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Results for “Maxwell-Boltzmann distribution”

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 NTRS1995

Theoretical overview and modeling of the sodium and potassium atmospheres of the moon

A general theoretical overview for the sources, sinks, gas-surface interactions, and transport dynamics of sodium and potassium in the exospheric atmosphere of the Moon is given. These four factors, which control the spatial distribution of these two alkali-group gases about the Moon, are incorporated in numerical models. The spatial nature and relative importance of the initial source atoms atmosphere (which must be nonthermal to explain observational data) and the ambient (ballistic hopping) atom atmosphere are examined. The transport dynamics, atmospheric structure, and lunar escape of the nonthermal source atoms are time variable with season of the year and lunar phase because of their dependence on the radiation acceleration experienced by sodium and potassium atoms as they resonantly scatter solar photons. The dynamic transport time of fully thermally accomodated ambient atoms along the surface because of solar radiation acceleration (only several percent of surface gravity) is larger than the photoionization lifetimes and hence unimportant in determining the local density, although for potassium the situation is borderline. The sodium model was applied to analyze sodium observations of the sunward brightness profiles acquired near last quarter by Potter & Morgan (1988b) extending from the surface to an altitude of 1200 km, and near first quarter by Mendillo, Baumgardner, & Flynn (1991), extending in altitude from approximately 1430 to approximately 7000 km. The observations at larger altitudes could be fitted only for source atoms having a velocity distribution with a tail that is mildly nonthermal (like an approximately 1000 K Maxwell-Boltzmann distribution). Solar wind sputtering appears to a be a viable source atom mechanism for the sodium observations with photon-simulated desorption also possible but highly uncertain, although micrometeoroid impact vaporization appears to have a source that is too small and too hot, with likely an incorrect angular distribution about the Moon.

Smyth, William H.↗
NASA NTRS1981

The ionization state in a gas with a non-Maxwellian electron distribution

The inferred degree of ionization of a gas is often used in astrophysics as a diagnostic of the gas temperature. In the solar transition region and corona, in the outer atmospheres of cool stars, and in some portions of the interstellar medium), photoionization can be neglected, and the ionization state is fixed by the balance between ion-electron collisional ionization and dielectronic and/or radiative recombination. Under these conditions, higher degrees of ionization result from higher energy ion-electron collisions which are common in a high temperature gas. Actually, ionization occurs through collisions with electrons that have kinetic energies greater than the ionization potential of the given ion, and so the ionization rate depends on to the number of such high-energy electrons in the tail of the electron velocity distribution. High-velocity electrons move across large distances between effective coulomb collisions, and, in a strong temperature or density gradient, the tail can be overpopulated relative to Maxwell-Boltzmann distribution of equivalent energy density. Thus, the ionization rate can also be greatly increased. These effects for a parameterized form of the electron distribution function with an enhanced high-velocity tail, namely the kappa distribution are illustrated.

Owocki, S. P.↗
NASA NTRS1976

Formation of the 0.511 MeV line in solar flares

The slowing down and annihilation of positrons and the formation of positronium in a solar flare plasma are investigated to determine how the width of the 0.511-MeV line and its strength relative to the three-photon continuum from positronium decay depend on the temperature and density of the medium in which the positron comes to rest. The calculations are limited to the cases of annihilation in a completely ionized plasma, in a partially ionized plasma with an electron/neutron density ratio of 1.0 or 0.1, and in an atomic gas with a very small ion density. Thermally averaged rate coefficients are obtained for the free annihilation of positrons and for positronium formation through radiative recombination in the fully ionized plasma. Positronium formation rates and the resultant energy distributions of the positronium atoms in the partially ionized medium are determined by numerically solving the Fokker-Planck equation in a medium where the ambient free electrons have a Maxwell-Boltzmann distribution of finite temperature but the density of the medium is sufficiently low that positronium atoms decay without further collisions following their formation. A Monte Carlo calculation is performed for the positron energy loss, positronium formation through charge exchange, and positronium breakup in the weakly ionized medium. The energy distributions of decaying positronium atoms and the relative number of triplet to singlet positronium decays are evaluated for ion concentrations and densities characteristic of the solar photosphere.

Crannell, C. J.↗
NASA NTRS1984

Physics of Nonmagnetic Relativistic Thermal Plasmas

A detailed treatment of the kinematics of relativistic systems of particles and photons is presented. In the case of a relativistic Maxwell-Boltzmann distribution of particles, the reaction rate and luminosity are written as single integrals over the invariant cross section, and the production spectrum is written as a double integral over the cross section differential in the energy of the produced particles (or photons) in the center-of-momentum system of two colliding particles. The results are applied to the calculation of the annihilation spectrum of a thermal electron-positron plasma, confirming previous numerical and analytic results. Relativistic thermal electron-ion and electron-electron bremsstrahlung are calculated exactly to lowest order, and relativistic thermal electron-positron bremsstrahlung is calculated in an approximate fashion. An approximate treatment of relativistic Comptonization is developed. The question of thermalization of a relativistic plasma is considered. A formula for the energy loss or exchange rate from the interaction of two relativistic Maxwell-Boltzmann plasmas at different temperatures is derived. Application to a stable, uniform, nonmagnetic relativistic thermal plasma is made. Comparison is made with other studies.

Dermer, C. D.↗
NASA NTRS1974

Observation of a driver gas-tangential discontinuity

A complete analysis of an interplanetary disturbance of Nov. 19, 1970 using the Apollo 12-SIDE (Suprathermal Ion Detector Experiment) is presented. The SIDE detectors were pointing at 26.3 degrees from the normal solar-wind direction during the observations. The data were least-squares fitted (using a parabolic hypersurface approximation) to a convected Maxwell-Boltzmann distribution function. The results of the fit combined with two other experiments showed a drastic change in the wind speed (from an steady 352 km/sec down to 219 km/sec), direction, and temperature. Except for a delta-function increase at the onset, the density remained constant. There was a considerable enhancement in the abundance of He and probably of heavier elements. The interplanetary magnetic field exhibited a jump of 21 gamma with a change in latitude from -56 to -76 degrees in solar ecliptic coordinates. It is concluded that the disturbance was due to the driver gas-tangential discontinuity of a solar flare-induced shock wave. The characteristic of the tangential discontinuity fit well with theoretical prediction.

Medrano, R. A.↗
NASA NTRS1976

Thermodynamics and statistical mechanics

The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.

Source record↗
NASA NTRS1981

Physics of planetary atmospheres and ionospheres

The traditional atmospheric regions, the distinction between homosphere and heterosphere, and changing atmospheric composition are discussed. The validity of the barometric law based on a Maxwell-Boltzmann distribution, for the major part of a planetary atmosphere and its breakdown in the exosphere due to escape of atmospheric particles is considered. The formation and maintenance of photochemical and diffusion-controlled ionospheric layers are treated. Their applicability to planetary ionospheres is dealt with. The spatial extent of magnetic and nonmagnetic planet ionospheres is investigated. Thermal and nonthermal processes responsible for the mass loss of planetary atmospheres are surveyed.

Bauer, S. J.↗
NASA NTRS1993

Ionospheric plasma flow about a system of electrically biased flat plates

The steady state interaction of two electrically biased parallel plates immersed in a flowing plasma characteristic of low earth orbit is studied numerically. Fluid equations are developed to describe the motion of the cold positively charged plasma ions, and are solved using finite-differences in two dimensions on a Cartesian grid. The behavior of the plasma electrons is assumed to be described by the Maxwell-Boltzmann distribution. Results are compared to an analytical and a particle simulation technique for a simplified flow geometry consisting of a single semi-infinite negatively biased plate. Comparison of the extent of the electrical disturbance into the flowing plasma and the magnitude of the current collected by the plate is very good. The interaction of two equally biased parallel plates is studied as a function of applied potential. The separation distance at which the current collected by either plate decreases by five and twenty percent is determined as a function of applied potential. The percent decreases were based on a non-interacting case. The decrease in overall current is caused by a decrease in ionic density in the region between the plates. As the separation between the plates decreases, the plates collect the ions at a faster rate than they are supplied to the middle region by the oncoming plasma flow. The docking of spacecraft in orbit is simulated by moving two plates of unequal potential toward one another in a quasi-static manner. One plate is held at a large negative potential while the other floats electrically in the resulting potential field. It is found that the floating plate does not charge continuously negative as it approaches the other more negatively biased plate. Instead, it charges more and then less negative as ionic current decreases and then increases respectively upon approach. When the two plates come into contact, it is expected that the electrically floating plate will charge rapidly negative to a potential near that of the other plate.

Herr, Joel L.↗
NASA NTRS2000

Some Thermodynamic Considerations on the Physical and Quantum Nature of Space and Time

It is suggested that the Planck h = m(sub k)c Lambda(sub k) and the Boltzmann k = m(sub k)c nu(sub k)Constants have stochastic foundation. It is further suggested that a body of fluid at equilibrium is composed of a spectrum of molecular clusters (energy levels) the size of which are governed by the Maxwell-Boltzmann distribution function. Brownian motions are attributed to equilibrium between suspensions and molecular clusters. Atomic (molecular) transition between different size atomic- (molecular-) clusters (energy levels) is shown to result in emission/absorption of energy in accordance with Bohr's theory of atomic spectra. Physical space is identified as a tachyonic fluid that is Dirac's stochastic ether or de Broglie's hidden thermostat. Compressibility of physical space, in accordance with Planck's compressible ether, is shown to result in the Lorentz-Fitzgerald contraction, thus providing a causal explanation of relativistic effect in accordance with the perceptions of Poincare and Lorentz. The invariant Schrodinger equation is derived from the invariant Bernoulli equation for incompressible potential flow. Following Heisenberg a temporal uncertainty relation is introduced as Delta(nu(sub Beta)) Delta(Rho(sub Beta)) > = k.

Sohrab, Siavash H.↗
NASA NTRS1999

A Simulation to Study Speed Distributions in a Solar Plasma

We have carried out a numerical simulation of a plasma with characteristics similar to those found in the core of the Sun. Particular emphasis is placed on the Coulomb interaction between the ions and electrons, which could result in a relative velocity distribution different from the Maxwell-Boltzmann (MB) distribution generally assumed for a plasma. The fact that the distribution may not exactly follow the MB distribution could have very important consequences for a variety of problems in solar physics, especially the neutrino problem. Very briefly, the neutrino problem is that the observed neutrino detections from the Sun are smaller than what the standard solar theory predicts. In Section I we introduce the problem and in section II we discuss the approach to try to solve the problem: i.e., a molecular dynamics approach. In section III we provide details about the integration method, and any simplifications that can be applied to the problem. In section IV (the core of this report) we state our results. First for the specific case of 1000 particles and then for other cases with different number of particles. In section V we summarize our findings and state our conclusions. Sections VI VII and VIII provide the list of figures, reference material and acknowledgements respectively.

Cheeseman, Peter↗
NASA NTRS1999

A Simulation to Study Speed Distributions in a Solar Plasma

We (Peter Cheeseman of NASA Ames/Caelum Research) & Jose Luis Alvarellos of the SJSU Physics Department/SJSU Foundation.) have carried out a numerical simulation of a plasma with characteristics similar to those found in the core of the Sun. Particular emphasis is placed on the Coulomb interaction between the ions and electrons, which could result in a relative velocity distribution different from the Maxwell-Boltzmann (MB) distribution generally assumed for a plasma. The fact that the distribution may not exactly follow the MB distribution could have very important consequences for a variety of problems in solar physics, especially the neutrino problem. Very briefly. the neutrino problem is that the observed neutrino detections from the Sun are smaller than what the standard solar theory predicts. In Section 1 we introduce the problem and in section 2 we discuss the approach to try to solve the problem: i.e., a molecular dynamics approach. In section 3 we provide details about the integration method, and any simplifications that can be applied to the problem. In section 4 (the core of this report) we state our results, first for the specific case of 1000 particles and then for other cases with different number of particles. In section 5 we summarize our findings and state our conclusions. Sections 6 and 7 provide the list of figures, reference material and acknowledgments respectively.

Cheeseman, Peter↗
NASA NTRS1978

Monte Carlo modeling of exospheric bodies - Mercury

In order to study the interaction with the surface, a Monte Carlo program is developed to determine the distribution with altitude as well as the global distribution of density at the surface in a single operation. The analysis presented shows that the appropriate source distribution should be Maxwell-Boltzmann flux if the particles in the distribution are to be treated as components of flux. Monte Carlo calculations with a Maxwell-Boltzmann flux source are compared with Mariner 10 UV spectrometer data. Results indicate that the presently operating models are not capable of fitting the observed Mercury exosphere. It is suggested that an atmosphere calculated with a barometric source distribution is suitable for more realistic future exospheric models.

Smith, G. R.↗
NASA NTRS1973

Sandstorms and eolian erosion on Mars.

Erosion rates are calculated for Mars from first principles and calibrated from wind tunnel experiments. The deduced abrasion rates are higher than eolian erosion rates on the earth because of the higher threshold velocities on Mars but lower than the total erosion rates on the earth because of the absence of aqueous erosion processes on contemporary Mars. The high erosion rates imply that, for scale lengths of less than a few hundred kilometers, Mars may be viewed only part way back to its ancient history. Because the meteorology of Mars is position-dependent, erosion rates may vary greatly from place to place. Martian sandstorms may be characterized by frequent grain-grain collisions, and the grain velocities and cloud height may approach values implied by the Maxwell-Boltzmann velocity distribution.

Sagan, C.↗
NASA NTRS1977

Some optical and kinetic properties of the nearby interstellar gas

A model for resonant scattering of sunlight by the nearby interstellar gas is developed which takes into account the modification of a Maxwell-Boltzmann velocity distribution by a central force. While the formalism applies to both hydrogen and helium, the latter is emphasized. Theoretical line profiles and integrated emission rates for helium are compared with those of approximate models and with existing observations. As a result of this analysis, an upward revision of the bulk flow velocity of interstellar helium relative to the solar system, previously deduced from He 584-A observations, is required. Velocities of 15-20 km/s, temperatures of the order of 5000-10,000 K, and densities of the order of 0.008-0.02 per cu cm are sufficient to explain the (helium) observations. However, higher-precision measurements are required in order to place more stringent limits on the gas parameters. Calculations of the flux of interstellar helium atoms impinging on earth's upper atmosphere show that the resulting impact ionization is small compared with terrestrial processes.

Meier, R. R.↗
NASA NTRS1981

Ion extraction from a plasma

The physical processes governing ion extraction from a plasma have been examined experimentally. The screen hole plasma sheath (the transition region wherein significant ion acceleration and complete electron retardation occurs) has been defined by equipotential plots for a variety of ion accelerator system geometries and operating conditions. It was found that the screen hole plasma sheath extends over a large distance, and influences ion and electron trajectories at least 15 Debye lengths within the discharge chamber. The electron density variation within the screen hole plasma sheath satisfied a Maxwell-Boltzmann density distribution at an effective electron temperature dependent on the discharge plasma primary-to-Maxwellian electron density ratio. Plasma ion flow up to and through the sheath was predominantly one-dimensional, and the ions entered the sheath region with a modified Bohm velocity. Low values of the screen grid thickness to screen hole diameter ratio were found to give good ion focusing and high extracted ion currents because of the effect of screen webbing on ion focusing.

Aston, G.↗
NASA NTRS1973

A spectroscopic study of CW chemical lasers.

A subsonic transverse-flow chemical laser has been instrumented to permit measurements of vibration-rotation state populations and laser output spectra under flow conditions typical of present CW hydrogen halide laser operation. Measurements are presented for the F + HI, F + HBr, F + CH4, F + HCl, F + H2, Cl + HI, and Cl + HBr atom-exchange reaction systems. CW operation was found to be characterized by relatively modest departures from Maxwell-Boltzmann vibrational energy distributions at all stages of reaction in contrast to pulsed operation based on similar reactions.

Rosen, D. I.↗
NASA NTRS1978

Monte Carlo solution of Boltzmann equation for a simple model of highly nonequilibrium diatomic gases - Translational rotational energy relaxation

Theoretical results pertaining to internally excited translational-rotational energy relaxation in a spatially uniform diatomic gas far removed from solid boundaries are obtained by solving the Boltzmann equation by means of the Monte Carlo direct simulation method. The analysis is based on calculations involving three different types of initial conditions: equilibrium, nonequilibrium-equipartition (i.e., equipartition is satisfied, but the distributions are perturbed), and nonequilibrium-nonequipartition (i.e., both equipartition and the distributions are perturbed). Results of monatomic-gas simulations are also included to facilitate comparisons with the coupled translational-rotational relaxation simulations, and some simulations for a normal shock-wave structure are briefly examined. The results show that: (1) single-step transitions are the significant mechanisms of intermodal energy transfer; (2) translational-rotational transitions are coupled most efficiently for low-lying states of rotationally excited molecules and least efficiently for highly rotationally excited molecules; and (3) relaxation occurs via a successive set of distributions that are not Maxwell-Boltzmann (nonlocal Maxwellian).

Yoshikawa, K. K.↗
NASA NTRS2001

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.↗