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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Solid state photomultiplier for astronomy, phase 2

Epitaxial layers with varying donor concentration profiles were grown on silicon substrate wafers using chemical vapor deposition (CVD) techniques, and solid state photomultiplier (SSPM) devices were fabricated from the wafers. Representative detectors were tested in a low background photon flux, low temperature environment to determine the device characteristics for comparison to NASA goals for astronomical applications. The SSPM temperatures varied between 6 and 11 K with background fluxes in the range from less than 5 x 10 to the 6th power to 10 to the 13th power photons/square cm per second at wavelengths of 3.2 and 20 cm. Measured parameters included quantum efficiency, dark count rate and bias current. Temperature for optimal performance is 10 K, the highest ever obtained for SSPMs. The devices exhibit a combination of the lowest dark current and highest quantum efficiency yet achieved. Experimental data were reduced, analyzed and used to generate recommendations for future studies. The background and present status of the microscopic theory of SSPM operation were reviewed and summarized. Present emphasis is on modeling of the avalanche process which is the basis for SSPM operation. Approaches to the solution of the Boltzmann transport equation are described and the treatment of electron scattering mechanisms is presented. The microscopic single-electron transport theory is ready to be implemented for large-scale computations.

Besser, P. J.↗
NASA NTRS1991

Computer aided radiation analysis for manned spacecraft

In order to assist in the design of radiation shielding an analytical tool is presented that can be employed in combination with CAD facilities and NASA transport codes. The nature of radiation in space is described, and the operational requirements for protection are listed as background information for the use of the technique. The method is based on the Boeing radiation exposure model (BREM) for combining NASA radiation transport codes and CAD facilities, and the output is given as contour maps of the radiation-shield distribution so that dangerous areas can be identified. Computational models are used to solve the 1D Boltzmann transport equation and determine the shielding needs for the worst-case scenario. BREM can be employed directly with the radiation computations to assess radiation protection during all phases of design which saves time and ultimately spacecraft weight.

Appleby, Matthew H.↗
NASA NTRS2005

An Algorithm for the Transport of Anisotropic Neutrons

One major obstacle to human space exploration is the possible limitations imposed by the adverse effect of long-term exposure to the space environment. Even before human spaceflight began, the potentially brief exposure of astronauts to the very intense random solar particle events (SPE) were of great concern. A new challenge appears in deep space exploration from exposure to the low-intensity heavy-ion flux of the galactic cosmic rays (GCR) since the missions are of long duration and the accumulated GCR exposures can be high. Because cancer induction rates increase behind low to rather large thicknesses of aluminum shielding, according to available biological data on mammalian exposures to GCR like ions, the shield requirements for a Mars mission are prohibitively expensive in terms of mission launch costs. Therefore, a critical issue in the Human Exploration and Development of Space enterprise is cost effective mitigation of risk associated with ionizing radiation exposure. In order to estimate astronaut risk to GCR exposure and associated cancer risks and health hazards, it is necessary to do shield material studies. To determine an optimum radiation shield material it is necessary to understand nuclear interaction processes such as fragmentation and secondary particle production which is a function of energy dependent cross sections. This requires knowledge of material transmission characteristics either through laboratory testing or improved theoretical modeling. Here ion beam transport theory is of importance in that testing of materials in the laboratory environment generated by particle accelerators is a necessary step in materials development and evaluation for space use. The approximations used in solving the Boltzmann transport equation for the space setting are often not sufficient for laboratory work and those issues are a major emphasis of the present work.

Tweed, J.↗
NASA NTRS2005

Cross Section Sensitivity and Propagated Errors in HZE Exposures

It has long been recognized that galactic cosmic rays are of such high energy that they tend to pass through available shielding materials resulting in exposure of astronauts and equipment within space vehicles and habitats. Any protection provided by shielding materials result not so much from stopping such particles but by changing their physical character in interaction with shielding material nuclei forming, hopefully, less dangerous species. Clearly, the fidelity of the nuclear cross-sections is essential to correct specification of shield design and sensitivity to cross-section error is important in guiding experimental validation of cross-section models and database. We examine the Boltzmann transport equation which is used to calculate dose equivalent during solar minimum, with units (cSv/yr), associated with various depths of shielding materials. The dose equivalent is a weighted sum of contributions from neutrons, protons, light ions, medium ions and heavy ions. We investigate the sensitivity of dose equivalent calculations due to errors in nuclear fragmentation cross-sections. We do this error analysis for all possible projectile-fragment combinations (14,365 such combinations) to estimate the sensitivity of the shielding calculations to errors in the nuclear fragmentation cross-sections. Numerical differentiation with respect to the cross-sections will be evaluated in a broad class of materials including polyethylene, aluminum and copper. We will identify the most important cross-sections for further experimental study and evaluate their impact on propagated errors in shielding estimates.

Heinbockel, John H.↗
NASA NTRS2010

GUI to Facilitate Research on Biological Damage from Radiation

A graphical-user-interface (GUI) computer program has been developed to facilitate research on the damage caused by highly energetic particles and photons impinging on living organisms. The program brings together, into one computational workspace, computer codes that have been developed over the years, plus codes that will be developed during the foreseeable future, to address diverse aspects of radiation damage. These include codes that implement radiation-track models, codes for biophysical models of breakage of deoxyribonucleic acid (DNA) by radiation, pattern-recognition programs for extracting quantitative information from biological assays, and image-processing programs that aid visualization of DNA breaks. The radiation-track models are based on transport models of interactions of radiation with matter and solution of the Boltzmann transport equation by use of both theoretical and numerical models. The biophysical models of breakage of DNA by radiation include biopolymer coarse-grained and atomistic models of DNA, stochastic- process models of deposition of energy, and Markov-based probabilistic models of placement of double-strand breaks in DNA. The program is designed for use in the NT, 95, 98, 2000, ME, and XP variants of the Windows operating system.

Cucinotta, Frances A.↗
NASA NTRS2011

On the Development of a Deterministic Three-Dimensional Radiation Transport Code

Since astronauts on future deep space missions will be exposed to dangerous radiations, there is a need to accurately model the transport of radiation through shielding materials and to estimate the received radiation dose. In response to this need a three dimensional deterministic code for space radiation transport is now under development. The new code GRNTRN is based on a Green's function solution of the Boltzmann transport equation that is constructed in the form of a Neumann series. Analytical approximations will be obtained for the first three terms of the Neumann series and the remainder will be estimated by a non-perturbative technique . This work discusses progress made to date and exhibits some computations based on the first two Neumann series terms.

Rockell, Candice↗
NASA NTRS2011

Advanced Multifunctional MMOD Shield: Radiation Shielding Assessment

As NASA is looking to explore further into deep space, multifunctional materials are a necessity for decreasing complexity and mass. One area where multifunctional materials could be extremely beneficial is in the micrometeoroid orbital debris (MMOD) shield. A typical MMOD shield on the International Space Station (ISS) is a stuffed whipple shield consisting of multiple layers. One of those layers is the thermal blanket, or multi-layer insulation (MLI). By increasing the MMOD effectiveness of MLI blankets, while still preserving their thermal capabilities, could allow for a less massive MMOD shield. Thus, a study was conducted to evaluate concept MLI blankets for MMOD shields. In conjunction, these MLI blankets and the subsequent MMOD shields were also evaluated for their radiation shielding effectiveness towards protecting crew. These concepts were evaluated against the ISS MLI blankets and the ISS MMOD shield, which acted as the baseline. These radiation shielding assessments were performed using the high charge and energy transport software (HZETRN). This software is based on a one-dimensional formula of the Boltzmann transport equation with a straight-ahead approximation. Each configuration was evaluated against the following environments to provide a diverse view of radiation shielding effectiveness in most space environments within the heliosphere: August 1972 solar particle event, October 1989 solar particle event, 1982 galactic cosmic ray environment (during solar maximum), 1987 galactic cosmic ray environment (during solar minimum), and a low earth orbit environment in 1970 that corresponded to an altitude of 400 km and inclination of 51.6 . Both the absorbed dose and the dose equivalent were analyzed, but the focus of the discussion was on the dose equivalent since the data is most concerned with radiation shielding of the crew. The following paper outlines the evaluations performed and discusses the results and conclusions of this evaluation for radiation shielding effectiveness. Future work will focus on optimizing the radiation shielding properties for the MMOD shield. Submission

Rojdev, Kristina↗
NASA NTRS1990

The generalized diffusion-convection equation

Starting from the Boltzmann equation, a transport equation is derived for energetic particles in a moving magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically; (2) in this frame the scattering will not disturb an isotropic distribution; and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified, the derivation should be as valid for plasma microturbulence as for hard-sphere scattering. The results show clearly which phenomena are responsible for tying the particles to the plasma in the transport equation.

Jones, Frank C.↗
NASA NTRS2002

Microscopic Foundation and Simulation of Coupled Carrier-Temperature Diffusions in Semiconductor Lasers

A typical semiconductor-based optoelectronic device, such as a diode laser, consists of three subsystems: an optical field, an electron-hole plasma (EHP), and a host crystal lattice. The physics of such a device involves the interplay of optical, electrical and thermal processes. A proper description of such a device requires that all three processes are treated on equal footing and in a self-consistent fashion. Furthermore, since a semiconductor laser has intrinsic spatial inhomogeneity, such a self-consistency naturally leads to a set of partial differential equations in space and time. There is a significant lacking of research interest and results on the transport aspects of optical devices in the literature with only a few exceptions. Even the most important carrier diffusion coefficient has not been properly derived and studied so far for optically excited plasma, while most of the work adopted results from electronics community where heavily doped semiconductors with mainly one type of carriers are dealt with. The corresponding transport equation for plasma energy or temperature has received even less attention. In this talk we describe our recent results on such a self-consistent derivation of temperature and carrier-density diffusion equations coupled with the lasing process. Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field. The equations derived above are implemented in various limiting cases to a typical diode laser to study the consequences of nonlinear diffusion and the cross diffusion terms on laser behavior, especially the dynamic behavior of a diode laser under modulation. Detailed results will be presented by comparing with the standard rate equation results.

Li, J.↗
NASA NTRS2001

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Li, Jianzhong↗
NASA NTRS1991

Energy Models for One-Carrier Transport in Semiconductor Devices

Moment models of carrier transport, derived from the Boltzmann equation, made possible the simulation of certain key effects through such realistic assumptions as energy dependent mobility functions. This type of global dependence permits the observation of velocity overshoot in the vicinity of device junctions, not discerned via classical drift-diffusion models, which are primarily local in nature. It was found that a critical role is played in the hydrodynamic model by the heat conduction term. When ignored, the overshoot is inappropriately damped. When the standard choice of the Wiedemann-Franz law is made for the conductivity, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime required empirical modification of this law, or nonstandard choices. Simulations of the hydrodynamic model in one and two dimensions, as well as simulations of a newly developed energy model, the RT model, are presented. The RT model, intermediate between the hydrodynamic and drift-diffusion model, was developed to eliminate the parabolic energy band and Maxwellian distribution assumptions, and to reduce the spurious overshoot with physically consistent assumptions. The algorithms employed for both models are the essentially non-oscillatory shock capturing algorithms. Some mathematical results are presented and contrasted with the highly developed state of the drift-diffusion model.

Jerome, Joseph W.↗