Search NASA⌕ Search

SEARCH · Search NASA

Results for “Boltzmann 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

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.↗
NASA NTRS1992

Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method

A lattice Boltzmann model is presented which gives the complete Navier-Stokes equation and may provide an efficient parallel numerical method for solving various fluid problems. The model uses the single-time relaxation approximation and a particular Maxwell-type distribution. The model eliminates exactly (1) the non-Galilean invariance caused by a density-dependent coefficient in the convection term and (2) a velocity-dependent equation of state.

Chen, Hudong↗
NASA NTRS1968

Nonlinear interactions of electromagnetic waves with a thermally generated cesium plasma.

The interaction of a large‐amplitude disturbing wave with a thermally generated, highly ionized cesium plasma has been investigated using a small‐amplitude sensing wave as a probe. The subsequent interaction between the disturbing and sensing waves is related to the plasma electron temperature. The plasma was contained in a magnetic field of 500–1000 G and had an electron plasma frequency near 10 GHz and an electron gyromagnetic frequency around 2 GHz. The sensing wave was a 10 GHz plane wave of approximately 1.5 mW input power and the disturbing wave was 7.5 GHz plane wave of about 1.2 W peak power. Measurements of the sensing‐wave transmitted power were made using standard microwave techniques. A notch filter in the sensing‐wave receiving circuit reduced the scattered disturbing‐wave interference to an immeasurably low level. Langmuir probes were used to detect disturbing‐wave modulation and to measure plasma temperatures and densities. Measurements of the interaction were correlated with a solution of the Boltzmann transport equation for a perturbed Maxwellian distribution function with binary Coulomb collisions.

Jack G Hewitt, Jr↗
NASA NTRS1973

Auroral ion velocity distributions using a relaxation model.

Calculation of ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields for application to the auroral ionosphere. By replacing the Boltzmann collision integral with a simple relaxation model, an exact solution to Boltzmann's equation could be obtained. This solution has the advantage over a series expansion in that all the higher-order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form, because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, it is possible to determine when the higher-order velocity moments affect the ion velocity distribution and the nature of their effect, but it is not possible to obtain accurate quantitative results.

St-Maurice, J.-P.↗
NASA NTRS1976

Spacecraft self-contamination due to back-scattering of outgas products

The back-scattering of outgas contamination near an orbiting spacecraft due to intermolecular collisions was analyzed. Analytical tools were developed for making reasonably accurate quantitative estimates of the outgas contamination return flux, given a knowledge of the pertinent spacecraft and orbit conditions. Two basic collision mechanisms were considered: (1) collisions involving only outgas molecules (self-scattering) and (2) collisions between outgas molecules and molecules in the ambient atmosphere (ambient-scattering). For simplicity, the geometry was idealized to a uniformly outgassing sphere and to a disk oriented normal to the freestream. The method of solution involved an integration of an approximation of the Boltzmann kinetic equation known as the BGK (or Krook) model equation. Results were obtained in the form of simple equations relating outgas return flux to spacecraft and orbit parameters. Results were compared with previous analyses based on more simplistic models of the collision processes.

Robertson, S. J.↗
NASA NTRS1976

Magnetic monopoles and cosmology

The number density of magnetic monopoles is calculated in the framework of big-bang cosmology on the basis of a solution to the Boltzmann transport equation in evolutionary cosmological models. The product of the mass and the transition probability of the annihilation process for magnetic monopoles is obtained relative to those for protons and is shown to be greater than about 10 to the 20th power. Based on this result, two likely conclusions are made: (1) monopoles exist, but possess a pole-antipole bound state with binding energy of the order of the monopole rest mass; or (2) magnetic monopoles do not exist.

Adams, P. J.↗
NASA NTRS1978

Exact results on the temperature dependence of the specific equilibrium recombination rate coefficient

Two theorems based on Laplace transforms are used to relate threshold and high energy behavior to a temperature dependent variable. A recombination reaction involving electrically neutral species is presented to illustrate the dynamics of the activation energy and the associated rate coefficient. The distribution functions are shown to correspond with those predicted by Boltzmann's equations.

Mickens, R. E.↗
NASA NTRS1983

Perturbed particle disks

The velocity ellipsoid in a particle disk near an isolated satellite resonance is determined by solving the Boltzmann moment equations, and solutions are obtained that are stationary functions of the azimuthal angle in a coordinate frame which rotates with the pattern speed of the perturbation potential. The magnitude of the deformation rate tensor in a perturbed particle disk is bounded from above by an expression which includes the orbital angular velocity, the optical depth, and a dimensionless constant of order unity. It is also found that, in sufficiently perturbed regions, there are ranges of azimuthal angle over which the radial component of the angular momentum flux is negative. It is also possible for the angular momentum luminosity to be negative. These results are pertinent to the understanding of sharp edges and density wave decay in planetary rings.

Borderies, N.↗
NASA NTRS1985

Calculation of recoil implantation profiles using known range statistics

A method has been developed to calculate the depth distribution of recoil atoms that result from ion implantation onto a substrate covered with a thin surface layer. The calculation includes first order recoils considering projected range straggles, and lateral straggles of recoils but neglecting lateral straggles of projectiles. Projectile range distributions at intermediate energies in the surface layer are deduced from look-up tables of known range statistics. A great saving of computing time and human effort is thus attained in comparison with existing procedures. The method is used to calculate recoil profiles of oxygen from implantation of arsenic through SiO2 and of nitrogen from implantation of phosphorus through Si3N4 films on silicon. The calculated recoil profiles are in good agreement with results obtained by other investigators using the Boltzmann transport equation and they also compare very well with available experimental results in the literature. The deviation between calculated and experimental results is discussed in relation to lateral straggles. From this discussion, a range of surface layer thickness for which the method applies is recommended.

Fung, C. D.↗
NASA NTRS1986

Stoichiometric disturbances in compound semiconductors due to ion implantation

A method is developed to calculate the depth distribution of the local stoichiometric disturbance (SD) resulting from ion implantation in binary-compound substrates. The calculation includes first-order recoils considering projected range straggle of projectiles and recoils and lateral straggle of recoils. The method uses tabulated final-range statistics to infer the projectile range distributions at intermediate energies. This approach greatly simplifies the calculation with little compromise on accuracy as compared to existing procedures. As an illustration, the SD profile is calculated for implantation of boron, silicon, and aluminum in silicon carbide. The results for the latter case suggest that the SD may be responsible for otherwise unexplained distortions in the annealed aluminum profile. A comparison with calculations by other investigators using the Boltzmann transport equation shows good agreement.

Avila, R. E.↗
NASA NTRS1987

The physics of charge separation preceding lightning strokes in thunderclouds

The physics of charge separation preceding lightning strokes in thunderclouds is presented by three types of arguments: An explanation is given for the aggregation of electrical charges of like sign overcoming Coulomb repulsion by attraction due to exchange interaction. The latter is well known in quantum mechanics from the theories of the nuclear bond and the covalent bond. A classical electrostatic model of charge balls of segregated positive and negative charges in the thundercloud is presented. These charge balls can only be maintained in temporarily stable locations by a containing vortex. Because they will be of different sizes and masses, they will stabilize at different altitudes when drag forces are included with the given electrostatic force. The question of how the charges become concentrated again after lightning discharges is approached by means of the collisional Boltzmann transport equation to explain quasi-periodic recharging. It is shown that solutions cannot be separable in both position and time if they are to represent aggregation.

Kyrala, Ali↗
NASA NTRS1987

Studies of HZE particle interactions and transport for space radiation protection purposes

The main emphasis is on developing general methods for accurately predicting high-energy heavy ion (HZE) particle interactions and transport for use by researchers in mission planning studies, in evaluating astronaut self-shielding factors, and in spacecraft shield design and optimization studies. The two research tasks are: (1) to develop computationally fast and accurate solutions to the Boltzmann (transport) equation; and (2) to develop accurate HZE interaction models, from fundamental physical considerations, for use as inputs into these transport codes. Accurate solutions to the HZE transport problem have been formulated through a combination of analytical and numerical techniques. In addition, theoretical models for the input interaction parameters are under development: stopping powers, nuclear absorption cross sections, and fragmentation parameters.

Townsend, Lawrence W.↗
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.↗