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NASA NTRS1974

Jupiter's radiation belts

Fluxes of electrons and protons in Jupiter's radiation belts are calculated with the source (radial diffusion inward from the solar wind) and the loss (synchroton radiation). The calculations are tested against the measured radio-wave wavelength distribution, the radio-wave distribution with distance from Jupiter, and the degree of polarization of the radio waves. The Fokker-Planck equation is solved by using the method of Farley and Walt (1971) with the fixed flux at the outer boundary and the zero flux at Jupiter's surface. It is found, in agreement with Brice and McDonough (1973), Jacques and Davis (1973), and Birmingham et al. (1974), that the usual magnetic and electric diffusions, which vary as L to the 10th power and L to the 6th power, respectively, are insufficient to furnish the required electrons and that the diffusion driven by ionospheric winds of Brice and McDonough is strong enough to furnish Jupiter's belts. An additional loss mechanism close to Jupiter is required to remove the electrons, particularly those at low energies.

Stansberry, K. G.↗

DOE OSTI2025

A geometric perspective on kinetic matter–radiation interaction and moment systems

Here, in this paper, we provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket approach. We discuss the interaction of kinetic theories via dissipative brackets, with our fundamental example being the coupling of matter, described by the Boltzmann equation, and radiation, described by the radiation transport equation. We explore the transition from kinetic systems to their corresponding moment systems, provide a Hamiltonian description of such moment systems, and give a geometric interpretation of the moment closure problem for kinetic theories. As an application, we discuss in detail diffusion radiation hydrodynamics as an example of a pair bracket formulation on a space of moments corresponding to kinetic matter–radiation interaction. Additionally, using the variable moment closure framework of Burby [J. W. Burby, Variable-moment fluid closures with Hamiltonian structure, Sci. Rep. 13 (2023) 18286, doi:10.1038/s41598-023-45416-5], we show how to construct Hamiltonian moment closures for kinetic transport equations with arbitrary Hamiltonian. Using this general construction, we derive novel Hamiltonian moment closures for pure radiation transport.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry↗

NASA NTRS1993

A numerical study of confined turbulent jets

A numerical investigation is reported of turbulent incompressible jets confined in two ducts, one cylindrical and the other conical with a 5 degree divergence. In each case, three Craya-Curtet numbers are considered which correspond, respectively, to flow situations with no moderate and strong recirculation. Turbulence closure is achieved by using the k-epsilon model and a recently proposed realizable Reynolds stress algebraic equation model that relates the Reynolds stresses explicitly to the quadratic terms of the mean velocity gradients and ensures the positiveness of each component of the turbulent kinetic energy. Calculations are carried out with a finite-volume procedure using boundary-fitted curvilinear coordinates. A second-order accurate, bounded convection scheme and sufficiently fine grids are used to prevent the solutions from being contaminated by numerical diffusion. The calculated results are compared extensively with the available experimental data. It is shown that the numerical methods presented are capable of capturing the essential flow features observed in the experiments and that the realizable Reynolds stress algebraic equation model performs much better than the k-epsilon model for this class of flows of great practical importance.

Zhu, J.↗

NASA NTRS1975

Theoretical investigations of plasma processes in the ion bombardment thruster

A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.

Wilhelm, H. E.↗

NASA NTRS2017

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

Full seven-equation Reynolds stress turbulence models are promising tools for today’s aerospace technology challenges. This paper examines two such models for computing challenging turbulent flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and were evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results computed using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

reynolds averaging↗

DOE OSTI2024

Classical-quantum simulation of non-equilibrium Marshak waves

In the radiation hydrodynamic simulations used to design inertial confinement fusion (ICF) and pulsed power experiments, nonlinear radiation diffusion tends to dominate CPU time. This raises the interesting question of whether a quantum algorithm can be found for nonlinear radiation diffusion which provides a quantum speedup. Recently, such a quantum algorithm was introduced based on a quantum algorithm for solving systems of nonlinear partial differential equations (PDEs) which provides a quadratic quantum speedup. Here, we apply this quantum PDE (QPDE) algorithm to the problem of a non-equilibrium Marshak wave propagating through a cold, semi-infinite, optically thick target, where the radiation and matter fields are not assumed to be in local thermodynamic equilibrium. The dynamics is governed by a coupled pair of nonlinear PDEs which are solved using the QPDE algorithm, as well as two standard PDE solvers: (i) Python's py-pde solver; and (ii) the KULL ICF simulation code developed at Lawrence-Livermore National Laboratory. We compare the simulation results obtained using the QPDE algorithm and the standard PDE solvers and find excellent agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Light transport with weak angular dependence in fog

Random scattering and absorption of light by tiny particles in aerosols, like fog, reduce situational awareness and cause unacceptable down-time for critical systems or operations. Computationally efficient light transport models are desired for computational imaging to improve remote sensing capabilities in degraded optical environments. To this end, we have developed a model based on a weak angular dependence approximation to the Boltzmann or radiative transfer equation that appears to be applicable in both the moderate and highly scattering regimes, thereby covering the applicability domain of both the small angle and diffusion approximations. An analytic solution was derived and validated using experimental data acquired at the Sandia National Laboratory Fog Chamber facility. The evolution of the fog particle density and size distribution were measured and used to determine macroscopic absorption and scattering properties using Mie theory. A three-band (0.532, 1.55, and 9.68 µ m) transmissometer with lock-in amplifiers enabled changes in fog density of over an order of magnitude to be measured due to the increased transmission at higher wavelengths, covering both the moderate and highly scattering regimes. The meteorological optical range parameter is shown to be about 0.6 times the transport mean free path length, suggesting an improved physical interpretation of this parameter.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1973

Analysis of heat transfer for a normally impinging liquid-metal slot jet

A two-dimensional liquid-metal slot jet that is impinging normally against a uniformly heated flat plate is analyzed. The distributions of wall temperature and heat-transfer coefficient are obtained as functions of position along the plate. The liquid-metal assumptions are made that the jet is inviscid and that molecular condition is dominating heat diffusion. The solution is obtained by mapping the jet flow region into a potential plane where it occupies a strip of uniform width. The energy equation is transformed into potential coordinates, and an exact solution obtained in the strip region. Conformal mapping is then used to transform the solution into the physical plane.

Siegel, R.↗

NASA NTRS1973

Ogo 6 measurements of supercooled plasma in the equatorial exosphere.

Plasma measurements performed on Ogo 6 reveal electron and ion temperature values that on occasion appear to be well below the expected neutral gas temperature. The phenomenon is observed only at night above 500 km near the magnetic equator. It is suggested that the expansion cooling of the plasma is accomplished by downward motions of the F region plasma induced by winds or diffusion, by outward E x B drift, or more probably by the upward flow of plasma during interhemisphere transport along magnetic field lines. It is also suggested that preferential cooling of electrons because of their greater thermal conductivity should tend to give ion temperatures greater than electron temperatures during the postsunset cooling of the plasmasphere when photoelectrons are absent.

Hanson, W. B.↗

NASA NTRS1976

The electron Boltzmann equation in a plasma generated by fission fragments

A Boltzmann equation formulation is presented for the determination of the electron distribution function in a plasma generated by fission fragments. The formulation takes into consideration ambipolar diffusion, elastic and inelastic collisions, recombination and ionization, and allows for the fact that the primary electrons are not monoenergetic. Calculations for He in a tube coated with fissionable material show that, over a wide pressure and neutron flux range, the distribution function is non-Maxwellian, but the electrons are essentially thermal. Moreover, about a third of the energy of the primary electrons is transferred into the inelastic levels of He. This fraction of energy transfer is almost independent of pressure and neutron flux but increases sharply in the presence of a sustainer electric field.

Hassan, H. A.↗

NASA NTRS1976

Electron distribution function in a plasma generated by fission fragments

A Boltzmann equation formulation is presented for the determination of the electron distribution function in a plasma generated by fission fragments. The formulation takes into consideration ambipolar diffusion, elastic and inelastic collisions, recombination and ionization, and allows for the fact that the primary electrons are not monoenergetic. Calculations for He in a tube coated with fissionable material shows that, over a wide pressure and neutron flux range, the distribution function is non-Maxwellian, but the electrons are essentially thermal. Moreover, about a third of the energy of the primary electrons is transferred into the inelastic levels of He. This fraction of energy transfer is almost independent of pressure and neutron flux.

Hassan, H. A.↗

NASA NTRS1981

On the origin of the MeV energy nucleon flux associated with CIRs

Measurements of recurrent enhancements of interplanetary nucleon flux in the MeV energy range are presented and interpreted. The features recur at the solar rotation period in association with stream-stream plasma interaction regions corotating with the sun. At distances from the sun less than 1 AU, the maximum intensities of the hydrogen and helium components increase with increasing distance between 300%/AU and 600%/AU. A model is proposed which predicts the acceleration of nuclei from keV plasma energies to MeV energies by means of transit time damping of magnetosonic waves as solar wind plasma flows from the sun. Numerical solutions of the transport equation are derived to demonstrate that the model does not reproduce radial variations of hydrogen and helium fluxes, and estimates are made of the radial diffusive mean free path. Finally, the observations are found to be consistent with nucleon acceleration at the CIR shocks beyond 1 AU with subsequent diffusion toward the sun.

Christon, S. P.↗

NASA NTRS1986

Effects of three-dimensional heliospheric structures on cosmic-ray modulation

The theory of cosmic-ray transport in the heliosphere contains four distinct physical processes - diffusion, convection, adiabatic cooling, and drifts. The last of these has only recently been evaluated. Extrapolation of present understanding of the regions near the heliospheric equator to high heliographic latitudes leads to the conclusion that particle drift in the large-scale magnetic field plays an important role in cosmic-ray modulation. The large-scale, three-dimensional structure of the interplanetary magnetic field is therefore very important in understanding cosmic rays. Several key observed modulation effects are summarized, each of which is a natural consequence of drift, but which requires special assumptions if drift plays no role. It is concluded that particle drifts play an important and possibly dominant role in transport in the heliosphere.

Jokipii, J. R.↗

NASA NTRS1988

A multidimensional model for aerosols - Description of computational analogs

The numerical algorithms used to simulate the advection, diffusion, sedimentation, coagulation, and condensational growth of atmospheric aerosols are described. The model can be used in one, two, or three spatial dimensions. The continuity equation in a generalized horizontal and vertical coordinate system is developed, which allows the model to be quickly adapted to a wide variety of dynamical models of global or regional scale. Algorithms are developed to treat the various physical processes, and the results of simulations are presented, which show the strengths and weaknesses of these algorithms. Although the emphasis is on the modeling of aerosols, the work is also applicable to the simulations of the transport of gases.

Toon, O. B.↗

NASA NTRS1990

Theory of Influence of a Low-Volatility, Soluble Impurity on Spherically-Symmetric Combustion of Fuel Droplets

Analyses are given for the evolution of liquid-phase mass fraction profiles and temperature during combustion of fuel droplets composed of binary miscible mixtures of low-volatility and high-volatility constituents, with small initial mass fractions of the low-volatility material, or slow introduction of low-volatility material into the liquid phase by absorption from the gas phase. The gas phase is assumed to remain quasi-steady and the liquid temperature spatially uniform. The ratio of the liquid-phase diffusion coefficient to the initial burning-rate constant is treated as a small parameter. Asymptotic analyses in this parameter are developed, and the conservation equations are integrated numerically in obtaining descriptions of the combustion history. It is shown that at the surface of the droplet a boundary layer arises in which the mass fraction of the low-volatility component increases with time. The results are used to explain qualitatively some observed conditions of flame contraction and liquid disruption in droplet combustion.

Shaw, B. D.↗

NASA NTRS1990

Influence of convection on microstructure

In eutectic growth, as the solid phases grow they reject atoms to the liquid. This results in a variation of melt composition along the solid/liquid interface. In the past, mass transfer in eutectic solidification, in the absence of convection, was considered to be governed only by the diffusion induced by compositional gradients. However, mass transfer can also be generated by a temperature gradient. This is called thermotransport, thermomigration, thermal diffusion or the Soret effect. A theoretical model of the influence of the Soret effect on the growth of eutectic alloys is presented. A differential equation describing the compositional field near the interface during unidirectional solidification of a binary eutectic alloy was formulated by including the contributions of both compositional and thermal gradients in the liquid. A steady-state solution of the differential equation was obtained by applying appropriate boundary conditions and accounting for heat flow in the melt. Following that, the average interfacial composition was converted to a variation of undercooling at the interface, and consequently to microstructural parameters. The results obtained show that thermotransport can, under certain circumstances, be a parameter of paramount importance.

Wilcox, William R.↗

NASA NTRS1992

Computer Program For Variable-Conductance Heat Pipes

VCHPDA provides accurate mathematical models of transient as well as steady-state performance of variable-conductance heat pipes over wide range of operating conditions. Applies to heat pipes with either cold, wicked or hot, nonwicked gas reservoirs and uses ideal-gas law and "flat-front" (negligible vapor diffusion) gas theory. Calculates length of gas-blocked region and temperature of vapor in active portion of heat pipe by solving set of nonlinear equations for conservation of energy and mass. Written in FORTRAN 77.

Antoniuk, D.↗