Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fokker-Planck”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Kinetic theory of relativistic plasmas

The thermalization of particle kinetic motion by binary collisions is considered for a plasma with a Boltzmann constant-temperature product approximately equal to 10 to 100 times the product of the electron mass with the square of the speed of light. At this temperature, the principal mechanism for relaxation of electron motion is via radiationless electron-electron collisions (Moller scattering). Ions are nonrelativistic, but are energetic enough so that their Coulomb scattering can be treated in the Born approximation. Relaxation times are computed and Boltzmann-equation Fokker-Planck operators are derived for the various binary-collision processes. The expression for the rate of kinetic energy exchange between electron and ion gases is derived for the case where the gases are at different temperatures.

Gould, R. J.↗
NASA NTRS1981

Fermi-Compton scattering due to magnetopause surface fluctuations in Jupiter's magnetospheric cavity

The effects of boundary surface fluctuations on a spectrum of electromagnetic radiation trapped in a high Q (quality) cavity are considered. Undulating walls introduce small frequency shifts at reflection to the radiation, and it is argued that the process is entirely analogous to both Fermi (particle) acceleration and inverse Compton scattering. A Fokker-Planck formalism is pursued; it yields a diffusion equation in frequency for which the Green's function and steady-state solutions are found. Applying this analysis to the Jovian continuum radiation discovered by Voyager spacecraft, it is suggested that characteristic diffusion times are greater than 1 year, and that in order to account for the steep frequency spectra observed, an unidentified loss mechanism must operate in the cavity with a decay time constant approximately equal to the characteristic diffusion time divided by 28. A radiator-reactor model of the cavity is investigated to provide an estimate for the intrinsic luminosity of the low frequency (approximately 100 Hz) continuum source whose power is approximately 7 x 10 to the 6th W.

Barbosa, D. D.↗
NASA NTRS1981

Interplanetary Alfvenic fluctuations - A stochastic model

The concept of minimum variance is investigated for nonplanar interplanetary Alfvenic fluctuations in which the field direction varies randomly. The theory of the random wandering of a vector of constant length is developed as a representation of the magnetic field, and it is found that the minimum variance tends to coincide with the mean field directions over the correlation time of the fluctuations. The Fokker-Planck limit of the theory is then developed and used to analyze the statistic distribution of field directions with and without a reflecting barrier. Results suggest that the tendency of the Alfvenic fluctuations to have a direction of minimum variance statistically aligned with the mean magnetic field may be purely a consequence of the randomness of the fluctuation and not imply that the fluctuations are necessarily plane waves. Extensive statistical studies of the observed directional variations of the interplanetary magnetic field are necessary to test this hypothesis.

Barnes, A.↗
NASA NTRS1980

Costas loop tracking performance in the presence of antenna switching transients

The present paper examines the impact of phase, amplitude and Doppler transients on the tracking performance of a Costas loop, both in the presence and absence of noise; the loop's lock maintenance capability is also examined. Specific considerations involve analyzing second order loop transient behavior in the absence of noise and the presence of the three transients noted above; here, the operational differential equations are formulated and numerically solved. In the context of noise presence, a first order loop is treated in conjunction with amplitude and phase transients; toward this end the time dependent version of the Fokker-Planck partial differential equation is developed and numerically solved. Selected performance curves describe second order loop behavior in the presence of transients, whose values are of varying severity. First order loop behavior in the presence of noise is characterized by the illustration of suitably defined time dependent 'truncated probability density functions' and associated loss of lock probabilities.

Weinberg, A.↗
NASA NTRS1981

Analytical description of charged particle transport along arbitrary guiding field configurations

Aspects of charged particle transport theory have been studied by Earl (1973, 1974, 1976) in a number of investigations. The investigations were conducted under the assumption that particles propagate along a DC guiding field with negligible perpendicular transport and that pitch-angle scattering by random fields can be described by the Fokker-Planck formalism. The present study provides a generalized and simplified treatment of focused transport. The first step is taken with respect to a perturbation analysis by which the Boltzmann equation is solved in terms of successively improved approximations to its exact solution. The first approximation is the sum of isotropic pseudodiffusive and anisotropic supercoherent components whose coefficients must satisfy two coupled partial differential equations. The normalization constant K and the pseudodiffusive velocity, which appear in the first-order transport equations, are given by simple integrals over the pitch angle.

Earl, J. A.↗
NASA NTRS1981

Impulsive phase of solar flares. I - Characteristics of high energy electrons

The models describing the operative physical processes occurring during the impulsive phase of a solar flare can be broadly classified as thermal or nonthermal models. The current investigation is part of a series of studies which analyze the general characteristics of the 'nonthermal' models. The results are presented of an analysis regarding the steady state distribution of energetic electrons within the flare plasma. The time independent Fokker-Planck equation is used to determine the steady state distribution of the electrons in the ambient plasma. The model investigated encompasses thick-target, thin-target, and trap aspects of nonthermal hard X-ray models. High energy electrons with some initial energy spectrum and pitch angle distribution are injected at a height above the photosphere either into a closed magnetic loop structure or into an open field structure. Some approximate analytic solutions are discussed and the results of a numerical analysis are presented.

Leach, J.↗
NASA NTRS1982

A note on Compton scattering

Calculations are presented on the energy exchange between free electrons and electromagnetic radiation. The full Klein-Nishina cross section is used in evaluating average scattering coefficients for an electron moving with arbitrary velocity. A number of useful series expansions for the mean energy and mean square energy transfer rates are presented. A Fokker-Planck equation that includes induced scattering is used in deriving a generalized diffusion equation in frequency for multiple scattering of photons of nonrelativistic electrons. The relationship of the Klein-Nishina cross section to that of classical electromagnetic radiation theory is elucidated.

Barbosa, D. D.↗
NASA NTRS1982

Effects of nuclear forces on ion thermalization in high-temperature plasmas

A number of investigations have been concerned with the kinetic theory and processes associated with a relativistic electron gas. Gould (1981) has considered a condition in which upon the ultimate thermalization the temperature can be such that the electron gas is highly relativistic while the gas of protons and other ions is nonrelativistic. With the nuclear component nonrelativistic but having energies in the MeV range and above, it is necessary to consider the effects of nuclear forces in the scattering of the ions in their thermalization. The effects of nuclear forces in the thermalization of ions in plasmas have been computed, principally in connection with problems of controlle; fusion. The present investigation is concerned with an attempt to express results in analytic form to as great a degree as possible. The p-p problem, which is the fundamental problem in astrophysical plasma, is studied. Attention is given to a low-energy formulation, the s-wave phase shift, the effective stopping number, Fokker-Planck operators, and the interaction with the electron gas.

Gould, R. J.↗
NASA NTRS1984

Theory and modeling of atmospheric turbulence, part 1

The cascade transfer which is the only function to describe the mode coupling as the result of the nonlinear hydrodynamic state of turbulence is discussed. A kinetic theory combined with a scaling procedure was developed. The transfer function governs the non-linear mode coupling in strong turbulence. The master equation is consistent with the hydrodynamical system that describes the microdynamic state of turbulence and has the advantages to be homogeneous and have fewer nonlinear terms. The modes are scaled into groups to decipher the governing transport processes and statistical characteristics. An equation of vorticity transport describes the microdynamic state of two dimensional, isotropic and homogeneous, geostrophic turbulence. The equation of evolution of the macrovorticity is derived from group scaling in the form of the Fokker-Planck equation with memory. The microdynamic state of turbulence is transformed into the Liouville equation to derive the kinetic equation of the singlet distribution in turbulence. The collision integral contains a memory, which is analyzed with pair collision and the multiple collision. Two other kinetic equations are developed in parallel for the propagator and the transition probability for the interaction among the groups.

Source record↗
DOE OSTI2026

Formation and Redshift Evolution of Dark Matter Spikes

Dark matter density spikes forming around adiabatically growing black holes can dramatically enhance indirect and direct detection signals. Canonical predictions, however, assume a zero-mass seed in a purely dark matter environment and do not track the long-term dynamical impact of surrounding stars. We present a semi-analytic framework that first generalizes adiabatic spike formation to include finite seed masses, stellar cusps, and non-circular orbits, and then studies the subsequent cosmic evolution by solving coupled Fokker-Planck equations for the dark matter and stellar phase-space distributions, with a heating rate modulated by the cosmic star formation rate. Starting conservatively from canonical Gondolo-Silk spikes and marginalizing over astrophysical uncertainties, we find that stellar gravitational heating drives the inner slope towards $γ_χ\simeq 1.5$ within a few Gyrs (e.g by $z \lesssim 2$ for spikes formed at $z\simeq 10$), yielding overdensities two to four orders of magnitude below canonical expectations but still well above an NFW-like cusp. We provide redshift-dependent benchmarks for the column density and $J$-factor relevant to scattering, decay and annihilation signatures. Any robust interpretation of indirect dark matter signals from galactic nuclei must account for this evolution.

Herrera, Gonzalo [MIT, LNS; MIT, MKI; Harvard U.]↗
DOE OSTI2025

Nonequilibrium effects in high-gain inertial confinement fusion

Recent experimental demonstrations of ignition and target gain in inertial confinement fusion (ICF) have stimulated interest in exploring the fundamental physics of violent deuterium-tritium (DT) burn in high-gain ICF targets. A significant DT-burn fraction is a necessary condition for high energy gain and large neutron yields (>100MJ). Using classical molecular-dynamics (MD) simulations and a hybrid fluid-kinetic model, we examine how a large fraction of low-energy 𝛼 particles can kick D and T ions out of equilibrium in high-gain ICF targets. The MD results suggest that (1) temperatures of 𝑇 𝐷 and 𝑇 𝑇 can differ by as much as ∼20% of their mean temperature and (2) the deviation of the DT energy distribution from the Maxwell-Boltzmann function can exceed ∼30%. Some of these MD observations, such as the preferential heating of D ions by low-energy 𝛼 particles and the temperature separation, can be explained by a proposed hybrid fluid-kinetic model. Furthermore, the implication of such nonequilibrium effects on the DT reactivity is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1966

Cosmic-ray propagation. I.

Charged particle motion in random magnetic field, describing time evolution of particle distribution in pitch angle and position in terms of Fokker- Planck coefficients

INTERPLANETARY MAGNETIC FIELD↗
NASA NTRS1967

Dynamical friction.

Chandrasekhar dynamical friction theory for star in cluster adapted to Fokker-Plank electron in two-component plasma theory and including multiple encounters

STAR CLUSTER↗