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DOE OSTI2024

Nonlinear susceptibilities for weakly turbulent magnetized plasma: Electrostatic approximation

The plasma weak turbulence theory is a perturbative nonlinear theory, which has been proven to be quite valid in a number of applications. However, the standard weak turbulence theory found in the literature is fully developed for highly idealized unmagnetized plasmas. As many plasmas found in nature and laboratory are immersed in a background static magnetic field, it is necessary to extend the existing discussions to include the effects of ambient magnetic field. Such a task is quite formidable, however, which has prevented fundamental and significant progresses in the subject matter. The central difficulty lies in the formulation of the complete nonlinear response functions for magnetized plasmas. The present paper derives the nonlinear susceptibilities for weakly turbulent magnetized plasmas up to the third order nonlinearity, but in doing so, a substantial reduction in mathematical complexity is achieved by the use of Bessel function addition theorem (or sum rule). The present paper also constructs the weak turbulence wave kinetic equation in a formal sense. For the sake of simplicity, however, the present paper assumes the electrostatic interaction among plasma particles. Fully electromagnetic generalization is a subject of a subsequent paper.

Physics↗
DOE OSTI2023

Generation of momentum transport in weakly turbulent β -plane magnetohydrodynamics

Magnetohydrodynamic turbulence on a β plane with an in-plane mean field, a system which serves as a simple model for the solar tachocline, is investigated analytically and computationally. We first derive two useful analytic constraints: We express the mean turbulent cross-helicity in terms of the mean turbulent magnetic energy, and then show that (for weak turbulence) the time-averaged momentum transport in the system can be expressed in terms of the cross-helicity spectrum. Here, we then complete a closure of the system using weak turbulence theory, appropriately extended to a system with multiple interacting eigenmodes. We use this closure to perturbatively solve for the spectra at lowest order in the Rossby parameter β and thereby show that the momentum transport in the system is O ⁡(β 2 ), thus quantifying the transition away from Alfvénized turbulence. Finally, we verify our theoretical results by performing direct numerical simulations of the system over a broad range of β.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Nonlinear susceptibilities for weakly turbulent magnetized plasma: Electromagnetic formalism

This is a companion paper to the previous work [P. H. Yoon, Phys. Plasmas 31, 032309 (2024)] in which the nonlinear susceptibilities of weakly turbulent magnetized plasma are derived under a simplifying assumption of electrostatic interaction. The present paper extends the analysis to a general situation of electromagnetic interaction. The main novelty of the previous and present papers is that by employing the Bessel function addition theorem, the mathematical definitions for the susceptibilities are substantially simplified, a procedure that has not been discussed in the existing literature. In the present paper, a full set of Maxwell’s equations are considered in conjunction with the nonlinear Vlasov equation, which is solved by a perturbative method. The result is a fully general nonlinear susceptibility, given in tensorial form, which is applicable for weakly turbulent magnetized plasmas.

Materials Science↗
DOE OSTI2022

Alternative formulation of weak magnetohydrodynamic turbulence theory

In a recent paper, the weak turbulence theory for incompressible magnetohydrodynamics is formulated by employing the method customarily applied in the context of kinetic weak plasma turbulence theory. Such an approach simplified certain mathematical procedures including achieving the closure relationship. The formulation in the above-cited paper starts from the equations of incompressible magnetohydrodynamic (MHD) theory expressed via Elsasser variables. The derivation of nonlinear wave kinetic equation therein is obtained via a truncated solution at the second-order of iteration following the standard practice. In the present paper, the weak MHD turbulence theory is alternatively formulated by employing the pristine form of incompressible MHD equation rather than that expressed in terms of Elsasser fields. The perturbative expansion of the nonlinear momentum equation is carried out up to the third-order iteration rather than imposing the truncation at the second order. Furthermore, it is found that while the resulting wave kinetic equation is identical to that obtained in the previous paper cited above, the third-order nonlinear correction plays an essential role for properly calculating derived quantities such as the total and residual energies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Physics↗
DOE OSTI2024

Weak magnetohydrodynamic turbulence theory revisited

Two recent papers, P. H. Yoon and G. Choe, Phys. Plasmas 28, 082306 (2021) and Yoon et al., Phys. Plasmas 29, 112303 (2022), utilized in the derivation of the kinetic equation for the intensity of turbulent fluctuations the assumption that the wave spectra are isotropic, that is, the ensemble-averaged magnetic field tensorial fluctuation intensity is given by the isotropic diagonal form, ⟨δBiδBj⟩k=⟨δB2⟩kδij. However, it is more appropriate to describe the incompressible magnetohydrodynamic turbulence involving shear Alfvénic waves by modeling the turbulence spectrum as being anisotropic. That is, the tensorial fluctuation intensity should be different in diagonal elements across and along the direction of the wave vector, ⟨δBiδBj⟩k=12 ⟨δB⊥2⟩k(δij−kikj/k2)+⟨δB∥2⟩k(kikj/k2). In the present paper, we thus reformulate the weak magnetohydrodynamic turbulence theory under the assumption of anisotropy and work out the form of nonlinear wave kinetic equation.

Physics↗
DOE OSTI2023

Multi-scale Dynamics of Kinetic Turbulence in Weakly Collisional, High-Beta Plasmas (Final Report for DOE Grant DE-SC0019046)

This grant was a collaborative grant between Prof Matt Kunz (Princeton) and Prof. Eliot Quataert. Quataert was initially a faculty member at UC Berkeley when the grant was funded but moved to Princeton during the timeframe of this grant. Over the course of this grant we made major progress on understanding turbulence and multi-scale dynamics in weakly collisional high-beta plasmas. The most important contributions included: We developed one of the most compelling theoretical explanations for a decades-old puzzle at the heart of our understanding of the origin of the solar wind. The puzzle is that many of the observations of ion temperatures and distribution functions in the solar wind are consistent with cyclotron resonant heating. However, theoretical models of MHD turbulence in the solar wind show that most of the turbulent energy remains at low frequencies below the cyclotron frequency. In Squire et al. (2022), we showed, however, that in imbalanced turbulence (in which there is an asymmetry in the Alfven-wave flux in opposite directions along the magnetic field), which is the norm in the fast solar wind, the turbulent energy reaches a ‘bottleneck’ near the ion Larmor radius, and the amplitude and characteristic frequency of the fluctuations grow until the cyclotron frequency is reached.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Features of mid- and high-latitude low-level clouds and their relation to strong aerosol effects in the Energy Exascale Earth System Model version 2 (E3SMv2)

The E3SMv2 model, like various other global models that include representations of aerosol–cloud interactions, uses an empirically chosen lower bound on the simulated in-cloud cloud droplet number concentration (CDNC) to help constrain the effective radiative forcing of anthropogenic aerosols, ERFaer. This study identifies where ultra-low CDNCs (i.e., concentrations lower than 10 cm−3) occur in the stratiform and shallow convective clouds simulated by E3SMv2 and which of the occurrences have the strongest impact on ERF aer . Process-level analyses are presented to reveal characteristics of the cloud droplet formation and removal processes associated with impactful ultra-low CDNCs. Simulations performed with present-day emissions show that ultra-low CDNCs are most frequently found over the mid- and high-latitude oceans in both hemispheres, while the occurrences are also frequent in polluted continental regions despite the high aerosol concentrations. Ultra-low CDNCs with the largest impacts on the simulated regional and global mean ERF aer are found in the lower troposphere in the Northern Hemisphere middle and high latitudes. These cases are typically associated with large cloud fractions, strong water vapor condensation, weak turbulence, and lack of cloud droplet nucleation from aerosol activation. Under such atmospheric conditions, boosting aerosol activation and enhancing turbulent mixing of cloud droplet number can increase the simulated CDNCs, although the magnitude of the global mean ERF aer increases undesirably. The reason for this model behavior is discussed. Overall, our study suggests that mid- and high-latitude low-level stratus occurring under weak turbulence is a cloud regime worth further investigating for the purpose of identifying and addressing the root causes of ultra-low CDNCs and strong ERF aer in E3SM.

Aerosol-Cloud Interaction↗
DOE OSTI2023

Exploring regular and turbulent flow states in active nematic channel flow via Exact Coherent Structures and their invariant manifolds

This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECS). ECS are stationary, periodic, quasiperiodic, or traveling wave solutions of the governing equations that, together with their invariant manifolds, organize the dynamics of nonlinear continuum systems. We extend our earlier work on ECS in the preturbulent regime by performing a comprehensive study of stable and unstable ECS for a wide range of activity values spanning the preturbulent and turbulent regimes. In the weakly turbulent regime, we compute more than 200 unstable ECS that co-exist at a single set of parameters, and uncover the role of symmetries in organizing the phase space geometry. We provide conclusive numerical evidence that in the preturbulent regime, generic trajectories shadow a series of unstable ECS before settling onto an attractor. Lastly, our studies hint at shadowing of quasiperiodic type ECS in the turbulent regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Idealized simulations of wind farm interactions with intermittent turbulence in stable boundary layer conditions

Stable atmospheric boundary layer conditions typically correspond to weak turbulence levels, but intermittent periods of elevated turbulence can occur during otherwise quiescent conditions. The interaction between intermittent turbulence and wind turbines is not well understood because of sparse observations, as well as the difficulty in realistically resolving small-scale turbulence during strongly stable conditions with numerical simulations. In this study, an explicit filtering and reconstruction approach for large-eddy simulation (LES) is used to simulate weakly and strongly stable conditions, with surface cooling rates of −0.2 and −2.0 K h −1 , respectively. This approach can sustain resolved background turbulence at relatively coarse grid spacing and stronger stratification compared to conventional closures, permitting more realistic intermittent stable boundary layer (SBL) turbulence. The idealized LES capability of the Weather Research and Forecasting model is employed with turbine rotors parameterized using generalized actuator disks to examine (1) how the presence of turbine wakes affects SBL evolution and (2) the effect of intermittent turbulence on power production and wake recovery. Wakes increase mixing and deepen the SBL, with a stronger effect under strongly stable conditions, primarily because the SBL is shallower and closer to the top of the wind turbine rotor layer. Intermittent turbulence does not have a significant impact on mean power generation and wake recovery because the relevant intermittent turbulent structures in this study only affect the bottom half of the rotor disk. Power production is, however, more variable during periods of elevated turbulence, demonstrating the impact of SBL intermittency. This study uses an idealized configuration, focusing on LES model performance and physical understanding, with the goal of informing future simulations of the conditions observed during the American Wake Experiment.

Energy - Wind↗
DOE OSTI2024

Effective viscosity, resistivity, and Reynolds number in weakly collisional plasma turbulence

ABSTRACT We examine dissipation and energy conversion in weakly collisional plasma turbulence, employing in situ observations from the Magnetospheric Multiscale mission and kinetic particle-in-cell simulations of proton–electron plasma. A previous result indicated the presence of viscous-like and resistive-like scaling of average energy conversion rates – analogous to scalings characteristic of collisional systems. This allows for extraction of collisional-like coefficients of effective viscosity and resistivity, and thus also determination of effective Reynolds numbers based on these coefficients. The effective Reynolds number, as a measure of the available bandwidth for turbulence to populate various scales, links turbulence macroscale properties with kinetic plasma properties in a novel way.

Astronomy & Astrophysics↗
DOE OSTI2020

Turbulence-level dependence of cosmic ray parallel diffusion

ABSTRACT Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic ray transport. The transition from a ballistic to a diffusive-propagation regime is presented in direct numerical calculations of diffusion coefficients for homogeneous magnetic field lines subject to turbulent perturbations. Simulation results are compared with theoretical derivations of the parallel diffusion coefficient’s dependences on the energy and the fluctuation amplitudes in the limit of weak turbulence. The present study shows that the widely used extrapolation of the energy scaling for the parallel diffusion coefficient to high turbulence levels predicted by quasi-linear theory does not provide a universally accurate description in the resonant-scattering regime. It is highlighted here that the numerically calculated diffusion coefficients can be polluted for low energies due to missing resonant interaction possibilities of the particles with the turbulence. Five reduced-rigidity regimes are established, which are separated by analytical boundaries derived in this work. Consequently, a proper description of cosmic ray propagation can only be achieved by using a turbulence-level-dependent diffusion coefficient and can contribute to solving the Galactic cosmic ray gradient problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A hybrid full-wave Markov chain approach to calculating radio-frequency wave scattering from scrape-off layer filaments

The interaction of radio-frequency (RF) waves with edge turbulence modifies the incident wave spectrum, and can significantly affect RF heating and current drive in tokamaks. Previous lower hybrid (LH) scattering models have either used the weak-turbulence approximation, or treated more realistic, filamentary turbulence in the ray tracing limit. In this study, a new model is introduced which retains full-wave effects of RF scattering in filamentary turbulence. First, a Mie-scattering technique models the interaction of an incident wave with a single Gaussian filament. Next, an effective differential scattering width is derived for a statistical ensemble of filaments. Lastly, a Markov chain solves for the transmitted wave spectrum in slab geometry. This model is applied to LH launching for current drive. The resulting wave spectrum is asymmetrically broadened in angular wavenumber space. This asymmetry is not accounted for in previous LH scattering models. The modified wave spectrum is coupled to a ray tracing/Fokker–Planck solver (GENRAY/CQL3D) to study its impact on current drive. The resulting current profile is greatly altered, and there is significant increase in the on-axis current and decrease in the off-axis peaks. This is attributed to a portion of the modified wave spectrum that is strongly dampened on-axis during the first pass.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Evidence and modeling of turbulence bifurcation in L-mode confinement transitions on Alcator C-Mod

Analysis and modeling of rotation reversal hysteresis experiments show that a single turbulent bifurcation is responsible for the Linear to Saturated Ohmic Confinement (LOC/SOC) transition and concomitant intrinsic rotation reversal on Alcator C-Mod. Plasmas on either side of the reversal exhibit different toroidal rotation profiles and therefore different turbulence characteristics despite the profiles of density and temperature, which are indistinguishable within measurement uncertainty. Elements of this bifurcation are also shown to persist for auxiliary heated L-modes. The deactivation of subdominant (in the linear growth rate and contribution to heat transport) ion temperature gradient and trapped electron mode instabilities is identified as the only possible change in turbulence within a reduced quasilinear transport model across the reversal, which is consistent with the measured profiles and inferred heat and particle fluxes. Experimental constraints on a possible change from strong to weak turbulence, outside the description of the quasilinear model, are also discussed. These results indicate an explanation for the LOC/SOC transition that provides a mechanism for the hysteresis through the dynamics of subdominant modes and changes in their relative populations and does not involve a change in the most linearly unstable ion-scale drift-wave instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Enhancing Turbulent Mixing and Microphysical Uniformity in a Tall Convection‐Cloud Chamber Through Idealized Heterogeneity of Boundaries

A large convection cloud chamber has been proposed for exploring aerosol–cloud–drizzle interactions under well‐controlled turbulent conditions. Recent theoretical and numerical studies suggest that a convection cloud chamber with two heated and two cooled sidewalls can significantly enhance the liquid water content and thus benefit drizzle initiation. However, a chamber with such a sidewall configuration develops stable stratification and extremely weak turbulence therein. In this study, we conduct large‐eddy simulations of a tall convection chamber with five different sidewall configurations consisting of alternating warm and cold patches. For each configuration, the total surface area of warm patches equals that of cold patches, resulting in the same expected cloud‐free supersaturation based on a flux budget model. Results show that changing the sidewall configuration, while keeping all other factors constant, can substantially enhance turbulent mixing and improve the uniformity of thermodynamic and cloud microphysical properties in the bulk region of the chamber. In addition, turbulence strength is positively correlated with liquid water content and negatively correlated with cloud droplet number concentration, consistent with theoretical predictions. Our results highlight the advantage of building a large cloud chamber using modular patches with individually controllable temperature and humidity to achieve well‐mixed conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Anticathode effect on electron kinetics in electron beam generated E × B plasma

Electron beam (e-beam) generated plasmas with applied crossed electric and magnetic (E x B) fields are promising for low damage processing of materials with applications to microelectronics and quantum information systems. In cylindrical e-beam E x B plasmas, radial confinement of electrons and ions is achieved by an axial magnetic field and radial electric field, respectively. To control the axial confinement of electrons, such e-beam generated plasma sources may incorporate a conducting boundary known as an anticathode, which is placed on the axially opposite side of the plasma from the cathode. In this work, it is shown that varying the anticathode voltage bias can control the degree to which the anticathode collects or repels incident electrons, allowing control of warm electron (electron energies in 10–30 eV range) and beam electron population confinement. It is suggested that the effect of the anticathode bias on the formation of these distinct electron populations is also associated with the transition between weak turbulence and strong Langmuir turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Strong suppression of heat conduction in a laboratory replica of galaxy-cluster turbulent plasmas

In conventional gases and plasmas, it is known that heat fluxes are proportional to temperature gradients, with collisions between particles mediating energy flow from hotter to colder regions and the coefficient of thermal conduction given by Spitzer’s theory. However, this theory breaks down in magnetized, turbulent, weakly collisional plasmas, although modifications are difficult to predict from first principles due to the complex, multiscale nature of the problem. Understanding heat transport is important in astrophysical plasmas such as those in galaxy clusters, where observed temperature profiles are explicable only in the presence of a strong suppression of heat conduction compared to Spitzer’s theory. To address this problem, we have created a replica of such a system in a laser laboratory experiment. Our data show a reduction of heat transport by two orders of magnitude or more, leading to large temperature variations on small spatial scales (as is seen in cluster plasmas).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Dynamic Phase Alignment in Inertial Alfvén Turbulence

In weakly collisional plasma environments with sufficiently low electron beta, Alfvénic turbulence transforms into inertial Alfvénic turbulence at scales below the electron skin depth, k ⊥ d e ≳ 1. We argue that, in inertial Alfvénic turbulence, both energy and generalized kinetic helicity exhibit direct cascades. We demonstrate that the two cascades are compatible due to the existence of a strong scale dependence of the phase alignment angle between velocity and magnetic field fluctuations, with the phase alignment angle scaling as cos α k ∝ $k$$^{–1}_{⊥}$. The kinetic and magnetic energy spectra scale as ∝ $k$$^{–5/3}_{⊥}$ and ∝ $k$$^{–11/3}_{⊥}$, respectively. As a result of the dual direct cascade, the generalized helicity spectrum scales as ∝ $k$$^{–5/3}_{⊥}$, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the k ⊥ d e >> 1 range. Turbulent eddies exhibit a phase-space anisotropy k ∥ ∝ $k$$^{5/3}_{⊥}$, consistent with critically balanced inertial Alfvén fluctuations. Furthermore, our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth’s magnetosheath and ionosphere, solar corona, and nonrelativistic pair plasmas, as well as to strongly rotating nonionized fluids.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗