Collision Frequencies and Energy Transfer- Electrons
Elastic collisions and energy transfer between gases with separate Maxwellian velocity distributions
ENERGY TRANSFER↗
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Results for “MAXWELL 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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Variable collision cross-section effects on electrical conductivity.
Conductivity of potassium-seeded argon plasma, assuming variable collision cross sections and Maxwellian distribution for electrons
MAXWELL DISTRIBUTION↗
Landau damping and growth of electrostatic modes with effects of spatial variation.
Landau damping and growth applied to electron plasma waves for Maxwellian velocity distribution in slab and cylindrical geometries
MAXWELL DISTRIBUTION↗
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.↗
Thermodynamically consistent incorporation of the Langmuir adsorption model into compressible fluctuating hydrodynamics
For a gas–solid interfacial system where chemical species undergo reversible adsorption, we develop a mesoscopic stochastic modeling method that simulates both gas-phase hydrodynamics and surface coverage dynamics by coupling the Langmuir adsorption model with compressible fluctuating hydrodynamics. To this end, we derive a thermodynamically consistent mass–energy update scheme that accounts for how the mass and energy variables in the gas and surface subsystems should be updated according to the changes in the number of molecules of each species in each subsystem due to adsorption and desorption events. By performing a stochastic analysis for the ideal Langmuir model and the full hydrodynamic system, we analytically confirm that our mass–energy update scheme captures thermodynamic equilibrium predicted by equilibrium statistical mechanics. We find that an internal energy correction term is needed, which is attributed to the difference in the mean kinetic energy of gas molecules colliding with the surface from that computed from the Maxwell–Boltzmann distribution. By performing an equilibrium simulation study for an ideal gas mixture of CO and Ar, with CO undergoing reversible adsorption, we validate our overall simulation method and implementation.
Adsorption↗
Numerical integration of kinetic equations.
Relaxation to Maxwellian of Balescu-Lenard equation solved numerically as initial value problem for isotropic distributions of electrons in background of positive charge
MAXWELL DISTRIBUTION↗
Heavy dark matter in rapidly evolving massive stars
We study the impact of heavy dark matter (DM) captured in massive stars via scattering(s) with the star constituents. We focus on the first stars and use stellar evolution simulations to track down how DM capture evolves over time from the zero-age main sequence to the late metal-rich stages of stellar evolution. During the early hydrogen-helium-dominated phase, the capture process is well described by scattering with two targets. As a star evolves, metal production leads to the formation of a dense core surrounded by a lighter envelope. The core significantly enhances the capture of ultra-heavy DM; in this case, three distinct nuclear species are required to accurately describe multiple-scattering capture. We use the Eddington inversion method to obtain a realistic DM velocity distribution, better suited when the star is near the center of a halo, than the widely used Maxwell-Boltzmann distribution. We find that heavy DM would be able to thermalize and achieve capture-annihilation equilibrium within a massive star's lifetime for regions of the parameter space not excluded by direct detection. For non-annihilating DM, because of the high amount of targets available for capture and despite massive stars being short-lived, it would even be possible for DM to achieve self-gravitation and collapse to a black hole, which eventually could swallow the star from within before the expected end of the star's life, for non-excluded regions of the parameter space. Our results highlight the dependence of DM capture on the stellar evolutionary stage, composition, and halo location, demonstrating that accurate modeling of massive stars is essential for constraining heavy DM with primordial stellar populations.
dark matter theory↗
A moment-conserving discontinuous Galerkin representation of the relativistic Maxwellian distribution
Kinetic simulations of relativistic gases and plasmas are critical for understanding diverse astrophysical and terrestrial systems, but the accurate construction of the relativistic Maxwellian, the Maxwell–Jüttner distribution, on a discrete simulation grid is challenging. Difficulties arise from the finite velocity bounds of the domain, which may not capture the entire distribution function, as well as errors introduced by projecting the function onto a discrete grid. Here, we present a novel scheme for iteratively correcting the moments of the projected distribution applicable to all grid-based discretizations of the relativistic kinetic equation. In addition, we describe how to compute the needed nonlinear quantities, such as Lorentz boost factors, in a discontinuous Galerkin scheme through a combination of numerical quadrature and weak operations. The resulting method accurately captures the distribution function and ensures that the moments match the desired values to machine precision.
astrophysical plasmas↗
Radiation-temperature measurements of the nitrogen afterglow plasma.
Microwave frequency measurements of radiation temperature of nitrogen afterglow plasma with Maxwellian electron velocity distributions
PLASMA TEMPERATURE↗
Electron tail suppression and effective collisionality due to synchrotron emission and absorption in mildly relativistic plasmas
Synchrotron radiation losses are a significant cause of concern for high-temperature aneutronic fusion reactions such as proton–Boron 11. The fact that radiation losses occur primarily in the high-energy tail, where the radiation itself has a substantial impact on the electron distribution, necessitates a self-consistent approach to modeling the diffusion and drag induced by synchrotron absorption and emission. Furthermore, an accurate model must account for the fact that the radiation emission spectrum is momentum-dependent, and the plasma opacity is frequency-dependent. Here, we present a simple Fokker–Planck operator, built on a newly solved-for blackbody synchrotron diffusion operator, which captures all relevant features of the synchrotron radiation. Focusing on magnetic mirror fusion plasmas, we show that significant suppression of the electron distribution occurs for relativistic values of the perpendicular electron momentum, which therefore emit much less radiation than predicted under the assumption of a Maxwell–Jüttner distribution.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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.↗
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↗
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↗
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.↗
Crater relaxation on Ganymede - Implications for ice rheology
Controversy has existed over whether or not viscous relaxation is an important process on the icy satellites. Previous models involved large extrapolations of Newtonian flow laws for ice, whereas ice is known to exhibit non-Newtonian behavior. Recently, the flow law parameters for ice at the appropriate temperatures and stresses have been measured. Numerical modeling of the viscous relaxation of basins on Ganymede using these parameters has given implausibly short relaxation times. However, this model treated ice as a purely viscous substance, so that no elastic lithosphere could develop near the surface. Here, ice is treated as a Maxwell visco-elastic material and numerically model the relaxation of basins on Ganymede. It is found that realistic Young's moduli lead to little relaxation occurring in basins even 4.0 Ga after their formation. Further, it is shown that within braod limits the near surface temperature gradient has little effect on this result. Finally, examination of the distribution of Maxwell times in the vicinity of the crater shows that most viscous relaxation occurs early in the basin's history when stresses are high, and thus Maxwell time is short. As stresses are relieved, the Maxwell time becomes long, and relaxation essentially ceases.
Hillgren, Valerie J.↗
Variationally consistent Maxwell stress in flexoelectric structures under finite deformation and immersed in free space
Maxwell stress refers to the mechanical stress exerted on a dielectric material due to the presence of electric fields. It plays a significant role in the interaction between a dielectric material and the surrounding free space under finite deformation. Previous research on finite deformation of flexoelectricity mainly adopted a modified form of Maxwell stress, potentially not able to correctly capture some physical phenomena, such as the compression of a dielectric droplet in an electric field. In this work, we propose a consistent and complete variational principle for flexoelectricity, in which the Maxwell stress emerges naturally from the derivation, without introducing additional assumptions. An Isogeometric analysis-based numerical framework is developed accordingly and verified by both linear and nonlinear benchmark cases compared with experimental results. The present framework successfully captures and quantifies the behaviors of conductive liquids and soft dielectric solids subjected to an external electric field. Finally, a novel scenario is investigated in which a flexoelectric beam immersed in free space is analyzed, showing the interesting distribution of Maxwell stress-induced tractions at opposing boundaries. The test demonstrates that a higher dielectric constant can effectively enhance the material's stiffness in response to the external electric loading.
36 MATERIALS SCIENCE↗
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.↗
Comprehensive Characterization of Water Group Ion Composition and Distributions in Saturn's Magnetosphere With Cassini Plasma Spectrometer Data
Saturn's magnetosphere is continuously supplied with neutrals from the Enceladus plume and the icy rings, which undergo ionization and charge-exchange to form a complex water-group plasma environment. While the Cassini Plasma Spectrometer (CAPS) instrument has provided extensive compositional information, detailed separation of individual water-group ion species in time-of-flight (TOF) data has not previously been achieved. In this study, we perform forward modeling of CAPS-IMS energy-per-charge (E/Q) and TOF spectra obtained between 2004 and 2012 to resolve O + , OH + , H 2 O + , and H 3 O + and to characterize their plasma properties, including number density, temperature, and thermodynamic κ. Our results demonstrate that O + is the dominant thermal ion species throughout Saturn's magnetosphere, comprising up to ∼70% of the total ion population beyond ∼5 Saturn radii (R S ). In contrast, molecular ions such as OH + , H 2 O + , and H 3 O + dominate closer to Enceladus but rapidly dissociate into atomic ions between ∼5 and 10 R S . This radial region is also characterized by the steepest increase in plasma flow speed, which rises from ∼40% to ∼80% of rigid corotation. Simultaneously, ion velocity distributions approach Maxwell–Boltzmann equilibrium, as indicated by high kappa values. These findings provide new constraints on the ion–neutral chemistry that regulates the balance between molecular and atomic ions in Saturn's magnetosphere. They also emphasize the critical role of the 5–10 R S region as a transition zone for both plasma composition and dynamics. Our results refine previous CAPS-based studies and underscore the need to incorporate seasonal variability and ionospheric coupling into future global models of Saturn's plasma environment.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗