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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
NASA NTRS1992

Quasi-linear theory and transport theory

The theory of energetic particle scattering by magnetostatic fluctuations is reviewed in so far as it fails to produce the rigidity-independent mean-free-paths observed. Basic aspects of interplanetary magnetic field fluctuations are reviewed with emphasis placed on the existence of dissipation range spectra at high wavenumbers. These spectra are then incorporated into existing theories for resonant magnetostatic scattering and are shown to yield infinite mean-free-paths. Nonresonant scattering in the form of magnetic mirroring is examined and offered as a partial solution to the magnetostatic problem. In the process, mean-free-paths are obtained in good agreement with observations in the interplanetary medium at 1 AU and upstream of planetary bow shocks.

Smith, Charles W.↗
NASA NTRS1976

Cosmic-ray transport theory and out-of-the-ecliptic exploration

The reasons for studying cosmic-ray transport theory are summarized and the fundamentally three-dimensional nature of the process is pointed out. It is shown that observations in the solar ecliptic plane cannot unambiguously test transport theories since the solutions to the transport equations depend critically on boundary conditions and variation of parameters such as diffusion tensor out of the ecliptic. Sample calculations (Fokker-Planck coefficient) are shown which illustrate the problem. It is concluded that out-of-the-ecliptic observations are essential to further test transport theory.

Jokipii, J. R.↗
NASA NTRS1972

General theory of spherically symmetric boundary-value problems of the linear transport theory.

A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.

Kanal, M.↗
NASA NTRS1990

Remarks on transport theories of interplanetary fluctuations

The structure of a transport theory presented by Zhou and Matthaeus (1989), in which coupling of 'inward' and 'outward'-type fluctuations appears in the leading order, is studied. Allowance is made for the dynamic behavior of the 'fast' scale variables, which are averaged over to obtain slow-scale transport equations. The relationship of the two-scale transport models to transport models derived from the WKB approximation (Jeffreys and Jeffreys, 1980: Weinberg 1962; Dewar, 1970) as it has been applied to the solar wind MHD wave problem (Parker, 1965; Hollweg, 1973, 1974) is discussed.

Zhou, YE↗
NASA NTRS1973

Invalidity of standard perturbation techniques in cosmic ray transport theory

It is contended that the existence of particles with arbitrarily long correlation times invalidates the condition necessary for the applicability of standard perturbation techniques in cosmic ray transport theory. It is also argued that Klimas and Sandri's (1971) conclusion about a non-Markovian time development of the particle distribution is unwarranted.

Kaiser, T. B.↗
NASA NTRS1992

Reactive collision terms for fluid transport theory

A modified Bhatnagar-Gross-Krook (BGK) collision method is used for the derivation of reactive collision terms to allow for complete higher-moment approximations in fluid transport theory. The general reactive collision terms for the 8-, 10- and 13-moment approximation for binary reactions are derived. Then, reactive collision terms for specific chemistry are derived with the assumptions: (1) all reactants and products have 13-moment distribution functions; (2) simple, classical assumptions provide sufficient models for reaction dynamics; and (3) the reaction rate is energy-independent. The derived specific formulas reflect two extremes in reactive collision dynamics: direct and indirect reaction mechanisms. Finally, considerations for correct use of the reactive collision terms are discussed in the context of space plasma environments.

Eccles, J. V.↗
NASA NTRS1994

Transport theory and the WKB approximation for interplanetary MHD fluctuations

An alternative approach, based on a multiple scale analysis, is presented in order to reconcile the traditional Wentzel-Kramer-Brillouin (WKB) approach to the modeling of interplanetary fluctuations in a mildly inhomogeneous large-scale flow with a more recently developed transport theory. This enables us to compare directly, at a formal level, the inherent structure of the two models. In the case of noninteracting, incompressible (Alven) waves, the principle difference between the two models is the presence of leading-order couplings (called 'mixing effects') in the non-WKB turbulence model which are absent in a WKB development. Within the context of linearized MHD, two cases have been identified for which the leading order non-WJB 'mixing term' does not vanish at zero wavelength. For these cases the WKB expansion is divergent, whereas the multiple-scale theory is well behaved. We have thus established that the WKB results are contained within the multiple-scale theory, but leading order mixing effects, which are likely to have important observational consequences, can never be recovered in the WKB style expansion. Properties of the higher-order terms in each expansion are also discussed, leading to the conclusion that the non-WKB hierarchy may be applicable even when the scale separation parameter is not small.

Matthaeus, William H.↗
NASA NTRS1985

Relativistic transport theory for cosmic-rays

Various aspects of the transport of cosmic-rays in a relativistically moving magnetized plasma supporting a spectrum of hydromagnetic waves that scatter the cosmic-rays are presented. A local Lorentz frame moving with the waves or turbulence scattering the cosmic-rays is used to specify the individual particle momentum. The comoving frame is in general a noninertial frame in which the observer's volume element is expanding and shearing, geometric energy change terms appear in the cosmic-ray transport equation which consist of the relativistic generalization of the adiabatic deceleration term and a further term involving the acceleration vector of the scatterers. A relativistic version of the pitch angle evolution equation, including the effects of adiabatic focussing, pitch angle scattering, and energy changes is presented.

Webb, G. M.↗
NASA NTRS1989

The diffusion approximation and transport theory for cosmic rays in relativistic flows

Equations describing the transport of cosmic rays in relativistic flows in the diffusion approximation are obtained. The analysis is based on the zeroth, first, and second differential moment equations of the relativistic Boltzmann equation with a BGK collision term. A perturbation solution of the moment equations in the diffusion approximation yields both the co-moving frame particle current and viscous stresses. The resultant cosmic-ray continuity equation contains three readily recognized energy change terms: the adiabatic energy change term; the viscous shear energy change term; and a term proportional to the scalar product of the acceleration vector of the scattering frame and the heat flux.

Webb, G. M.↗
NASA NTRS1992

A review of transport theory

Ways in which energy change terms arise in the transport equation and how the various terms relate to the modes of energy exchange between the particles and plasma are shown. It is argued that the transport equation cannot be used to describe the initial acceleration of thermal particles by plasma shocks or relativistic shocks where the energetic particle speeds are never much greater than the flow speeds. In most other situations, it describes almost any acceleration process that can be caused by a moving plasma. It describes shock acceleration for both parallel shocks and oblique ones, and stochastic acceleration by the turbulent motion of the scatterers as well as by their motion across the magnetic field.

Jones, Frank C.↗
NASA NTRS1991

Transport theory for a leaf canopy of finite-dimensional scattering centers

A formalism for photon transport in leaf canopies with finite-dimensional scattering centers that cross shade mutually is developed. Starting from first principles, expressions for the interaction cross sections are derived. The problem of illumination by a monodirectional source is studied in detail using a successive collisions approach. A balance equation is formulated in R3 and the interaction between a leaf canopy and the adjacent atmosphere is discussed. Although the details are those relating to a leaf canopy, the formalism is equally applicable to other media where the constituents cross shade mutually such as planetary surfaces, rings and ridged-ice in polar regions, i.e., media that exhibit opposition brightening.

Myneni, Ranga B.↗
NASA NTRS2003

Some Remarks on GMRES for Transport Theory

We review some work on the application of GMRES to the solution of the discrete ordinates transport equation in one-dimension. We note that GMRES can be applied directly to the angular flux vector, or it can be applied to only a vector of flux moments as needed to compute the scattering operator of the transport equation. In the former case we illustrate both the delights and defects of ILU right-preconditioners for problems with anisotropic scatter and for problems with upscatter. When working with flux moments we note that GMRES can be used as an accelerator for any existing transport code whose solver is based on a stationary fixed-point iteration, including transport sweeps and DSA transport sweeps. We also provide some numerical illustrations of this idea. We finally show how space can be traded for speed by taking multiple transport sweeps per GMRES iteration. Key Words: transport equation, GMRES, Krylov subspace

Patton, Bruce W.↗