Exact semiclassical theory for galvanomagnetic effects in metals
Closed form solution for conductivity tensor for magnetic field strength obtained from linearized Boltzmann equation for electron conduction distribution function
TENSOR FIELD↗
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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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On the structure of the BBGKY hierarchy for a Boltzmann gas
Structure of BBGKY hierarchy for Boltzmann gas and particle distributions
Frieman, E. A.↗
On the Cauchy problem of the relativistic Boltzmann equation.
Cauchy problem for relativistic Boltzmann equation, discussing initial distribution function and scattering cross section
Bichteler, K.↗
Quantum statistical theory of semiconductor junctions in thermal equilibrium
Free carrier and electric field distributions of one-dimensional semiconductor junctions are evaluated using a quantum mechanical phase-space distribution and its corresponding Boltzmann equation. Attention is given to quantum and exchange corrections in cases of high doping concentrations when carrier densities become degenerate. Quantitative differences between degenerate and classical junction characteristics, e.g., maximum electric field and built-in voltage and carrier concentration within the transition region, are evaluated numerically.
Von Roos, O.↗
Heat transfer in a discrete-velocity gas
Heat transfer of a discrete-velocity gas composed of identical hard sphere molecules between two parallel plates is studied numerically. A finite-difference method recently developed by the authors is used for solving the discrete Boltzmann equations. The temperature distributions between the plates of temperature ratios 2.0 and 4.0, and the heat transfer of temperature ratio 4.0 are presented and are compared with results of other methods.
Inamuro, Takaji↗
Shock Radiation Tests for Saturn and Uranus Entry Probes
This paper describes a test series in the Electric Arc Shock Tube at NASA Ames Research Center with the objective of quantifying shock-layer radiative heating magnitudes for future probe entries into Saturn and Uranus atmospheres. Normal shock waves are measured in Hydrogen-Helium mixtures (89:11 by volume) at freestream pressures between 13-66 Pa (0.1-0.5 Torr) and velocities from 20-30 kms. No shock layer radiation is detected within measurement limits below 25 kms, a finding consistent with predictions for Uranus entries. Between 25-30 kms, radiance is quantified from the Vacuum Ultraviolet through Near Infrared, with focus on the Lyman-a and Balmer series lines of Hydrogen. Shock profiles are analyzed for electron number density and electronic state distribution. The shocks do not equilibrate over several cm, and in many cases the state distributions are non-Boltzmann. Radiation data are compared to simulations of Decadal Survey entries for Saturn and shown to be as much as 8x lower than predicted with the Boltzmann radiation model. Radiance is observed in front of the shock layer, the characteristics of which match the expected diffusion length.
Hydrogen↗
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↗
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.↗
Electron distribution function in a slightly ionized moving gas.
Lorentz gas approximation to Boltzmann collision operator generalized for heavy molecule nonMaxwellian gas distribution function, obtaining equilibrium distribution applicable to ionized gas
Mintzer, D.↗
Numerical solution of the complete Krook- Boltzmann equation for strong shock waves.
Iterative solution to Krook-Boltzmann kinetic equation noting Navier-Stokes numerical solution, computation and analysis of distribution function within shock wave
BOLTZMANN EQUATION↗
Model for rotating and nonuniform planetary exospheres.
The model neutral exosphere with a uniformly rotating exobase is generalized by allowing variations in exobase density and temperature which characterize the thermosphere just below the base. The corresponding velocity distribution function, satisfying the collisionless Boltzmann equation, is constructed and used to form a general expression for the velocity moments. Resulting density profiles of rotating exospheres with nonuniform densities and temperatures on the exobase are compared with corresponding nonrotating exospheres. Density enhancements due to rotation are found to be greatest above regions of exobase density or temperature minima. Equatorial density enhancements of terrestrial hydrogen, resulting from rotation, are estimated to be 15%-17% at altitudes of 10-20 earth radii. Corresponding increases in terrestrial helium are 30%-50% on the equator at altitudes of 0.7 to 1 earth radii even when there is a polar density bulge in the barosphere.
Hartle, R. E.↗
Mathematical physics approaches to lightning discharge problems
Mathematical physics arguments useful for lightning discharge and generation problems are pursued. A soliton Ansatz for the lightning stroke is treated including a charge generation term which is the ultimate source for the phenomena. Equations are established for a partially ionized plasma inding the effects of pressure, magnetic field, electric field, gravitation, viscosity, and temperature. From these equations is then derived the non-stationary generalized Ohm's Law essential for describing field/current density relationships in the horizon channel of the lightning stroke. The discharge initiation problem is discussed. It is argued that the ionization rate drives both the convective current and electric displacement current to increase exponentially. The statistical distributions of charge in the thundercloud preceding a lightning dischage are considered. The stability of the pre-lightning charge distributions and the use of Boltzmann relaxational equations to determine them are discussed along with a covered impedance path provided by the aircraft.
Kyrala, A.↗
Implications of C2H photochemistry on the modeling of C2 distributions in comets
Laboratory studies of the secondary photolysis of the C2H radical are summarized and used to explain some discrepancies between models of C2 emission in comets. These studies show that several states of the C2 radicals produced in the photolysis of C2H2 at 193 nm have bimodal rotational distributions when plotted as a Boltzmann diagram. They also establish that the C2 radicals are formed with varying degrees of vibrational excitation, so that if they are formed in a similar manner in comets, the C2 radicals must start out with this initial vibrational excitation.
Jackson, William M.↗
Preliminary Study of Electron Emission for Use in the PIC Portion of MAFIA
This memorandum summarizes a study undertaken to apply the program MAFIA to the modeling of an electron gun in a traveling wave tube (TWT). The basic problem is to emit particles from the cathode in the proper manner. The electrons are emitted with the classical Maxwell-Boltzmann (M-B) energy distribution; and for a small patch of emitting surface; the distribution with angle obeys Lambert's law. This states that the current density drops off as the cosine of the angle from the normal. The motivation for the work is to extend the analysis beyond that which has been done using older codes. Some existing programs use the Child-Langmuir, or 3/2 power law, for the description of the gun. This means the current varies as the 3/2 power of the anode voltage. The proportionality constant is termed the perveance of the gun. This is limited, however, since the 3/2 variation is only an approximation. Also, if the cathode is near saturation, the 3/2 law definitely will not hold. In most of the older codes, the electron beam is decomposed into current tubes, which imply laminar flow in the beam; even though experiments show the flow to be turbulent. Also, the proper inclusion of noise in the beam is not possible. These older methods of calculation do, however, give reasonable values for parameters of the electron beam and the overall gun, and these values will be used as the starting point for a more precise particle-in-cell (PIC) calculation. To minimize the time needed for a given computer run, all beams will use the same number of particles in a simulation. This is accomplished by varying the mass and charge of the emitted particles (macroparticles) in a certain manner, to be consistent with the desired beam current.
Freeman, Jon C.↗
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↗
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.↗
Exospheric Escape: A Parametrical Study
The study of exospheres can help us understand the long-term loss of volatiles from planetary bodies due to interactions of planets, satellites, and small bodies with the interplanetary medium, solar radiation, and internal forces including diffusion and outgassing. Recent evidence for water and OH on the Moon has spurred interest in processes involving chemistry and sequestration of volatile species at the poles and in voids. In recent years, NASA has sent spacecraft to asteroids including Vesta and Ceres, and ESA sent Rosetta to comet 67P/Churyumov-Gerasimenko and the asteroids Lutetia and Steins. Japan's Hayabusa spacecraft returned a sample from asteroid Itakowa, and OSIRIS-REX will return a sample from a primitive asteroid, Bennu, to Earth. In a surface-bounded exosphere, the gases are derived from the surface and thus reflect the composition of the body's regolith, although not in a one-to-one ratio. Observation of an escaping exosphere, termed a corona, is challenging. We have therefore embarked on a parametrical study of exospheres as a function of mass of the exospheric species, mass of the primary body and source velocity distribution, specifically thermal (Maxwell-Boltzmann) and sputtering. The goal is to provide a quick look to determine under what conditions and for what mass of the primary body the species of interest are expected to be bound or escaping and to quickly estimate the observability of exospheric species. This work does not provide a comprehensive model but rather serves as a starting point for further study. These parameters will be useful for mission planning as well as for students beginning a study of planetary exospheres.
Volatilels↗
Exospheric Escape: A Parametrical Study
The study of exospheres can help us understand the long-term loss of volatiles from planetary bodies due to interactions of planets, satellites, and small bodies with the interplanetary medium, solar radiation, and internal forces including diffusion and outgassing. Recent evidence for water and OH on the Moon has spurred interest in processes involving chemistry and sequestration of volatile species at the poles and in voids. In recent years, NASA has sent spacecraft to asteroids including Vesta and Ceres, and ESA sent Rosetta to comet 67P/Churyumov–Gerasimenko and the asteroids Lutetia and Steins. Japan's Hayabusa spacecraft returned a sample from asteroid Itakowa, and OSIRIS-REX will return a sample from a primitive asteroid, Bennu, to Earth. In a surface-bounded exosphere, the gases are derived from the surface and thus reflect the composition of the body's regolith, although not in a one-to-one ratio. Observation of an escaping exosphere, termed a corona, is challenging. We have therefore embarked on a parametrical study of exospheres as a function of mass of the exospheric species, mass of the primary body and source velocity distribution, specifically thermal (Maxwell-Boltzmann) and sputtering. The goal is to provide a quick look to determine under what conditions and for what mass of the primary body the species of interest are expected to be bound or escaping and to quickly estimate the observability of exospheric species. This work does not provide a comprehensive model but rather serves as a starting point for further study. These parameters will be useful for mission planning as well as for students beginning a study of planetary exospheres.
Exospheres↗