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DOE OSTI2021

Collisional effects on resonant particles in quasilinear theory

A careful examination of the effects of collisions on resonant wave-particle interactions leads to an alternate interpretation and deeper understanding of the quasilinear operator originally formulated by Kennel and Engelmann (Phys. Fluids vol. 9, 1966, pp. 2377- 2388) for collisionless, magnetized plasmas, and widely used to model radio frequency heating and current drive. The resonant and nearly resonant particles are particularly sensitive to collisions that pitch angle scatter them out of and into resonance. As a result, the resonant particle-wave interactions occur in the center of a narrow collisional boundary when the collision frequency nu is very small compared to the wave frequency omega. The diffusive nature of the pitch angle scattering combined with the wave-particle resonance condition enhances the collision frequency by (omega/nu)2/3 >>1, resulting in an effective resonant particle collision time of tau_int ~ (nu /omega)2/3 nu <<1/ nu . A rigorous collisional boundary layer analysis generalizes the standard quasilinear operator to a form that is fully consistent with Kennel-Englemann, but allows replacing the delta function appearing in the diffusivity with a simple integral (having the appropriate delta function limit) retaining the new physics associated with the narrow boundary layer, while preserving the entropy production principle. The limitations of the collisional boundary layer treatment are also estimated, and indicate that substantial departures from Maxwellian are not permitted.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Multilevel Convergence Analysis of Multigrid-Reduction-in-Time

This study presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time-stepping operator, analyzed directly and bounded in the norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time-stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge--Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge--Kutta schemes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Improving Wind Energy Forecasting through Numerical Weather Prediction Model Development

The primary goal of the Second Wind Forecast Improvement Project (WFIP2) is to advance the state-of-the-art of wind energy forecasting in complex terrain. To achieve this goal, a comprehensive 18-month field measurement campaign was conducted in the region of the Columbia River basin. The observations were used to diagnose and quantify systematic forecast errors in the operational High-Resolution Rapid Refresh (HRRR) model during weather events of particular concern to wind energy forecasting. Examples of such events are cold pools, gap flows, thermal troughs/marine pushes, mountain waves, and topographic wakes. WFIP2 model development has focused on the boundary layer and surface-layer schemes, cloud–radiation interaction, the representation of drag associated with subgrid-scale topography, and the representation of wind farms in the HRRR. Additionally, refinements to numerical methods have helped to improve some of the common forecast error modes, especially the high wind speed biases associated with early erosion of mountain–valley cold pools. This study describes the model development and testing undertaken during WFIP2 and demonstrates forecast improvements. Specifically, WFIP2 found that mean absolute errors in rotor-layer wind speed forecasts could be reduced by 5%–20% in winter by improving the turbulent mixing lengths, horizontal diffusion, and gravity wave drag. The model improvements made in WFIP2 are also shown to be applicable to regions outside of complex terrain. Ongoing and future challenges in model development will also be discussed.

17 WIND ENERGY↗

NASA NTRS2011

Towards Simulating a Realistic Planetary Seismic Wavefield: The Contribution of the Megaregolith and Low-Velocity Waveguides

Lunar seismograms are distinctly different from their terrestrial counterparts. The Apollo lunar seismometers recorded moonquakes without distinct P- or S-wave arrivals; instead waves arrive as a diffuse coda that decays over several hours making the identification of body waves difficult. The unusual character of the lunar seismic wavefield is generally tied to properties of the megaregolith: it consists of highly fractured and broken crustal rock, the result of extensive bombardment of the Moon. The megaregolith extends several kilometers into the lunar crust, possibly into the mantle in some regions, and is covered by a thin coating of fine-scale dust. These materials possess very low seismic velocities that strongly scatter the seismic wavefield at high frequencies. Directly modeling the effects of the megaregolith to simulate an accurate lunar seismic wavefield is a challenging computational problem, owing to the inherent 3-D nature of the problem and the high frequencies (greater than 1 Hz) required. Here we focus on modeling the long duration code, studying the effects of the low velocities found in the megaregolith. We produce synthetic seismograms using 1-D slowness integration methodologies, GEMINI and reflectivity, and a 3-D Cartesian finite difference code, Wave Propagation Program, to study the effect of thin layers of low velocity on the surface of a planet. These codes allow us generate seismograms with dominant frequencies of approximately 1 Hz. For background lunar seismic structure we explore several models, including the recent model of Weber et al., Science, 2011. We also investigate variations in megaregolithic thickness, velocity, attenuation, and seismogram frequency content. Our results are compared to the Apollo seismic dataset, using both a cross correlation technique and integrated envelope approach to investigate coda decay. We find our new high frequency results strongly support the hypothesis that the long duration of the lunar seismic codes is generated by the presence of the low velocity megaregolith, and that the diffuse arrivals are a combination of scattered energy and multiple reverberations within this layer. The 3-D modeling indicates the extreme surface topography of the Moon adds only a small contribution to scattering effects, though local geology may play a larger role. We also study the effects of the megaregolith on core reflected and converted phases and other body waves. Our analysis indicates detection of core interacting arrivals with a polarization filter technique is robust and lends the possibility of detecting other body waves from the Moon.

Schmerr, Nicholas C.↗

NASA NTRS1983

Plasmapause diffusion

The Bohm diffusion coefficient and observed electrostatic wave scattering are used as the bases of estimates of the smoothing effect that diffusion may have on steep plasmapause density gradients. The estimate for diffusion resulting from scattering by observed electrostatic waves is found to be much lower than that of the perpendicular Bohm diffusion coefficient for characteristic plasma temperatures and magnetic fields. This diffusion rate estimate may be too small, however, if the wave amplitudes are significantly higher for steep plasmapauses. The effects are therefore negligible for most considerations of macroscopic plasmapause dynamics, but may be significant in limiting drift wave instabilities and similar phenomena driven by the steepness of the plasmapause density gradient.

Horwitz, J. L.↗

DOE OSTI2025

jaxhps: An elliptic PDE solver built with machine learning in mind

Elliptic partial differential equations (PDEs) can model many physical phenomena, such as electrostatics, acoustics, wave propagation, and diffusion. In scientific machine learning settings, a high-throughput PDE solver may be required to generate a training dataset, run in the inner loop of an iterative algorithm, or interface directly with a deep neural network. To provide value to machine learning users, such a PDE solver must be compatible with standard automatic differentiation frameworks, scale efficiently when run on graphics processing units (GPUs), and maintain high accuracy for a large range of input parameters. We have designed the jaxhps package with these use-cases in mind by implementing a highly efficient and accurate solver for elliptic problems with native hardware acceleration and automatic differentiation support.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1968

Quasilinear theory of resonant diffusion in a magnetoactive, relativistic plasma.

Quasi-linear behavior of collisionless relativistic plasma in uniform magnetic field, discussing resonant diffusion and turbulent waves effects

Lerche, I.↗

NASA NTRS1983

The relationship between Saturn kilometric radiation and the solar wind

Voyager spacecraft radio, interplanetary plasma, and interplanetary magnetic field data are used to show that large amplitude fluctuations in the power generated by the Saturn kilometric radio emission are best correlated with solar wind ram pressure variation. In all, thirteen solar wind quantities previously found important in driving terrestrial magnetospheric substorms and other auroral processes were examined for evidence of correlations with the Saturn radio emission. The results are consistent with hydromagnetic wave or eddy diffusion processes driven by large scale solar wind pressure changes at Saturn's dayside magnetopause.

Desch, M. D.↗

NASA NTRS1983

The relationship between Saturn kilometric radiation and the solar wind

Desch, M. D.↗

NASA NTRS1984

A detailed X-ray and radio comparison of Kepler's supernova remnant

High-resolution radio images of Kepler's SNR (SNR (SN 1604) at 6 and 21 cm have been obtained using the VLA. The orientation of linear polarization in the SNR implies a substantial nonrandom radial component for the magnetic field of the remnant. Based on a new X-ray picture of the SNR, obtained using the Einstein Observatory, a detailed comparison of the X-ray and radio morphology is carried out. There is a good correlation between rotation measure, obtained from the radio maps, and emission measure, an X-ray-derived quantity in the SNR shell. From the mean electron density value infered from an analysis of X-ray fluxes, a mean radial magnetic field of 14 micro G and a total magnetic field of 70 microG are estimated. The energy density of relativistic electrons in Kepler's SNR in the shell comparable to the energy density in the magnetic field; the relativistic electron-pressure is 2 percent of the thermal gas pressure. The strong correlation between radio emissivity and X-ray emissivity found over the SNR in somewhat large scale can be ascribed to acceleration of thermal electrons at the shock wave and insignificant diffusion of resultant relativistic electrons.

Matsui, Y.↗

NASA NTRS1986

Applications of a Venus thermospheric circulation model

A variety of Pioneer Venus observations suggest a global scale, day-to-night Venus thermospheric circulation. Model studies of the dynamics and energetics of the Venus thermosphere are presented in order to address new driving, mixing and cooling mechanisms for an improved model simulation. The adopted approach was to reexamine the circulation by first using a previous two dimensional code to quantify those physical processes which can be inferred from the Pioneer Venus observations. Specifically, the model was used to perform sensitivity studies to determine the degree to which eddy cooling, eddy or wave drag, eddy diffusion and 15 micrometer radiational cooling are necessary to bring the model temperature and composition fields into agreement with observations. Three EUV heating cases were isolated for study. Global temperature and composition fields in good agreement with Pioneer data were obtained. Large scale horizontal winds 220 m/s were found to be consistent with the observed cold nightside temperatures and dayside bulges of O, CO and CO2. Observed dayside temperatures were obtained by using a 7 to 19% EUV heating efficiency profile. The enhanced 15 micrometer cooling needed for thermal balance is obtained using the best rate coefficient available for atomic O collisional excitation of CO2(0,1,0). Eddy conduction was not found to be a viable cooling mechanism due to the weakened global circulation. The strong 15 micrometer damping and low EUV efficiency imply a very weak dependence of the general circulation to solar cycle variability. The NCAR terrestrial thermospheric general circulation model was adapted for Venus inputs using the above two dimensional model parameters, to give a three dimensional benchmark for future Venus modelling work.

Bougher, S. W.↗

NASA NTRS1987

The physics of interstellar shock waves

This review discusses the observations and theoretical models of interstellar shock waves, in both diffuse cloud and molecular cloud environments. It summarizes the relevant gas dynamics, atomic, molecular and grain processes, radiative transfer, and physics of radiative and magnetic precursors in shock models. It then describes the importance of shocks for observations, diagnostics, and global interstellar dynamics. It concludes with current research problems and data needs for atomic, molecular and grain physics.

Shull, J. Michael↗

NASA NTRS1988

Computer simulation of the Farley-Buneman instability and anomalous electron heating in the auroral ionosphere

The nonlinear saturation of the Farley-Buneman instability in a collisional plasma is studied by a 2 1/2 dimensional electrostatic particle simulation which includes inelastic and elastic collisions of electrons and elastic collision of ions with neutrals. In the simulation, a uniform convection electric field is applied externally so that the relative velocity between the electrons and ions is greater than the ion sound speed and destabilizes the instability. A nonlinear frequency shift from higher to lower frequencies and diffusion of the wave spectrum in two dimensional wave number space are found. It is found that the dominant mechanism for electron heating is due to an enhanced effective electron collision frequency and hence enhanced resistive heating as suggested by Primdahl (1986) and not due to the heating of electrons by the electric field of the waves parallel to the magnetic field. For the ionospheric conditions discussed by Schlegel and St.-Maurice (1981)an anomalous heating rate of about 4 x 10 to the 7th W/cu cm is found.

Machida, S.↗

NASA NTRS1989

A space-time discretization procedure for wave propagation problems

Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.

Davis, Sanford↗

NASA NTRS1990

Electron acceleration by magnetosonic waves in solar flares

Results of a simulation of electron acceleration by magnetosonic waves in a solar coronal loop are presented. The dependence of the energization rate on the strength and shape of the wave spectrum is discussed. Comparisons are made with the predictions of quasilinear theory and of a model describing stochastic acceleration by waves as isotropic diffusion in momentum space.

Zweibel, Ellen G.↗

NASA NTRS1999

Influence of Transport on Two-Dimensional Model Simulation. Tracer Sensitivity to 2-D Model Transport: Long Lived Tracers - 1

In this study, we examine the sensitivity of long lived tracers to changes in the base transport components in our 2-D model. Changes to the strength of the residual circulation in the upper troposphere and stratosphere and changes to the lower stratospheric K(sub zz) had similar effects in that increasing the transport rates decreased the overall stratospheric mean age, and increased the rate of removal of material from the stratosphere. Increasing the stratospheric K(sub yy) increased the mean age due to the greater recycling of air parcels through the middle atmosphere, via the residual circulation, before returning to the troposphere. However, increasing K(sub yy) along with self-consistent increases in the corresponding planetary wave drive, which leads to a stronger residual circulation, more than compensates for the K(sub yy)-effect, and produces significantly younger ages throughout the stratosphere. Simulations with very small tropical stratospheric K(sub yy) decreased the globally averaged age of air by as much as 25% in the middle and upper stratosphere, and resulted in substantially weaker vertical age gradients above 20 km in the extratropics. We found only very small stratospheric tracer sensitivity to the magnitude of the horizontal mixing across the tropopause, and to the strength of the mesospheric gravity wave drag and diffusion used in the model. We also investigated the transport influence on chemically active tracers and found a strong age-tracer correlation, both in concentration and calculated lifetimes. The base model transport gives the most favorable overall comparison with a variety of inert tracer observations, and provides a significant improvement over our previous 1995 model transport. Moderate changes to the base transport were found to provide modest agreement with some of the measurements. Transport scenarios with residence times ranging from moderately shorter to slightly longer relative to the base case simulated N2O lifetimes that were within the observational estimates of Volk et al. [1997]. However, only scenarios with rather fast transport rates were comparable with the Volk et al. estimates of CFCl3 lifetimes. This is inconsistent with model-measurement comparisons of mean age in which the base model or slightly slower transport rates compared the most favorably with balloon SF6 data. For all comparisons shown, large transport changes away from the base case resulted in simulations that were outside the range of measurements, and in many cases, far outside this range.

Fleming, Eric L.↗

NASA NTRS2000

Discrete and Diffuse Aurora During Varying Activity Levels: Simultaneous Fast and Polar UVI Observations

We examine simultaneous measurements of auroral electron precipitation obtained in-situ by the FAST spacecraft and remotely by Polar Ultraviolet Imagery (UVI) images for activity levels ranging from quiet to storm-time intervals. The incident energy flux measured by FAST and inferred from the UVI images agree well during quiescent periods, particularly in regions of discrete aurora in which the electron precipitation spectra are dominated by the component accelerated by a field-aligned potential. During magnetospheric substorms and active storm periods, such as those following Coronal Mass Ejection (CME) disturbances of the magnetosphere, the energy flux inferred from the UVI images generally exceeds that measured locally by FAST at the same location by as much as an order of magnitude. The auroral electrons during these active periods are dominated by diffuse precipitation which is observed up the to the highest energy channel of FAST (30 keV). These storm-time observations imply that a high energy component above 30 keV not observed by FAST may be contributing significantly to the total energy flux carried by the precipitating electrons. Observations suggest that as magnetospheric activity increases acceleration processes in the magnetosphere and pitch-angle diffusion by wave-particle interactions become more important than the ionospheric acceleration in producing the measured auroral energy fluxes.

Chua, D.↗

NASA NTRS2011

Rapid Rebuilding of the Outer Radiation Belt

Recent observations by the radiation monitor (RDM) on the spacecraft Akebono have shown several cases of greater than 2.5 MeV radiation belt electron enhancements occurring on timescales of less than a few hours. Similar enhancements are also seen in detectors on board the NOAA/POES and TWINS 1 satellites. These intervals are shorter than typical radial diffusion or wave-particle interactions can account for. We choose two so-called "rapid rebuilding" events that occur during high speed streams (4 September 2008 and 22 July 2009) and simulated them with the Space Weather Modeling Framework configured with global magnetosphere, radiation belt, ring current, and ionosphere electrodynamics model. Our simulations produce a weaker and delayed dipolarization as compared to observations, but the associated inductive electric field in the simulations is still strong enough to rapidly transport and accelerate MeV electrons resulting in an energetic electron flux enhancement that is somewhat weaker than is observed. Nevertheless, the calculated flux enhancement and dipolarization is found to be qualitatively consistent with the observations. Taken together, the modeling results and observations support the conclusion that storm-time dipolarization events in the magnetospheric magnetic field result in strong radial transport and energization of radiation belt electrons.

Glocer, A.↗