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Results for “Boltzmann Transport Equation”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Charged-particle transport in one dimension

A numerical solution to high-energy charged-particle transport is found by evaluation of the integral equations obtained by inverting the Boltzmann differential operator. An algorithm has been written for either continuous or discrete spectra at the boundary, which allows efficient and accurate evaluation of this rather complicated problem. Present results are compared with analytic solutions based on the perturbation theory.

NASA Discipline Radiation Health↗
NASA NTRS1991

The linear Boltzmann equation in slab geometry - Development and verification of a reliable and efficient solution

The linear Boltzmann equation can be cast in a form mathematically identical to the radiation-transport equation. A multigroup procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative-transfer problem, and existing software is used to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well-suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of the formalism to include external forces and spherical geometry are also feasible.

Stamnes, K.↗
NASA NTRS1983

The composition, propagation and acceleration of energetic solar particles - A review of United States research 1979-1982

The present review has the objective to cover major developments in American research related to solar energetic particles, both observational and theoretical, taking into account the period from late 1978 to late 1982. It is pointed out that particular progress has been made in the area of solar energetic particle composition with respect to elemental, isotopic, and the distribution of charge states. This progress is primarily the result of improved instrumentation available at a time of higher solar activity. An important aspect of solar particle studies is to understand the propagation of particles from the vicinity of the sun through interplanetary space to wherever the observing instruments are located. Almost all mathematical models for the transport of solar cosmic rays are derived in some sense from the same general Boltzmann or Vlasov equations. Attention is also given to advances related to an understanding of coronal propagation, and acceleration and injection processes.

Mcguire, R. E.↗
NASA NTRS1988

BRYNTRN: A baryon transport computer code, computation procedures and data base

The development is described of an interaction data base and a numerical solution to the transport of baryons through the arbitrary shield material based on a straight ahead approximation of the Boltzmann equation. The code is most accurate for continuous energy boundary values but gives reasonable results for discrete spectra at the boundary with even a relatively coarse energy grid (30 points) and large spatial increments (1 cm in H2O).

Wilson, John W.↗
NASA NTRS1989

BRYNTRN: A baryon transport model

The development of an interaction data base and a numerical solution to the transport of baryons through an arbitrary shield material based on a straight ahead approximation of the Boltzmann equation are described. The code is most accurate for continuous energy boundary values, but gives reasonable results for discrete spectra at the boundary using even a relatively coarse energy grid (30 points) and large spatial increments (1 cm in H2O). The resulting computer code is self-contained, efficient and ready to use. The code requires only a very small fraction of the computer resources required for Monte Carlo codes.

Wilson, John W.↗
NASA NTRS2017

Tortuosity Computations of Porous Materials using the Direct Simulation Monte Carlo

Low-density carbon fiber preforms, used as thermal protection systems (TPS) materials for planetary entry systems, have permeable, highly porous microstructures consisting of interlaced fibers. Internal gas transport in TPS is important in modeling the penetration of hot boundary-layer gases and the in-depth transport of pyrolysis and ablation products. The gas effective diffusion coefficient of a porous material must be known before the gas transport can be modeled in material response solvers; however, there are very little available data for rigid fibrous insulators used in heritage TPS.The tortuosity factor, which reflects the efficiency of the percolation paths, can be computed from the effective diffusion coefficient of a gas inside a porous material and is based on the micro-structure of the material. It is well known, that the tortuosity factor is a strong function of the Knudsen number. Due to the small characteristic scales of porous media used in TPS applications (typical pore size of the order of 50 micron), the transport of gases can occur in the rarefied and transitional regimes, at Knudsen numbers above 1. A proper way to model the gas dynamics at these conditions consists in solving the Boltzmann equation using particle-based methods that account for movement and collisions of atoms and molecules.In this work we adopt, for the first time, the Direct Simulation Monte Carlo (DSMC) method to compute the tortuosity factor of fibrous media in the rarefied regime. To enable realistic simulations of the actual transport of gases in the porous medium, digitized computational grids are obtained from X-ray micro-tomography imaging of real TPS materials. The SPARTA DSMC solver is used for simulations. Effective diffusion coefficients and tortuosity factors are obtained by computing the mean-square displacement of diffusing particles.We first apply the method to compute the tortuosity factors as a function of the Knudsen number for computationally designed materials such as random cylindrical fibers and packed bed of spheres with prescribed porosity. Results are compared to literature values obtained using random walk methods in the rarefied and transitional regime and a finite-volume method for the continuum regime. We then compute tortuosity factors for a real carbon fiber material with a transverse isotropic structure (FiberForm), quantifying differences between through-thickness and in-plain tortuosities at various Knudsen regimes.

Tortuosity↗
NASA NTRS1976

Deviation from a Maxwellian velocity distribution in regions of interstellar molecular hydrogen

The deviation from a Maxwellian velocity distribution caused by excitation of the J = 2 rotational level of parahydrogen (followed by radiative decay) in a molecular hydrogen gas is investigated. It is noted that inelastic collisions deplete the high-velocity tail of the distribution, while elastic collisions tend to refill it; the resulting steady-state distribution has a small depletion in the tail which slightly reduces the cooling rate of the gas. The elastic-collision transport is approximated by a continuous process, a simplified expression is obtained for the inelastic-collision operator, and the Boltzmann equation is then solved analytically. A correction to the inelastic-collision rate is evaluated, and it is found that the relative magnitude of the effect of tail depletion on the inelastic-collision rate is strongly temperature-dependent. The critical molecular density above which the J = 2 level deexcites by superelastic collisions is shown to be a weak function of temperature.

Gould, R. J.↗
NASA NTRS1979

Ion velocity distributions in the high-latitude ionosphere

The theory and observations relating to ion velocity distributions in the high-latitude F region are reviewed. The review covers three basic aspects, including methods for calculating ion velocity distributions, experimental evidence for the existence of non-Maxwellian ion velocity distributions, and the ionospheric consequences of non-Maxwellian distributions. Specific topics covered include closed form solutions to Boltzmann's equation for a simple collision model, series solutions to the Boltzmann equation for more general collision models, retarding potential analyzer measurements, excitation of VLF electrostatic emissions, ion-neutral reaction rates, and transport effects.

St-Maurice, J.-P.↗
NASA NTRS1993

Calculations of cosmic-ray helium transport in shielding materials

The transport of galactic cosmic-ray helium nuclei and their secondaries through bulk shielding is considered using the straight-ahead approximation to the Boltzmann equation. A data base for nuclear interaction cross sections and secondary particle energy spectra for high-energy light-ion breakup is presented. The importance of the light ions H-2, H-3, and He-3 for cosmic-ray risk estimation is discussed, and the estimates of the fractional contribution to the neutron flux from helium interactions compared with other particle interactions are presented using a 1977 solar minimum cosmic-ray spectrum.

Cucinotta, Francis A.↗
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 NTRS2003

Particle Size Distributions in Atmospheric Clouds

In this note, we derive a transport equation for a spatially integrated distribution function of particles size that is suitable for sparse particle systems, such as in atmospheric clouds. This is done by integrating a Boltzmann equation for a (local) distribution function over an arbitrary but finite volume. A methodology for evolving the moments of the integrated distribution is presented. These moments can be either tracked for a finite number of discrete populations ('clusters') or treated as continuum variables.

Paoli, Roberto↗
NASA NTRS1993

The telegraph equation in charged particle transport

We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

Gombosi, T. I.↗
NASA NTRS1988

Preshock region acceleration of implanted cometary H(+) and O(+)

A self-consistent, three-fluid model of plasma transport and implanted ion acceleration in the unshocked solar wind is presented. The solar wind plasma is depleted by charge exchange with the expanding cometary exosphere, while implanted protons and heavy ions are produced by photoionization and charge transfer and lost by charge exchange. A generalized transport equation describing convection, adiabatic and diffusive velocity change, and the appropriate production terms is used to describe the evolution of the two cometary ion components, while the moments of the Boltzmann equation are used to calculate the solar wind density and pressure. The flow velocity is obtained self-consistently by combining the conservation equations of the three ion species. The results imply that second-order Fermi acceleration can explain the implanted spectra observed in the unshocked solar wind. Comparison of measured and calculated distribution indicates that spatial diffusion of implanted ions probably plays an important role in forming the energetic particle environment in the shock vicinity.

Gombosi, Tamas I.↗
NASA NTRS1997

Generalized Kinetic Description of Steady-State Collisionless Plasmas

We present a general solution to the collisionless Boltzmann (Vlasov) equation for a free-flowing plasma along a magnetic field line using Liouville's theorem, allowing for an arbitrary potential structure including non-monotonicities. The constraints of the existing collisionless kinetic transport models are explored, and the need for a more general approach to the problem of self- consistent potential energy calculations is described. Then a technique that handles an arbitrary potential energy distribution along the field line is presented and discussed. For precipitation of magnetospherically trapped hot plasma, this model yields moment calculations that vary by up to a factor of two for various potential energy structures with the same total potential drop. The differences are much greater for the high-latitude outflow scenario, giving order of magnitude variations depending on the shape of the potential energy distribution.

Khazanov, G. V.↗
NASA NTRS2000

An Improved Elastic and Nonelastic Neutron Transport Algorithm for Space Radiation

A neutron transport algorithm including both elastic and nonelastic particle interaction processes for use in space radiation protection for arbitrary shield material is developed. The algorithm is based upon a multiple energy grouping and analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. The algorithm is then coupled to the Langley HZETRN code through a bidirectional neutron evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for an aluminum water shield-target configuration is then compared with MCNPX and LAHET Monte Carlo calculations for the same shield-target configuration. With the Monte Carlo calculation as a benchmark, the algorithm developed in this paper showed a great improvement in results over the unmodified HZETRN solution. In addition, a high-energy bidirectional neutron source based on a formula by Ranft showed even further improvement of the fluence results over previous results near the front of the water target where diffusion out the front surface is important. Effects of improved interaction cross sections are modest compared with the addition of the high-energy bidirectional source terms.

Clowdsley, Martha S.↗
NASA NTRS1975

Theory of photoelectron thermalization and transport in the ionosphere

A new theoretical approach for calculating the equilibrium photoelectron flux energy and pitch angle distribution in the ionosphere is presented. Photoelectron transport, secondary electron production, and energy degradation by the excitation of the discrete energy states of the neutral atmospheric constituents and by continuous energy transfer to the ambient thermal electron gas are included in a manner consistent with the Boltzmann equation which constitutes the foundation of the theory. A difference equation, suitable for numerical solution, is given, and a numerical method for the solution of this equation is discussed in detail.

Mantas, G. P.↗
NASA NTRS1973

Composition dependence of ion transport coefficients in gas mixtures

A simple momentum-transfer theory for the composition dependence of ion mobilities and diffusion coefficients in gas mixtures at arbitrary field strengths is corrected, extended, and compared with a similar theory based on momentum and energy transfer, and with results based on direct solution of the Boltzmann equation by Kihara's method. Final equations are recommended for predicting composition dependences, given only results on ion mobilities and diffusion coefficients in the pure component gases.

Whealton, J. H.↗
NASA NTRS1974

Composition dependence of ion-transport coefficients in gas mixtures

Simple momentum-transfer theory for the composition dependence of ion mobilities and diffusion coefficients in gas mixtures at arbitrary field strengths is corrected and extended, and compared with a similar theory based on momentum and energy transfer, and with results based on direct solution of the Boltzmann equation by Kihara's method. Final equations are recommended for predicting composition dependences, given only results on ion mobilities and diffusion coefficients in the pure component gases.

Whealton, J. H.↗