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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Spatiotemporal spread of perturbations in power-law models at low temperatures: Exact results for classical out-of-time-order correlators

Here, we present exact results for the classical version of the out-of-time-order commutator (OTOC) for a family of power-law models consisting of N particles in one dimension and confined by an external harmonic potential. These particles are interacting via power-law interaction of the form ∝ $Σ_{i,j=(i≠j)}^{N}$ |x i -x j | -k for every k>1 where x i is the position of the i th particle. We present numerical results for the OTOC for finite N at low temperatures and short enough times so that the system is well approximated by the linearized dynamics around the many-body ground state. In the large-N limit, we compute the ground-state dispersion relation in the absence of external harmonic potential exactly and use it to arrive at analytical results for OTOC. We find excellent agreement between our analytical results and the numerics. We further obtain analytical results in the limit where only linear and leading nonlinear (in momentum) terms in the dispersion relation are included. The resulting OTOC is in agreement with numerics in the vicinity of the edge of the “light cone.” We find remarkably distinct features in OTOC below and above k=3 in terms of going from non-Airy behavior (1 < k < 3) to an Airy universality class (k>3). We present certain additional rich features for the case k=2 that stem from the underlying integrability of the Calogero-Moser model. We present a field theory approach that also assists in understanding certain aspects of OTOC such as the sound speed. Our findings are a step forward towards a more general understanding of the spatiotemporal spread of perturbations in long-range interacting systems.

1-dimensional systems↗
DOE OSTI2026

Rigid-Mode Limit of the Yokoya Matrix Formalism and the Burov-Lebedev Dispersion Equation

Transverse single-bunch instabilities of space-charge-dominated coasting beams with round and flat transverse geometries are studied using a unified dispersion-relation framework. The analysis combines the Burov-Lebedev formalism, which captures space-charge tune spread, Landau damping, and instability threshold behavior, with Yokoya’s projection method for representing coherent transverse mode structure and its dependence on beam aspect ratio. In the rigid-beam limit, the formulation reduces to a scalar dispersion relation of Burov-Lebedev paper. For non-rigid transverse oscillations, truncation of Yokoya’s Hermite-based expansion yields a finite-dimensional matrix eigenvalue problem in which space-charge and coupling impedance effects enter through Burov-Lebedev–type denominators. This approach provides a consistent basis for comparing rigid and non-rigid instability behavior in round and flat beams and for assessing the role of beam ellipticity in modifying coherent mode structure and stability thresholds.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Theoretical and global simulation analysis of collisional microtearing modes

Microtearing modes (MTMs) are suggested as a candidate for anomalous thermal transport in tokamak H-mode discharges. This study investigates MTMs in tokamak plasmas, employing simulations in the BOUT++ framework. It simplifies and linearizes the governing equations in detailed linear simulations. The study meticulously evaluates various conductivity models under diverse plasma conditions and collision regimes. The research thoroughly assesses different conductivity models across a range of plasma conditions and collision regimes. A unified dispersion relation that includes both MTM and Drift-Alfvén Wave (DAW) instabilities is derived, showing that DAW and MTM instabilities occur at varying distances from the rational surface. Specifically, MTMs become unstable near the rational surface but stabilize farther away, while drift-Alfvén instability appears farther from the rational surface. The study also re-derives MTM dispersion relations using Ohm's law and the vorticity equation, providing a thorough analysis of electromagnetic and electrostatic interactions in tokamaks. Global simulations demonstrate an inverse correlation between MTM growth rates and collisionality, and a direct correlation with temperature gradients. The nonalignment of the rational surface with the peak ω*e stabilizes the MTMs. Nonlinear simulations highlight electron temperature relaxation as the primary saturation mechanism for MTMs, with magnetic flutter identified as the dominant mode of electron thermal transport.

Fan, K. (ORCID:0000000227518809)↗
DOE OSTI2020

The Lifshitz Regime and its Experimental Signals

We discuss the possibility of a Lifshitz regime, where the dispersion relation for Goldstone bosons and related fields has a minimum at nonzero momenta. Studies with the Functional Renormalization Group suggest that this occurs over a wide region in the plane of temperature and baryon chemical potential. Conversely, the FRG finds that the region in which fluctuations from a critical endpoint are significant is rather small. Here, we suggest that this is due generically to the narrowness of the tricritical region in the chiral limit. Even if particles are produced in thermal equilibrium, a dispersion relation which is non-monotonic in momenta produces what appears to be non-thermal behavior.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Polarization and properties of low-frequency waves in warm magnetized two-fluid plasma

This paper presents the derivation of a general wave dispersion relation for warm magnetized plasma under the two-fluid formalism. The discussion is quite general except for the assumption of low frequency and slow phase speed, for which the displacement current is negligible, under the implicit assumption that the plasma is sufficiently dense to satisfy the condition ωpe>ωce, where ωpe and ωce denote the plasma oscillation frequency and electron gyro frequency, respectively. The present discussion does not invoke charge neutrality associated with the fluctuations although it is implicitly satisfied. The resulting dispersion relation that includes the fluid thermal effects shows that there are three eigen modes, which include those corresponding to ideal MHD, namely, fast, slow, and kinetic Alfvén waves, as well as higher-frequency modes including the ion and electron cyclotron and lower-hybrid resonances. The fluid effects in the ideal MHD wave branches are influenced by the finite Larmor radius scales, and when the wave number in the cross field direction is comparable to these values, the fluid effects become significant. It is found that the Larmor radius should be interpreted in the sense as ion-acoustic gyro-radius instead of ion thermal gyro radius only. That is, it is found that the electrons also contribute to the non-ideal effect associated with the kinetic Alfvén wave. A comprehensive explanation of the polarization of each mode is also presented. The present findings indicate that the polarity may change its sign only for the kinetic Alfvén mode branch and that such a transition is based on the propagation angle. When such a change does take place, it is found that the kinetic Alfvén wave transits to an ion-acoustic mode. For each branch, it is also found that the electric field along the ambient magnetic field is purely transverse.

Physics↗
DOE OSTI2022

Magnetized laser–plasma interactions in high-energy-density systems: Parallel propagation

In this study, we investigate parametric processes in magnetized plasmas, driven by a large-amplitude pump light wave. Our focus is on laser–plasma interactions relevant to high-energy-density (HED) systems, such as the National Ignition Facility and the Sandia MagLIF concept. We present a self-contained derivation of a “parametric” dispersion relation for magnetized three-wave interactions, meaning the pump wave is included in the equilibrium, similar to the unmagnetized work of Drake et al., Phys. Fluids 17, 778 (1974). For this, we use a multi-species plasma fluid model and Maxwell's equations. The application of an external B field causes right- and left-polarized light waves to propagate with differing phase velocities. This leads to Faraday rotation of the polarization, which can be significant in HED conditions. Phase-matching and linear wave dispersion relations show that Raman and Brillouin scattering have modified spectra due to the background B field, though this effect is usually small in systems of current practical interest. We study a scattering process we call stimulated whistler scattering, where a light wave decays to an electromagnetic whistler wave (ω≲ω ce ) and a Langmuir wave. This only occurs in the presence of an external B field, which is required for the whistler wave to exist.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Nonlinear waves in a thin dielectric film on the surface of a topological insulator

Based on the dispersion relation for a wave localised in a thin film of a nonlinear dielectric, which is located on the surface of a topological insulator, we have derived a system of equations that describes the propagation of a surface wave. It is shown that the longitudinal and transverse tangential components of the electric field vector are related due to the nonlinearity of the film and change periodically during propagation. It is found that the rotation period of this vector is determined by the axion charge of the topological dielectric and the nonlinear susceptibility of the thin film. (paper)

36 MATERIALS SCIENCE↗
DOE OSTI2026

Modification of ion-temperature-gradient turbulence by impurities in stellarator plasmas

Recent nonlinear gyrokinetic simulations have shown that impurities can strongly modify the turbulent heat flux in stellarator plasmas. Here, the ion-temperature-gradient (ITG) dispersion relation in a plasma containing impurities is analytically solved in certain limits and an expression for the modification of the ITG growth rate by impurities is derived. The analytical expression is the sum of three terms corresponding to three different physical causes (impurity density gradient, impurity temperature gradient and dilution) of the change in the growth rate. The scalings predicted analytically for the modification of the growth rate are shown to be reproduced by linear gyrokinetic simulations. The conditions for reduction or increase of the ITG growth by impurities are also correctly predicted by the analytical solution to the dispersion relation. Finally, a remarkable correlation is found between the analytical expression for the modification of the growth rate and the modification of the turbulent heat flux obtained from nonlinear gyrokinetic simulations.

Calvo, Iván [Research Centre for Energy, Environme↗
DOE OSTI2020

Observation of intravalley phonon scattering of 2s excitons in MoSe 2 and WSe 2 monolayers

Abstract We present a high-resolution resonance Raman study of hBN encapsulated MoSe 2 and WSe 2 monolayers at 4 K using excitation energies from 1.6 eV to 2.25 eV. We report resonances with the WSe 2 A2s and MoSe 2 A2s and B2s excited Rydberg states despite their low oscillator strength. When resonant with the 2s states we identify new Raman peaks which are associated with intravalley scattering between different Rydberg states via optical phonons. By calibrating the Raman scattering efficiency and separately constraining the electric dipole matrix elements, we reveal that the scattering rates for k = 0 optical phonons are comparable for both 1s and 2s states despite differences in the envelope functions. We also observe multiple new dispersive Raman peaks including a peak at the WSe 2 A2s resonance that demonstrates non-linear dispersion and peak-splitting behavior that suggests the dispersion relations for dark excitonic states at energies near the 2s state are extremely complex.

Materials Science↗
DOE OSTI2020

Self-consistent theory of the Darrieus–Landau and Rayleigh–Taylor instabilities with self-generated magnetic fields

The Rayleigh–Taylor (RT) and Darrieus–Landau (DL) instabilities are studied in an inertial confinement fusion context within the framework of small critical-to-shell density ratio D R and weak acceleration regime, i.e., large Froude number Fr. The quasi-isobaric analysis in Sanz et al. is completed with the inclusion of non-isobaric and self-generated magnetic-field effects. The analysis is restricted to perturbation wavelengths k~1 larger than the conduction length scale at the ablation front, yet its validity ranges from wavelengths shorter and larger than the conduction layer width (distance between the ablation front and the critical surface). The use of a sharp boundary model leads to a single analytical expression of the dispersion relation encompassing both instabilities. The two new effects come into play by modifying the perturbed mass and momentum fluxes at the ablation front. The momentum flux (perturbed pressure at the spike) is the predominant stabilizing mechanism in the RT instability (overpressure) and the driving mechanism in the DL instability (underpressure). The non-isobaric effects notably modify the scaling laws in the DL limit, leading to an underpressure scaling as ~k –11/15 rather than ~k –2/5 obtained in the quasi-isobaric model. The magnetic fields are generated due to misalignment between pressure and density gradients (Biermann battery effect). They affect the hydrodynamics by bending the heat flux lines. Within the framework of this paper, they enhance ablation, resulting in a stabilizing effect that peaks for perturbation wavelengths comparable to the conduction layer width. Here, the combination of parameters D R Fr 2/3 defines the region of predominance of each instability in the dispersion relation. It is proven that the DL region falls outside of the parameter range in inertial confinement fusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Vertical variation of turbulent entrainment mixing processes in marine stratocumulus clouds using high-resolution digital holography

Marine stratocumulus clouds contribute signi?cantly to the Earth’s radiation budget due to their extensive coverage and high albedo. Yet, subgrid variability in cloud properties such as aerosol concentration, droplet number and precipitation rates lead to considerable errors in global climate models. While these clouds usually have small vertical ex-tent, turbulent entrainment-mixing and precipitation can generate signi?cant variations in droplet number, size and relative dispersion with altitude. In this paper, we analyze turbulent entrainment-mixing processes and the variability in cloud microphysical properties as a function of height within a warm marine stratocumulus cloud layer over the Eastern North Atlantic. We use high resolution airborne holographic measurements and compare them with local turbulence measurements. We ?nd that entrainment-mixing is primarily inhomogeneous near cloud top leading to larger droplet sizes and homogeneous near cloud base leading to smaller droplet sizes. Further analysis of Damk¨ohler number measurements are able to explain the mixing mechanisms at di?erent cloud heights, reinforcing the importance of turbulent mixing and microphysical time scales in deter-mining cloud microphysics.

Desai, Neel↗
DOE OSTI2022

Tunable phononic bandgap materials designed via topology optimization

Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet–Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion–deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.

42 ENGINEERING↗
DOE OSTI2024

Turbulence, Waves, and Taylor’s Hypothesis for Heliosheath Observations

Magnetic field fluctuations measured in the heliosheath by the Voyager spacecraft are often characterized as compressible, as indicated by a strong fluctuating component parallel to the mean magnetic field. However, the interpretation of the turbulence data faces the caveat that the standard Taylor’s hypothesis is invalid because the solar wind flow velocity in the heliosheath becomes subsonic and slower than the fast magnetosonic speed, given the contributions from hot pickup ions (PUIs) in the heliosheath. We attempt to overcome this caveat by introducing a 4D frequency-wavenumber spectral modeling of turbulence, which is essentially a decomposition of different wave modes following their respective dispersion relations. Isotropic Alfvén and fast mode turbulence are considered to represent the heliosheath fluctuations. We also include two dispersive fast wave modes derived from a three-fluid theory. We find that (1) magnetic fluctuations in the inner heliosheath are less compressible than previously thought, an isotropic turbulence spectral model with about 25% in compressible fluctuation power is consistent with the observed magnetic compressibility in the heliosheath; (2) the hot PUI component and the relatively cold solar wind ions induce two dispersive fast magnetosonic wave branches in the perpendicular propagation limit, PUI fast wave may account for the spectral bump near the proton gyrofrequency in the observable spectrum; (3) it is possible that the turbulence wavenumber spectrum is not Kolmogorov-like although the observed frequency spectrum has a −5/3 power-law index, depending on the partitioning of power among the various wave modes, and this partitioning may change with wavenumber.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Kinetic simulation study of magnetized collisionless shock formation on a terawatt laser system

Perpendicular, magnetized, collisionless shocks in hydrogen and neon plasmas are studied with 2-D particle-in-cell simulations for parameters accessible to experiments on OMEGA EP. The simulations are performed with realistic ion-electron mass ratios by which the relative importance of different micro-instabilities can be accurately captured. The dispersion relation of the modified two-stream instability (MTSI), the main dissipation mechanism for these shocks, is used to find suitable parameters for upcoming experiments. Simulations show that magnetized collisionless shocks can be readily formed within a few tenths of an ion gyro-period in both hydrogen and neon gases, with a background magnetic field of 50 T, achievable using the magneto-inertial fusion electrical discharge system (MIFEDS). Here, a portion of the ions are reflected to the upstream region and accelerated in both shock normal and tangential directions, indicating the formation of a supercritical shock. Shock front reformation is seen in longer time 1-D simulations. The results show that the formation time and width of these shocks are determined by MTSI.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

What is the iε for the S-matrix?

Can the S-matrix be complexified in a way consistent with causality? Since the 1960's, the affirmative answer to this question has been well-understood for 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε -like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. In addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view, we illustrate all the points on explicit examples, both symbolically and numerically. Furthermore, to help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points.

Anomalous thresholds↗
DOE OSTI2026

Dispersive and nondispersive 𝐾-matrix formalisms

The modeling of coupled-channel effects has become increasingly important due to the availability of highly precise data for a large variety of hadronic (re)scattering processes. The 𝐾-matrix is a powerful, yet comparatively simple, method to describe scattering amplitudes, including coupled-channel effects, with the aim of interpreting experimental data. Throughout the literature, a range of dispersive and nondispersive 𝐾-matrix methods are employed. Here, we compare the dispersive and nondispersive formulations in the context of the N/D method. It is shown that the methods are equivalent in the physical region under 𝐾-matrix reparametrization. Differences away from the physical region are examined. Applications to synthetic data are used to illustrate the effects of model choices concerning form factors and the application of dispersion relations, with the goal of clarifying best practices. We find no clear preference with regard to dispersive modeling. In contrast, we find that interpretational ambiguity of the bare model parameters—and even of the form of the bare model—is endemic, and recommend a thorough sampling of data and model spaces to assess conclusion robustness.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Reynolds number dependence of Lagrangian dispersion in direct numerical simulations of anisotropic magnetohydrodynamic turbulence

Large-scale magnetic fields thread through the electrically conducting matter of the interplanetary and interstellar medium, stellar interiors and other astrophysical plasmas, producing anisotropic flows with regions of high-Reynolds-number turbulence. It is common to encounter turbulent flows structured by a magnetic field with a strength approximately equal to the root-mean-square magnetic fluctuations. In this work, direct numerical simulations of anisotropic magnetohydrodynamic (MHD) turbulence influenced by such a magnetic field are conducted for a series of cases that have identical resolution, and increasing grid sizes up to $2048^3$ . The result is a series of closely comparable simulations at Reynolds numbers ranging from 1400 up to 21 000. We investigate the influence of the Reynolds number from the Lagrangian viewpoint by tracking fluid particles and calculating single-particle and two-particle statistics. The influence of Alfvénic fluctuations and the fundamental anisotropy on the MHD turbulence in these statistics is discussed. Single-particle diffusion curves exhibit mildly superdiffusive behaviours that differ in the direction aligned with the magnetic field and the direction perpendicular to it. Competing alignment processes affect the dispersion of particle pairs, in particular at the beginning of the inertial subrange of time scales. Scalings for relative dispersion, which become clearer in the inertial subrange for a larger Reynolds number, can be observed that are steeper than indicated by the Richardson prediction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Dispersive sum rules in AdS 2

Dispersion relations for S-matrices and CFT correlators translate UV consistency into bounds on IR observables. In this note, we construct dispersive sum rules for 1D CFTs. We use them to prove bounds on higher-derivative couplings in weakly-coupled non-gravitational EFTs in AdS2. At the leading order in the bulk-point limit, the bounds agree with the flat-space result. We compute the leading universal effect of finite AdS radius on the bounds. Along the way, we give an explicit formula for anomalous dimensions in general higher-derivative contact Witten diagrams in AdS 2 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗