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DOE OSTI2023

Advancement of hybrid fluid-kinetic modeling for HEDP and ICF science

We report on the development progress of a hybrid fluid-kinetic code for simulating fluids and plasmas in a wide range of environments, such as laser–matter interactions, inertial confinement fusion, magnetic confinement fusion, and pulsed power. The suite of numerical tools under development utilizes heterogeneous computer architectures and leverages the benefits of particle–based simulation techniques. By working to combine the kinetic particle-in-cell (PIC) model with a particle-based fluid simulation technique, such as smoothed particle hydrodynamics, we are developing a flexible framework capable of accurately modeling complex flows within and between kinetic and fluid regimes. The TriForce code is under development as a C++ framework for parallel, 3D, particle-based, hybrid ﬂuid-kinetic plasma simulations. The ﬂuid half of TriForce will be based upon the meshless smoothed-particle-hydrodynamics (SPH) approach, well-suited for shear, mixing, and turbulence, whereas the kinetic half resembles a traditional particle-in-cell (PIC) code; other particle-based approaches to fluid modeling that do use a mesh are also possible to use and are under investigation. Maxwell’s electromagnetic field equations are solved either via explicit or implicit algorithms or approximated via resistive magnetohydrodynamics (MHD) using an Ohm’s law and resulting induction equation (extended MHD is under development). A primary goal of enabling direct comparisons, from the same code, between results from the variants of MHD and implicit electromagnetic solutions is to improve our fundamental understanding of systems with magnetic ﬁelds. The code is under development to recover results from both radiation-MHD and fully kinetic codes in those limits, and is continuing to be developed from other follow-on grants to operate in between where both descriptions may co-exist and interact. For certain applications, it is desired for a simulation to contain ﬂuid ions and electrons as well as kinetic ions and electrons. Typically, it is too computationally intensive to model a full-scale ICF or HEDP experiment fully kinetically since many cycles are expended with very small time steps on modeling the ﬂuid part of a material that is well treated by the ﬂuid approximation. In this case, many traditional PIC particles can be replaced with a single ﬂuid particle representing the thermal part of the distribution function, and there are fewer needed kinetic particles, which describe the non-thermal part and can be sub-cycled relative to the ﬂuid particle advance. Furthermore, a pure ﬂuid code may, depending on the problem, simply lack many physically important details that are beyond the scope of its reduced approximations and assumptions. In this report, we summarize the objectives achieved in the development of the collisional and kinetic half of the code, and the physics problems to which the code has been applied in the areas of advanced and innovative fusion concepts, pulsed power, and magneto-inertial fusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1994

Theoretical calculations of ion acceleration in the vicinity of comet Giacobini-Zinner

Ionization of cometary neutral molecules produces ions which are picked up by the solar wind. The cometary ion pickup process for comet Giacobini-Zinner is studied in two ways: (1) with a test particle method in which trajectories are numerically calculated for several thousand ions whose initial locations were chosen randomly with probability proportional to the neutral density and (2) with a quasi-linear diffusion model. The cometary ion distribution function was calculated with the test particle model at several locations upstream of the bow shock and for several types of magnetic fluctuations (or waves). These waves were allowed to propagate in both directions along the magnetic field at the Alfven speed. Both pitch angle scattering and energy diffusion are evident in the derived ion distributions. The monochromatic waves result in less ion acceleration than turbulent fluctuations with about the same amplitude. The calculated ion distribution functions are in reasonable agreement with the distributions measured in the vicinity of comet Giacobini-Zinner in 1985 by particle detectors on the ICE spacecraft when the ratio of power in sunward propagating Alfven waves to the power in antisunward propagating waves is assumed to lie between about 20% and 50%. However, the quasi-linear diffusion model results agree best with the measured distribution functions when the power ratio is only about 3 percent.

Mckenzie, M. L.↗

DOE OSTI2021

Velocity-Space Hybridization of Direct Simulation Monte Carlo and a Quasi-Particle Boltzmann Solver

This paper presents a new method for modeling rarefied gas flows based on hybridization of direct simulation Monte Carlo (DSMC) and discrete velocity method (DVM)-based quasi-particle representations of the velocity distribution function. It is aimed at improving the resolution of the tails of the distribution function (compared with DSMC) and computational efficiency (compared with DVM). Details of the method, such as the collision algorithm and the particle merging scheme, are discussed. The hybrid approach is applied to the study of noise in a Maxwellian distribution, computation of electron-impact ionization rate coefficient, as well as numerical simulation of a supersonic Couette flow. The hybrid-based solver is compared with pure DSMC and DVM approaches in terms of accuracy, computational speed, and memory use. It is shown that such a hybrid approach can provide a lower computational cost than a pure DVM approach, while being able to retain accuracy in modeling high-velocity tails of the distribution function. For problems where trace species have a significant impact on the flow physics, the proposed method is shown to be capable of providing better computational efficiency and accuracy compared with standard fixed-weight DSMC.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1976

Trapped particles and waves, and what can be learned from multisatellite experiments

Calculations concerning the pitch-angle diffusion resulting from resonant wave-particle interactions can lead to definitive predictions of equatorial pitch-angle distributions and rates of particle loss as a function of particle energy and L-value. Thus, given simultaneous high-altitude measurements of pitch-angle distributions and low-altitude measurements of precipitating fluxes as a function of energy and L, the importance of proposed wave-particle interactions can be verified or discarded. Since many wave-particle phenomena occur over large spatial and temporal scales, exact simultaneity in longitude and time is not necessary. Simultaneous low and high altitude (preferably nearly equatorial) particle measurements could thus greatly increase our understanding of trapped particles and their effects on the ionosphere. Furthermore, given a verified pitch-angle diffusion mechanism and simultaneous low- and high-altitude measurements, accurate lowto high-altitude mappings of field lines and magnetospheric boundaries (such as the plasmapause) could be obtained.

Lyons, L. R.↗

NASA NTRS1973

Airborne Laser Polar Nephelometer

A polar nephelometer has been developed at NCAR to measure the angular variation of the intensity of light scattered by air molecules and particles. The system has been designed for airborne measurements using outside air ducted through a 5-cm diameter airflow tube; the sample volume is that which is common to the intersection of a collimated source beam and the detector field of view within the airflow tube. The source is a linearly polarized helium-neon laser beam. The optical system defines a collimated field-of-view (0.5deg half-angle) through a series of diaphragms located behind a I72-mm focal length objective lens. A photomultiplier tube is located immediately behind an aperture in the focal plane of the objective lens. The laser beam is mechanically chopped (on-off) at a rate of 5 Hz; a two-channel pulse counter, synchronized to the laser output, measures the photomultiplier pulse rate with the light beam both on and off. The difference in these measured pulse rates is directly proportional to the intensity of the scattered light from the volume common to the intersection of the laser beam and the detector field-of-view. Measurements can be made at scattering angles from 15deg to 165deg with reference to the direction of propagation of the light beam. Intermediate angles are obtained by selecting the angular increments desired between these extreme angles (any multiple of 0.1deg can be selected for the angular increment; 5deg is used in normal operation). Pulses provided by digital circuits control a stepping motor which sequentially rotates the detector by pre-selected angular increments. The synchronous photon-counting system automatically begins measurement of the scattered-light intensity immediately after the rotation to a new angle has been completed. The instrument has been flown on the NASA Convair 990 airborne laboratory to obtain data on the complex index of refraction of atmospheric aerosols. A particle impaction device is operated simultaneously to collect particles from the same airflow tube used to make the scattered-light measurements. A size distribution function is obtained by analysis of the particles collected by the impaction device. Calculated values of the angular variation of the scattered-light intensity are obtained by applying Mie scattering theory to the observed size distribution function and assuming different values of the complex index of refraction of the particles. The calculated values are then compared with data on the actual variation of the scattered-light intensity obtained with the polar nephelometer. The most probable value of the complex refractive index is that which provides the best fit between the experimental light scattering data and the parameters calculated from the observed size distribution function.

Grams, Gerald W.↗

NASA NTRS1984

Solar-flare-induced Forbush decreases - Dependence on shock wave geometry

It is argued that the principal mechanism for the association of Forbush decreases with the passage of a solar flare shock wave is prolonged containment of cosmic ray particles behind the flare compression region, which acts as a semipermeable obstacle to particle motion along the field lines, leading to additional adiabatic cooling of the particles. Liouville's theorem is used to calculate the instantaneous distribution function at 1 AU for each particle arriving at the earth. By averaging over a large number of individual estimates, a representative estimate of the omnidirectional phase space density and the corresponding particle intensity is obtained. The energy change of individual particles at the shocks is found to be small in comparison to the energy lost by adiabatic cooling of the cosmic rays between the shock wave and the sun. The effects of particle rigidity, diffusion coefficient, and flare longitude on the magnitude of the Forbush decrease are quantitatively investigated.

Thomas, B. T.↗

NASA NTRS1992

Determining water cloud particle sizes from lidar depolarization measurements and time dependent multiple scattering coefficients

We present a technique of extracting water cloud particle size information from lidar measurements in conjunction with double scattering calculations. In this presentation, we describe the technique and give examples using data taken with the Air Force Phillips Laboratory's (Geophysics Directorate) low altitude Nd:YAG, elastic backscatter lidar. In a related presentation we describe the double scattering lidar model which we developed for this work. The technique uses simultaneous measurements of two orthogonal linear polarization components of lidar returns from water clouds or other media composed of spherical particles. Any depolarization of the incident lidar radiation backscattered by such a media can only be due to multiple scattering. The amount of depolarization is dependent on the extinction coefficient and the single scatter phase matrix, both of which are functions of position in the medium. The phase matrix is dependent on the index of refraction of the particles and the particle size distribution. Our technique is a modification of a procedure presented in Reference 1. There, particle sizes of water clouds are determined from double scattering calculations together with measurements of radiation scattered from volumes outside the lidar receiver's field of view (which can only be multiply scattered radiation). The methodology of our technique is similar but our 'probe' of the scattering phase function (and thus the particle size distribution) is different.

Garner, R. C.↗

NASA NTRS1985

Integral functions of electron lateral distribution and their fluctuations in electron-photon cascades

Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.

Ivanenko, I. P.↗

DOE OSTI2025

Approximating the particle distribution in rotating and tandem mirror traps

Steady-state distribution functions can be used to calculate stability conditions for modes, radiation energy losses and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions such as the relative speeds of different transport processes while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form ana- lytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady- state simulations outside of a narrow range of low confining potentials. We demonstrate the model’s suitability in the high confining potential regime for applications such as loss-cone stability thresholds, fusion yields and available energy.

Li, G.X.↗

DOE OSTI2025

Approximating the particle distribution in rotating and tandem mirror traps

Steady-state distribution functions can be used to calculate stability conditions for modes, radiation energy losses and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions such as the relative speeds of different transport processes while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form analytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady-state simulations outside of a narrow range of low confining potentials. We demonstrate the model’s suitability in the high confining potential regime for applications such as loss-cone stability thresholds, fusion yields and available energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1987

Variations of electron distribution functions in the solar wind

Variations of electron distribution functions in the solar wind have been investigated using the electron data observed aboard Helios 2 during the first four months of its mission in 1976 in the distance range between 0.3 and 1 AU. In particular, variations across the sector structure of the interplanetary magnetic field and across the plasma stream structures have been studied. It has been found that there is a strong correlation between the electron properties and the sector structure of the magnetic field. Within the interior of magnetic sectors the electron distribution functions are extremely anisotropic and skewed with respect to the magnetic field direction at high particle energies. Toward sector boundaries the electron distribution functions become less anisotropic and less skewed. Right at sector boundaries the electrons are relatively cool, and their distributions are nearly isotropic often showing a slight bidirectional anisotropy. These observations have been interpreted to indicate that scattering of electrons with energies above 100 eV is weak within the interior of magnetic sectors but anomalous scattering increases drastically toward sector boundaries for all energies in the halo regime up to several hundred eV. There is evidence for closed magnetic field structures, probably occurring frequently in the solar wind, where the magnetic field lines should usually be connected to the sun outside sector boundaries but may or may not be disconnected from the sun at sector boundaries.

Pilipp, W. G.↗

DOE OSTI2022

Modeling rarefied gas chemistry with QuiPS, a novel quasi-particle method

The goal of this work is to build up the capability of quasi-particle simulation (QuiPS), a novel flow solver, such that it can adequately model the rarefied portion of an atmospheric reentry trajectory. Direct simulation Monte Carlo (DSMC) is the conventional solver for such conditions, but struggles to resolve transient flows, trace species, and high-level internal energy states due to stochastic noise. Quasi-particle simulation (QuiPS) is a novel Boltzmann solver that describes a system with a discretized, truncated velocity distribution function. The resulting fixed-velocity, variable weight quasi-particles enable smooth variation of macroscopic properties. The distribution function description enables the use of a variance-reduced collision model, greatly minimizing expense near equilibrium. This work presents the addition of a neutral air chemistry model to QuiPS and some demonstrative 0D simulations. The explicit representation of internal distributions in QuiPS reveals some of the flaws in existing physics models. Overall, variance reduction, a key feature of QuiPS, can greatly reduce expense of multi-dimensional calculations, but is only cheaper when the gas composition is near chemical equilibrium.

42 ENGINEERING↗

NASA NTRS1988

Precision cleaning methods for spacecraft applications

A small CO2 snow cleaning apparatus to clean both molecular films and particles from small and large components and surfaces was constructed. Various types of surfaces were cleaned using the CO2 technique. Vacuum deposited and sputtered metallic coatings such as germanium, aluminum, and silver and silicon wafers, and polished copper conical mirrors were purposely contaminated with everyday aerospace contaminants, including particle fallout and fingerprints. Precleaning characterization by Bidirectional Reflectance Distribution Function (BRDF), ellipsometry, nonvolatile residue, and microscopic particle evaluation served as evaluation of cleaning efficiency. Good results were obtained in trial application.

Ryan, L. E.↗

NASA NTRS1990

A computationally efficient model for turbulent droplet dispersion in spray combustion

A novel model for turbulent droplet dispersion is formulated having significantly improved computational efficiency in comparison to the conventional point source stochastic sampling methodology. In the proposed model, a computational parcel representing a group of physical particles is considered to have a normal (Gaussian) probability density function (PDF) in three-dimensional space. The mean of each PDF is determined by Lagrangian tracking of each computational parcel, either deterministically or stochastically. The variance is represented by a turbulence-induced mean squared dispersion which is based on statistical inferences from the linearized direct modeling formulation for particle/eddy interactions. Convolution of the computational parcel PDF's produces a single PDF for the physical particle distribution profile. The validity of the new model is established by comparison with the conventional stochastic sampling method, where in each parcel is represented by a delta function distribution, for non-evaporating particles injected into simple turbulent air flows.

Litchford, Ron J.↗

NASA NTRS1980

Distribution function representation of energy spectra of H, He, C, O and Fe in corotating particle streams

From an analysis of nine corotating events observed near 1 AU during the 1974-1976 solar minimum, the spectral parameters for H, He, C, O and Fe and relative abundances of these elements and of Ne, Mg, Si, and S-Ca were determined. The distribution functions of H, He, O and Fe are well represented by an exponential in particle speed over the energy range of the measurements from 0.3 to 5 MeV/nucleon. The composition resembles that of the solar corona, particularly in the O/C ratio which is 0.95 + or - 0.19, and the He/H and He/Ne ratios are similar to the respective ratios in the solar wind. The results are consistent with interplanetary statistical acceleration of these particles out of the high-energy tail of the high-speed solar wind.

Gloeckler, G.↗

DOE OSTI2020

A velocity space hybridization-based Boltzmann equation solver

In the present research, a new method for simulation of rarefied gas flows is proposed, a velocity-space hybrid of both a DSMC representation of particles and a discrete velocity quasi-particle representation of the distribution function. The hybridization scheme is discussed in detail, and is numerically verified for two test-cases: the BKW relaxation problem and a stationary Maxwellian distribution. It is demonstrated that such a velocity-space hybridization can provide computational benefits when compared to a pure discrete velocity method or pure DSMC approach, while retaining some of the more attractive properties of discrete velocity methods. Further possible improvements to the velocity-space hybrid approach are discussed.

97 MATHEMATICS AND COMPUTING↗

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 OSTI2024

Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas

We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The equilibrium system comprises a Grad–Shafranov partial differential equation and an integral equation. These equations can be utilized to calculate the equilibrium magnetic field and ion distribution function, respectively, for given particle density or given ion and electron toroidal current density profiles. The resulting solutions describe states characterized by toroidal plasma rotation and toroidal electric current density. Additionally, due to the presence of fluid electrons, these equilibria also exhibit a poloidal current density component. This is in contrast to the fully kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate toroidal currents and flows, given the absence of a third integral of the microscopic motion.

Physics↗