in entry systems modeling. The program was organized by Bruno Dias, Sergio Fraile-Izquierdo, and Jeremie Meurisse from Analytical Mechanics Associates, Inc., in collaboration with Marc Massot (Ecole Polytechnique), Jean Lachaud (University of Bordeaux), and Thierry Magin (VKI). The MSV program traces its origins to an initiative started by Nagi N. Mansour in 2018, with this 2025 edition representing a consolidation and expansion of that original vision. The projects were organized into six thematic groups: Porous Media, Numerical Methods, Plasma/Rarefied Methods, Experimental Reconstruction, Flow and Material Coupling Methods, and Transition and High-Speed Flows. Throughout the four-week program, participants presented their work in three public presentations (July 7th, July 21st, and August 1st), allowing for continuous feedback and discussion of their evolving research.

Plasmas↗
DOE OSTI2016

Hydrodynamic model for expansion and collisional relaxation of x-ray laser-excited multi-component nanoplasma

The irradiation of an atomic cluster with a femtosecond x-ray free-electron laser pulse results in a nanoplasma formation. This typically occurs within a few hundred femtoseconds. By this time the x-ray pulse is over, and the direct photoinduced processes no longer contributing. All created electrons within the nanoplasma are thermalized. The nanoplasma thus formed is a mixture of atoms, electrons, and ions of various charges. While expanding, it is undergoing electron impact ionization and three-body recombination. Below we present a hydrodynamic model to describe the dynamics of such multi-component nanoplasmas. The model equations are derived by taking the moments of the corresponding Boltzmann kinetic equations. We include the equations obtained, together with the source terms due to electron impact ionization and three-body recombination, in our hydrodynamic solver. Model predictions for a test case, expanding spherical Ar nanoplasma, are obtained. With this model, we complete the two-step approach to simulate x-ray created nanoplasmas, enabling computationally efficient simulations of their picosecond dynamics. Moreover, the hydrodynamic framework including collisional processes can be easily extended for other source terms and then applied to follow relaxation of any finite non-isothermal multi-component nanoplasma with its components relaxed into local thermodynamic equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Simulation studies of the interaction of laser radiation with additively manufactured foams

The interaction of laser radiation with foams of various porosities and low densities has been the subject of several numerical and experimental studies. In all cases, the modeling of low-Z under-dense foams as uniform gases of equivalent average density using standard radiation-hydrodynamics codes has resulted in heat-front velocities that are considerably faster than those observed experimentally. It has been theoretically conjectured that this difference may be attributed to the breakdown of the foam’s morphology, leading to a dynamics of filament expansion where the ion and electron energy partitions are significantly different from those calculated using the uniform gas model. We found that 3D computer simulations employing a disconnected representation of the foam’s microstructure which allowed for the dynamics of foam element heating, expansion, and stagnation largely supported the theoretical picture. Simulations using this model for laser experiments on under-dense 2 mg cc -1 SiO 2 aerogel foams reproduced the experimental data fairly well. We used the validated model in simulations of low-density structured foam-like materials (produced via additive manufacturing) with a variety of morphologies. We found that the log-pile configurations were consistent with the analytical propagation model of Gus’kov et al. Further validation of the model was obtained by simulating experiments performed at the Jupiter Laser Facility using the log-pile and octet-truss foam morphologies. Simulations of the foam-laser interaction using a wave propagation code showed that the microstructure was able to enhance stimulated Brillouin scattering (SBS) by concentrating the light energy into density holes. In turn, this promotes laser filamentation, reducing SBS and bringing the predicted values closer to the experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Dispersion relations for slow and fast resistive wall modes within the Haney-Freidberg model

The dispersion relation for the resistive wall modes (RWMs) is derived by using the trial function for the magnetic perturbation proposed in S. W. Haney and J. P. Freidberg, Phys. Fluids B 1, 1637 (1989). The Haney-Freidberg (HF) approach is additionally based on the expansion in d{sub w}/s≪1, where d{sub w} is the wall thickness and s is the skin depth. Here, the task is solved without this constraint. The derivation procedure is different too, but the final result is expressed in a similar form with the use of the quantities entering the HF relation. The latter is recovered from our more general relation as an asymptote at d{sub w}≪s, which proves the equivalence of the both approaches in this case. In the opposite limit (d{sub w}≫s), we obtain the growth rate γ of the RWMs as a function of γ{sub HF} calculated by the HF prescription. It is shown that γ∝γ{sub HF}{sup 2} and γ≫γ{sub HF} in this range. The proposed relations give γ for slow and fast RWMs in terms of the integrals calculated by the standard stability codes for toroidal systems with and without a perfectly conducting wall. Also, the links between the considered and existing toroidal and cylindrical models are established with estimates explicitly showing the relevant dependencies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗