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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Resolution of a Few Problems in the Application of Quasilinear Theory to Calculating Diffusion Coefficients in Heliophysics

A theory of quasilinear diffusion for obliquely propagating electromagnetic waves was developed in the 1960's and applied in the 1970's to model scattering of relativistic electrons by a prescribed distribution of waves. In the latter work, a transformation of variables, from wavevector space to the temporal frequency and tangent of the wave normal angle, was used so that simple Gaussian functions of frequency and tangent of the wave normal angle could be multiplied together to define the distribution of wave power, although arbitrary distributions of power in these two variables is also permitted. Finally, in 2005, previous work was consolidated and has been widely used in heliophysics studies that require computation of quasilinear diffusion coefficients. Here it is shown that this transformation is inppropriate when the precise wave vector distribution is known. The correct transformation is derived and used to produce diffusion coefficients that can differ by orders of magnitude from those computed using the inappropriate transformation. The differences are largest when the distribution of wave power extends to wave normal angles near the resonance cone. When the ratio of the plasma frequency to the gyrofrequency is large, only low energies (keV) are affected, but as the ratio decreases higher energies (MeV) also show differences. It is also shown that the derivation from the 1960's uses a notation that results in the diffusion coefficients depending on the distribution of wave power with respect to the wave azimuthal angle whereas there should be no such dependence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Quasilinear theory: the lost ponderomotive effects and why they matter

Quasilinear theory (QLT) has been used for modeling wave–plasma interactions for decades but remains largely heuristic. Plasma inhomogeneity, ponderomotive effects, microscopic fluctuations, and collisions are not easily accommodated from first principles in QLT, and typically are ignored entirely, due to the limitations of the standard Fourier–Laplace global-mode approach. This results in inconsistencies, for example, violation of the action conservation for nonresonant waves. However, these issues can be avoided, and the theory can be substantially generalized and corrected, if QLT is formulated using more suitable analytical tools, particularly, the Weyl symbol calculus. Here, an attempt is made to deliver an accessible review of this modern formulation, provide intuitive calculations for special cases, and elaborate on the connection with the ‘oscillation-center QLT’ originally proposed by Dewar (Phys Fluids 16:1102, 1973). A Fokker–Planck equation for a ‘dressed’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, ponderomotive forces, and interactions with background fields for a generic Hamiltonian, so many known formulations of QLT for specific plasma models become corollaries of a single unifying theory. Also, waves are allowed to be off-shell (not constrained by a dispersion relation), which allows them to accommodate microscopic fluctuations. This leads to a collision integral of the Balescu–Lenard type that has all the usual properties but is not restricted to any specific plasma model. For on-shell waves, a generalized version of the classic oscillation-center QLT is obtained. Finally, combined with the wave-kinetic equation, this formulation not only conserves particles, momentum, and energy, like the classic QLT but also reinstates the action conservation for nonresonant waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Quasilinear theory and modelling of gyrokinetic turbulent transport in tokamaks

The theory, development, and validation of reduced quasilinear models of gyrokinetic turbulent transport in the closed flux surface core of tokamaks is reviewed. In combination with neoclassical collisional transport, these models are successful in accurately predicting core tokamak plasma temperature, density, rotation, and impurity profiles in a variety of confinement regimes. Refined experimental tests have been performed to validate the predictions of the quasilinear models, probing changes in the dominant gyrokinetic instabilities, as reflected in fluctuation measurements, cross-phases, and transport properties. These tests continue to produce a deeper understanding of the complex mix of instabilities at both electron and ion gyroradius scales.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Understanding cold electron impact on parallel-propagating whistler chorus waves via moment-based quasilinear theory

Earth's magnetosphere hosts a wide range of collisionless particle populations that interact through various wave-particle processes. Among these, cold electrons, with energies below 100 eV, often dominate the plasma density but remain poorly characterized due to measurement challenges such as spacecraft charging and photoelectron contamination. Understanding the contribution of these cold populations to wave–particle interaction is of significant interest. Recent kinetic simulations identified a secondary drift-driven instability, in which parallel-propagating whistler-mode chorus waves excite oblique electrostatic whistler waves near the resonance cone and Bernstein-mode turbulence. These secondary modes enable a new channel of energy transfer from the parallel-propagating whistler wave to the cold electrons. In this work, we develop a moment-based quasilinear theory of the secondary instabilities to quantify such energy exchange. Our results show that these secondary instabilities persist for a wide range of parameters and, in many cases, lead to nearly complete damping of the primary wave. Such secondary instability might limit the amplitude of parallel-propagating whistler waves in Earth's magnetosphere and might explain why high-amplitude oblique whistler or electron Bernstein waves are rarely observed simultaneously with high-amplitude field-aligned whistler waves in the inner magnetosphere.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Resolution of a few problems in the application of quasilinear theory to calculating diffusion coefficients in heliophysics [Slides]

Three problems with the historical literature were discussed. Kennel and Engelmann (1966): ‘notational error’ that implies that diffusion coefficients depend on the distribution of wave power with respect to ψ. This dependence is unphysical and is not present in Lyons+ 1971. Kennel and Engelmann (1966) assume that only a single frequency can be associated with each wave vector: not necessarily true for EMIC, e.g. Lyons (1974a, 1974b) incorrectly used the Jacobian to relate the power spectral density in (ω,χ) space to that into (κ ⊥ , κ ∥ space. The correct use of the Jacobian: (1) Eliminates undesirable properties associated with N(ω) : lack of integrability, lack of superposition; and (2) Can produce orders of magnitude changes to the diffusion coefficients, but depends on the wave distribution: bigger effect for more oblique waves, and depends on the plasma parameter: bigger effect for smaller $ω_{pe}/ω_{ce}$.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Quasilinear theory of Brillouin resonances in rotating magnetized plasmas

Both spin and orbital angular momentum can be exchanged between a rotating wave and a rotating magnetized plasma. Through resonances the spin and orbital angular momentum of the wave can be coupled to both the cyclotron rotation and the drift rotation of the particles. It is, however, shown that the Landau and cyclotron resonance conditions which classically describe resonant energy–momentum exchange between waves and particles are no longer valid in a rotating magnetized plasma column. In this case a new resonance condition which involves a resonant matching between the wave frequency, the cyclotron frequency modified by inertial effects and the harmonics of the guiding centre rotation is identified. A new quasilinear equation describing orbital and spin angular momentum exchanges through these new Brillouin resonances is then derived, and used to expose the wave-driven radial current responsible for angular momentum absorption.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

When do waves drive plasma flows?

Flows and rotation, particularly E×B rotation, are critical to improving plasma performance, and waves are a primary tool of plasma control. Thus, it is paramount to understand under what conditions waves can drive E×B flows in plasmas. In this didactic review, an invited paper accompanying the 2023 Marshall N. Rosenbluth Doctoral Thesis Award, this question is answered in the context of momentum-conserving quasilinear theory. There are two primary frameworks for momentum-conserving quasilinear theories that can handle both resonant and nonresonant particles: Eulerian averaging theories and oscillation-center Hamiltonian theories. There are also two different paradigmatic wave problems: plane-wave initial value problems, and steady-state boundary value problems. Here, it is shown that each of these frameworks “naturally” works better with a different problem type. By using these theories, one finds a great difference in the behavior of time- vs space-dependent waves. A time-evolving plane wave can only drive flow if the electromagnetic momentum of the wave, given by the Poynting flux, changes. This result precludes flow drive by any planar electrostatic wave. In contrast, a steady-state spatially evolving wave can drive flow whenever there is divergence in the flux of Minkowski momentum, a completely different physical quantity. This review aims to provide a high-level, intuitive understanding of the very different behaviors observed for these two types of problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Parameterized anomalous transport model for current-carrying collisionless plasmas in pulsed power inertial confinement fusion

Current delivery in pulsed power inertial confinement fusion is influenced by collisionless current-carrying microturbulent plasmas, which are sourced from electrode surfaces. In this setting, the lower hybrid drift instability—triggered by plasma acceleration—is a leading candidate driver of difficult-to-predict momentum and energy transport. To characterize the nonlinear state of the microturbulent plasma, a parameterized anomalous transport model is developed for the instability, with analytic formulas for anomalous collision frequency, resistivity, and species heating rates. The formulas are expressed in terms of linear-theory variables and four dimensionless parameters that characterize the macroscopic plasma state. The model is built on linear theory analysis, power law analysis, and quasilinear theory analysis, and is validated using a series of nonlinear continuum kinetic Vlasov–Poisson simulations. The theoretical and computational investigation demonstrates that the anomalous collision frequency associated with the instability can be reliably approximated, within about a factor of five or better, by the unscaled linear theory growth rate of the fastest-growing wavenumber mode. This finding enables efficient calculation of anomalous resistivity and species heating rates over a wide range of plasma conditions, resulting in improved predictive capabilities.

Complex functions↗
DOE OSTI2025

Quasilinear Analysis in the Source Region of Jovian Hectometric Emission Associated With Upward Electron Beams

Abstract Intense upward electron beams were measured by the Juno JADE instrument in the northern hemisphere, low‐latitude auroral zone source region. In this study we report on how these electron beams interact with plasma near and within the Jovian hectometric (HOM) emission (1 MHz 5 MHz) source region. Within the source region large upward loss cones are observed in the northern polar region at radial distances of 2Rj, magnetic latitude of . Intense, narrow electron beams ( 3 keV) are then observed, but within one second wave‐particle scattering is observed, filling the loss cone to energies 50 keV. These energies persist for several seconds before fading, leaving an empty loss cone again. The loss cone provides a free‐energy source for HOM emission resulting from the cyclotron maser instability. We use quasilinear analysis to examine the generation of HOM and the dynamics of wave‐particle interaction of the electron beams with HOM, and the generation via Landau interaction of whistler mode emission. The dynamic spectrum of the HOM emission generated by the loss‐cone electrons as well as that of the low‐frequency whistler‐mode waves generated by the up‐going electron beam can be constructed by quasilinear theory, which compare well with observation. The saturated state of the energetic electron velocity distribution function constructed via quasilinear theory also compare reasonably with observation.

Yoon, P. H. [Institute for Physical Science and Te↗
DOE OSTI2023

Gauge-invariant gravitational waves in matter beyond linearized gravity

Modeling the propagation of gravitational waves (GWs) in media other than vacuum is complicated by the gauge freedom of linearized gravity in that, once nonlinearities are taken into consideration, gauge artifacts can cause spurious acceleration of the matter. To eliminate these artifacts, we propose how to keep the theory of dispersive GWs gauge-invariant beyond the linear approximation and, in particular, obtain an unambiguous gauge-invariant expression for the energy–momentum of a GW in a dispersive medium. Using analytic tools from plasma physics, we propose an exactly gauge-invariant 'quasilinear' theory, in which GWs are governed by linear equations and also affect the background metric on scales large compared to their wavelength. As a corollary, the gauge-invariant geometrical optics of linear dispersive GWs in a general background is formulated. As an example, we show how the well-known properties of vacuum GWs are naturally and concisely yielded by our theory in a manifestly gauge-invariant form. We also show how the gauge invariance can be maintained within a given accuracy to an arbitrary order in the GW amplitude. These results are intended to form a physically meaningful framework for studying dispersive GWs in matter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Electrostatic upper-hybrid mode instability driven by a ring electron distribution

Quasi electrostatic fluctuations in the upper-hybrid frequency range are commonly detected in the planetary magnetospheric environment. The origin of such phenomena may relate to the instability driven by a loss-cone feature associated with the electrons populating the dipole-like magnetic field. The present paper carries out a one-dimensional electrostatic particle-in-cell simulation accompanied by a reduced quasilinear kinetic theoretical analysis to investigate the dynamics of the upper-hybrid mode instability driven by an initial ring electron distribution function, which is a form of loss-cone distribution. A favorable comparison is found between the two approaches, which shows that the reduced quasilinear theory, which is grounded in the concept of a model of the particle distribution function that is assumed to maintain a fixed mathematical form except that the macroscopic parameters that define the distribution are allowed to evolve in time, can be an effective tool in the study of plasma instabilities, especially if it is guided by and validated against the more rigorous simulation result.

Physics↗
DOE OSTI2023

Anomalous cross-field transport in a Hall thruster inferred from direct measurement of instability growth rates

The contribution of the electron drift instability to anomalous electron transport is experimentally assessed in a Hall effect discharge. The transport is represented by an anomalous collision frequency, which is related through quasilinear theory to the energy and growth rate of the instability. The wave energy is measured directly with ion saturation probes, while estimates of the growth rate are employed based on both linearized theory and direct measurement. The latter measurement is performed with a bispectral analysis method. The wave-driven collision frequency is compared to measurements of the actual collision frequency inferred from a method based on laser- induced fluorescence. It is found that estimates for transport using linearized theory for the growth differ by over an order of magnitude from the actual anomalous collision frequency in the plasma. The wave-driven anomalous collision frequency with measured growth, however, is shown to agree with the electron collision frequency in magnitude and capture aspects of the trends in spatial variation. This result demonstrates experimentally that wave-driven effects ultimately can explain the observed cross-field transport in these devices. As a result, the implications of this finding are discussed in the context of the key lengthscales that drive the transport as well as the implications identifying reduced fidelity models that could be used to predict anomalous collision frequency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Comparison of Saturation Rules Used for Gyrokinetic Quasilinear Transport Modeling

Theory-based transport modeling has been widely successful and is built on the foundations of quasilinear theory. Specifically, the quasilinear expression of the flux can be used in combination with a saturation rule for the toroidal mode amplitude. Most transport models follow this approach. Saturation rules are heuristic and difficult to rigorously derive. We compare three common saturation rules using a fairly accurate quasilinear expression for the fluxes computed using local linear gyrokinetic simulation. We take plasma parameters from experimental H-mode profiles and magnetic equilibrium and include electrons, deuterium, and carbon species. We find that the various saturation rules provide qualitatively similar behavior. This may help to explain why the different theory-based transport models can all predict core tokamak profiles reasonably well. Comparisons with nonlinear local and global gyrokinetic simulations are discussed.

Parker, Scott E. (ORCID:000000030942630X)↗
DOE OSTI2023

Expanding-box Quasilinear Model of the Solar Wind

The expanding-box model of the solar wind has been adopted in the literature within the context of magnetohydrodynamics, hybrid, and full particle-in-cell simulations to investigate the dynamic evolution of the solar wind. The present paper extends such a method to the framework of self-consistent quasilinear kinetic theory. It is shown that the expanding-box quasilinear methodology is largely equivalent to the inhomogeneous steady-state quasilinear model discussed earlier in the literature, but a distinction regarding the description of wave dynamics between the two approaches is also found. The expanding-box quasilinear formalism is further extended to include the effects of a spiraling solar-wind magnetic field as well as collisional age effects. The present finding shows that the expanding-box quasilinear approach and the steady-state global-kinetic models may be employed interchangeably in order to address other more complex problems associated with the solar-wind dynamics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Ponderomotive recoil for electromagnetic waves

When waves damp or amplify on resonant particles in a plasma, nonresonant particles experience a recoil force that conserves the total momentum between particles and electromagnetic fields. This force is important to understand, as it can completely negate current drive and rotation drive mechanisms that are predicted on the basis of only resonant particles. Here, the existing electrostatic theory of this recoil force is extended to electromagnetic waves. While the result bears close similarity to historical fluid theories of laser–plasma interactions, it now incorporates both resonant and nonresonant particles, allowing momentum conservation to be self-consistently proven. Furthermore, the result is shown to be generally valid for kinetic plasmas, which is verified through single-particle hot-plasma simulations. Here, the new form of the force provides physical insight into the nature of the generalized Minkowski (plasmon) momentum of geometrical optics, which is shown to correspond to the momentum gained by the field and nonresonant particles as the wave is self-consistently ramped up from vanishing amplitude.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas

We propose a conservative Galerkin scheme for the quasilinear model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. We construct an unconditionally conservative weak form and use a discretization that preserves conservation properties independent of the wave emission probability. The discrete operators, combined with a consistent quadrature rule, preserve all the conservation laws rigorously. The proposed scheme is quite general: it works for both relativistic and non-relativistic systems, for both magnetized and unmagnetized plasmas, and even for problems with time-dependent dispersion relations. We represent the particle distribution by continuous basis functions and use discontinuous basis functions for the wave spectral energy density, which enables the application of a positivity-preserving technique. We adopt the marching simplex algorithm, designed initially for computer graphics, for numerical integration on the resonance manifold. Furthermore, the numerical examples with a bump-on-tail initial configuration show how the unstable waves produce strong momentum space diffusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Marginal stability constraint on runaway electron distribution

High-frequency kinetic instabilities of the strongly anisotropic runaway electrons (RE) can enhance the pitch-angle scattering of the runaways significantly. This wave-induced scattering can easily prevail over runaway scattering on high-Z impurities. In a steady state, collisional damping balances the kinetic drive of the unstable waves, keeping the RE distribution function at marginal stability. The marginal stability constraint limits the achievable RE densities and the shape of the RE distribution function. In this study, we consider whistler and compressional Alfvén waves as the primary source of enhanced elastic scattering of the runaways. By balancing the anomalous Doppler resonance drive with the collisional wave damping, we find the RE distribution function in the ultra-relativistic range of the phase space. We also derive an expression for the spectral energy density of the waves. We show that the power needed to compensate for the wave dissipation is negligible compared to the work of the electric field. The latter is in balance with the synchrotron losses of the runaway electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗