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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 [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 OSTI2018

On the Solvability of a Boundary-Value Problem for a Second-Order Singular Quasilinear Equation

We obtain solvability conditions for a two-point boundary-value problem for a second-order quasilinear equation. The equation is singular with respect to the independent variable. The result is based on the properties of the Green operator of the corresponding linear problem. In particular, we prove its boundedness and obtain an upper estimate of its norm. Conditions of existence of a solution of the original problem are obtained from the solvability condition of an auxiliary operator equation.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2015

Dust heating by Alfvén waves using non-Maxwellian distribution function

Quasilinear theory is employed in order to evaluate the resonant heating rate by Alfvén waves, of multiple species dust particles in a hot, collisionless, and magnetized plasma, with the underlying assumption that the dust velocity distribution function can be modeled by a generalized (r, q) distribution function. The kinetic linear dispersion relation for the electromagnetic dust cyclotron Alfvén waves is derived, and the dependence of the heating rate on the magnetic field, mass, and density of the dust species is subsequently investigated. The heating rate and its dependence on the spectral indices r and q of the distribution function are also investigated. It is found that the heating is sensitive to negative value of spectral index r.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Velocity diffusion of energetic electrons in the solar wind

Particle diffusion in velocity space is studied on the basis of 1D simulations of Langmuir turbulence generated by electron beams in solar wind plasmas. Using a large amount of particle trajectories calculated with a great accuracy and over long times and analyzing them with statistical algorithms, the diffusion coefficients of particles in wave packets are estimated, as well as their relation to the waves’ intensities and spectra and their dependence on the average level of background plasma density fluctuations. Results are compared with analytical solutions provided by the quasilinear theory of weak turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave is defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Evaluation of toroidal torque by non-resonant magnetic perturbations in tokamaks for resonant transport regimes using a Hamiltonian approach

Toroidal torque generated by neoclassical viscosity caused by external non-resonant, non-axisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks. In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant neoclassical toroidal viscosity regimes including superbanana-plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbations on toroidally symmetric flux surfaces of the unperturbed equilibrium without specific assumptions on geometry or aspect ratio. The resulting expressions are shown to match the existing analytical results in the large aspect ratio limit. Numerical results from the newly developed code NEO-RT are compared to calculations by the quasilinear version of the code NEO-2 at low collisionalities. The importance of the magnetic shear term in the magnetic drift frequency and a significant effect of the magnetic drift on drift-orbit resonances are demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

SCATTER-DOMINATED INTERPLANETARY TRANSPORT OF SOLAR ENERGETIC PARTICLES IN LARGE GRADUAL EVENTS AND THE FORMATION OF DOUBLE POWER-LAW DIFFERENTIAL FLUENCE SPECTRA OF GROUND-LEVEL EVENTS DURING SOLAR CYCLE 23

The effects of scatter-dominated interplanetary transport on the spectral properties of the differential fluence of large gradual solar energetic particle (SEP) events are investigated analytically. The model assumes for simplicity radial constant solar wind and radial magnetic field. The radial diffusion coefficient is calculated with quasilinear theory by assuming a spectrum of Alfvén waves propagating parallel to the magnetic field. Cross-field transport is neglected. The model takes into consideration several essential features of gradual event transport: nearly isotropic ion distributions, adiabatic deceleration in a divergent solar wind, and particle radial scattering mean free paths increasing with energy. Assuming an impulsive and spherically symmetric injection of SEPs with a power-law spectrum near the Sun, the predicted differential fluence spectrum exhibits at 1 AU three distinctive power laws for different energy domains. The model naturally reproduces the spectral features of the double power-law proton differential fluence spectra that tend to be observed in extremely large SEP events. We select nine western ground-level events (GLEs) out of the 16 GLEs during Solar Cycle 23 and fit the observed double power-law spectra to the analytical predictions. The compression ratio of the accelerating shock wave, the power-law index of the ambient wave intensity, and the proton radial scattering mean free path are determined for the nine GLEs. The derived parameters are generally in agreement with the characteristic values expected for large gradual SEP events.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

COSMIC-RAY PITCH-ANGLE SCATTERING IN IMBALANCED MHD TURBULENCE SIMULATIONS

Pitch-angle scattering rates for cosmic-ray particles in MHD simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfvén waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Diffusion of energetic electrons in turbulent plasmas of the solar wind

A method of calculation of the diffusion coefficients D(v) of particles in velocity space, based on the statistical analysis of the motion of a great number of test electrons, is proposed. In the case of Langmuir turbulence developing in plasmas with fluctuating density inhomogeneities such as the solar wind, simulations provide coefficients D(v) which mainly depend on the Langmuir wave spectra and agree well with the analytical predictions D{sub th}(v) of the quasilinear theory of weak turbulence. Nevertheless, some noticeable differences exist with this theory: in the range of phase velocity of the short waves where the main part of the wave energy is concentrated, D(v) is noticeably smaller than D{sub th}(v), due to the scattering, the reflection, and the focusing effects encountered by the Langmuir waves when they interact with the plasma density inhomogeneities. Moreover, the probability of large velocity jumps in the particles’ trajectories essentially exceeds the probability of a Gaussian distribution. These large jumps, which are connected with the waves’ transformation processes, modify the nature of the particle diffusion, which is no more classical. These higher order effects cause the discrepancies observed with the quasilinear theory, which does not take them into account in its perturbative approach. The solar wind plasmas, which present fluctuating density inhomogeneities of noticeable average levels, are a very good laboratory to study such diffusion processes, which can eventually influence significantly on the development of essential physical phenomena, as electromagnetic radio emissions by type III solar radio bursts, for example.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Determining pitch-angle diffusion coefficients from test particle simulations

The transport and acceleration of charged particles in turbulent media are topics of great interest in space physics and interstellar astrophysics. These processes are dominated by the scattering of particles off magnetic irregularities. The scattering process itself is usually described by small-angle scattering, with the pitch-angle coefficient D{sub μμ} playing a major role. Since the diffusion coefficient D{sub μμ} can be determined analytically only for the approximation of quasilinear theory, the determination of this coefficient from numerical simulations has become more important. So far these simulations have yielded particle tracks for small-scale scattering, which can then be interpreted using the running diffusion coefficients. This method has a limited range of validity. This paper presents two new methods that allow for the calculation of the pitch-angle diffusion coefficient from numerical simulations. These methods no longer analyze particle trajectories and instead examine the change of particle distribution functions. It is shown that these methods provide better resolved results and allow for the analysis of strong turbulence. The application of these methods to Monte Carlo simulations of particle scattering and hybrid MHD-particle simulations is presented. Both analysis methods are able to recover the diffusion coefficients used as input for the Monte Carlo simulations and provide better results in MHD simulations, especially for stronger turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

On the Effects of Pickup Ion-driven Waves on the Diffusion Tensor of Low-energy Electrons in the Heliosphere

The effects of Alfvén cyclotron waves generated due to the formation in the outer heliosphere of pickup ions on the transport coefficients of low-energy electrons is investigated here. To this end, parallel mean free path (MFP) expressions are derived from quasilinear theory, employing the damping model of dynamical turbulence. These are then used as inputs for existing expressions for the perpendicular MFP and turbulence-reduced drift coefficient. Using outputs generated by a two-component turbulence transport model, the resulting diffusion coefficients are compared with those derived using a more typically assumed turbulence spectral form, which neglects the effects of pickup ion-generated waves. It is found that the inclusion of pickup ion effects greatly leads to considerable reductions in the parallel and perpendicular MFPs of 1–10 MeV electrons beyond ∼10 au, which are argued to have significant consequences for studies of the transport of these particles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Quasilinear saturation of the aperiodic ordinary mode streaming instability

In collisionless plasmas, only kinetic instabilities and fluctuations are effective in reducing the free energy and scatter plasma particles, preventing an increase of their anisotropy. Solar energetic outflows into the interplanetary plasma give rise to important thermal anisotropies and counterstreaming motions of plasma shells, and the resulting instabilities are expected to regulate the expansion of the solar wind. The present paper combines quasilinear theory and kinetic particle-in-cell simulations in order to study the weakly nonlinear saturation of the ordinary mode in hot counter-streaming plasmas with a temperature anisotropy as a follow-up of the paper by Seough et al. [Phys. Plasmas 22, 082122 (2015)]. This instability provides a plausible mechanism for the origin of dominating, two-dimensional spectrum of transverse magnetic fluctuations observed in the solar wind. Stimulated by the differential motion of electron counterstreams the O mode instability may convert their free large-scale energy by nonlinear collisionless dissipation on plasma particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Simulation and quasilinear theory of aperiodic ordinary mode instability

The purely growing ordinary (O) mode instability driven by excessive parallel temperature anisotropy for high-beta plasmas was first discovered in the 1970s. This instability receives renewed attention because it may be applicable to the solar wind plasma. The electrons in the solar wind feature temperature anisotropies whose upper values are apparently limited by plasma instabilities. The O-mode instability may be important in this regard. Previous studies of O mode instability have been based on linear theory, but the actual solar wind electrons may be in saturated state. The present paper investigates the nonlinear saturation behavior of the O mode instability by means of one-dimensional particle-in-cell simulation and quasilinear theory. It is shown that the quasilinear method accurately reproduces the simulation results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Verification and application of resonance broadened quasi-linear (RBQ) model with multiple Alfvénic instabilities

The resonance broadened quasilinear (RBQ) model for the problem of relaxing the hot ion distribution function in constant-of-motion 3D space [Gorelenkov et al., Nucl. Fusion 58, 082016 (2018)] is presented with the self-consistent evolution of multiple Alfvén eigenmode amplitudes. The RBQ model represents the generalization of the earlier published model [Berk et al., Nucl. Fusion 35, 1661 (1995)] by carefully examining the wave particle interaction in the presence of realistic Alfvén eigenmode (AE) structures and pitch angle scattering with the help of the guiding center code ORBIT. One aspect of the generalization is that the RBQ model goes beyond the local perturbative-pendulumlike approximation for the wave particle dynamics near the resonance. An iterative procedure is introduced to account for eigenstructures varying within the resonances. It is found that a radially localized mode structure implies a saturation level 2–3 times smaller than that predicted by an earlier bump-on-tail quasilinear model that employed uniform mode structures. We apply the RBQ code to a DIII-D plasma with an elevated q-profile where the beam ion profiles exhibit stiff transport properties [Collins et al., Phys. Rev. Lett. 116, 095001 (2016)]. Finally, the properties of AE driven fast ion distribution relaxation are studied for validations of the applied RBQ model in DIII-D discharges. Initial results show that the model is robust, is numerically efficient, and can predict fast ion relaxation in present and future burning plasma experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

On a Certain First-Order Differential Equation with Delay

We consider the Cauchy problem for a first-order quasilinear differential equation with delayed argument of neutral type, and obtain sufficient conditions of existence and uniqueness of its solutions. Proofs of the solvability of nonlinear problems, estimates of solutions, and constructions of approximate methods are based on Chaplygin-type theorems on differential inequalities.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2016

Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the height of the free boundary on the density of the fluid. Self-similar continuous and discontinuous solutions are obtained for a system on a slope, and a solution is found to the initial discontinuity decay problem in this case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗