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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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At least 235 records · Page 13
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NASA NTRS1974

Magnetic field dependence of plasma relaxation times

A previously derived Fokker-Planck collision integral for an electron plasma in a dc magnetic field is examined in the limit in which the Debye length is greater than the thermal gyroradius, which is in turn greater than the mean distance of closest approach. It is demonstrated that the collision integral can be satisfactorily approximated by the classical Landau value (which ignores the presence of a dc magnetic field) if the following replacement is made: In the Coulomb logarithm, the Debye length is replaced by the gyroradius. This induces a fundamental logarithmic dependence on magnetic field in the relaxation times. Numerical comparison of the asymptotic approximations with the previously derived exact results is made, and good agreement is found. The simplification this introduces into the description of collision processes in magnetized plasma is considerable.

Montgomery, D.↗
NASA NTRS1975

Modulation of low-energy cosmic rays

The relation between the diffusion coefficient of cosmic rays in the solar wind and the power spectrum of interplanetary magnetic field fluctuations, established in recent theories, is tested directly for low energy protons (below 80 MeV). In addition, an attempt is made to determine whether the particles are scattered by magnetic field discontinuities or by fluctuations between discontinuities. Predictions of a perturbation solution of the Fokker-Planck equation are compared with observations of the cosmic ray radial gradient. It is found that at energies between 40 and 80 MeV, galactic cosmic ray protons respond to changes in the predicted diffusion coefficients (i.e., the relationship under consideration holds at these low energies). The relation between changes in the proton flux and modulation parameters is best when the contribution of discontinuities is subtracted, which means that scattering is caused by fluctuations between discontinuities. There appears to be no distinct relation between changes in the modulation parameters and changes in the intensity of 20 to 40 MeV protons.

Sari, J. W.↗
NASA NTRS1975

Formation of molecular lines in stellar atmospheres

Statistical equilibrium of electronic states of diatomic molecules in stellar atmospheres is examined. Atmospheres discussed are representative of the sun, Arcturus (K-giant) and Betelgeuse (M-supergiant). A comparison of the relative collisional and radiative contributions to the equilibrium of the ground electronic state shows that this state is collisionally controlled and that the line source function for vibration-rotation transitions within this state is equivalent to the Planck function. Examination of the equilibrium for excited electronic states demonstrates that the exchange between these states and the ground electronic state is most probably determined by radiative excitation. This result implies that scattering rather than pure absorption is the appropriate mechanism for the formation of lines belonging to these electronic transitions. The scattering hypothesis is given a preliminary check against solar observations. Areas for future investigations are outlined.

Hinkle, K. H.↗
NASA NTRS1975

Cosmic ray propagation in interplanetary space

The validity of the test-particle picture, the approximation of static fields, and the spatial-diffusion approximation are discussed in a general way before specific technical assumptions are introduced. It is argued that the spatial-diffusion equation for the intensity per unit energy has a much wider range of applicability than the kinetic (Fokker-Planck) equation it is derived from. This gives strong weight to the phenomenological propagation theory. The general success (and possible failure at small energies) of the phenomenological theory for the modulation of galactic cosmic rays and solar events is described. Apparent effects such as the 'free boundary' are given disproportionate weight since they establish the connection with the detailed plasma physics of the solar wind. Greatest attention is paid to the pitch-angle diffusion theory. A general theory is presented which removes the well-known secularities of the quasi-linear approximation. The possible breakdown of any pitch-angle diffusion theory at very small energies is perhaps connected with the observed 'turn up' of the spectrum at low energies. A first attempt to derive the spatial dependence of the diffusion coefficient in the solar cavity, using such a divergence free scattering theory, is described and compared with recent observations out to 5 AU.

Voelk, H. J.↗
NASA NTRS1975

Polarization tracking of a partially coherent signal using a double loop

We consider the problem of simultaneously estimating the phase and polarization angles of a linearly polarized electromagnetic wave. The solution of this problem has applications to space communications and ionospheric probing. The nonlinear stochastic characteristics of a cross-coupled double-loop implementation for the tracker are evaluated using the multidimensional Fokker-Planck equation. The exact stationary probability density is found for a special case of equal signal-to-noise ratio (SNR) in the two loops. The stationary probability density is obtained for a general class of double loops when the two loop bandwidths differ greatly.

Ohlson, J. E.↗
NASA NTRS1976

Cosmic-ray transport theory and out-of-the-ecliptic exploration

The reasons for studying cosmic-ray transport theory are summarized and the fundamentally three-dimensional nature of the process is pointed out. It is shown that observations in the solar ecliptic plane cannot unambiguously test transport theories since the solutions to the transport equations depend critically on boundary conditions and variation of parameters such as diffusion tensor out of the ecliptic. Sample calculations (Fokker-Planck coefficient) are shown which illustrate the problem. It is concluded that out-of-the-ecliptic observations are essential to further test transport theory.

Jokipii, J. R.↗
NASA NTRS1976

Cosmic ray modulation in three dimensions

A brief critique of spherically symmetric conventional modulation theory is supplied. Estimates are made of the cosmic ray intensity at high solar latitudes. Direct evidence for significant off-ecliptic cosmic ray gradients is reviewed in support of the requirement for an off-ecliptic spacecraft mission. The possibility of measuring the galactic spectrum is discussed. The effect of interplanetary magnetic fields on cosmic ray motion is examined, and calculations (Fokker-Planck equation) are shown.

Quenby, J. J.↗
NASA NTRS1975

Exact solution of the Lifshitz equations governing the growth of fluctuations in cosmology

The exact solution of the Lifshitz equations governing the cosmological evolution of an initial fluctuation is presented. Lifshitz results valid for squares of the sound velocity equal to zero and 1/3 are extended in closed form to any equation of state where the pressure equals the total energy density times the square of the sound velocity. The solutions embody all the results found previously for special cases of the square of the sound velocity. It is found that the growth of any initial fluctuation is only an exponential function of time with an exponent of not more than 4/3 and is insufficient to produce galaxies unless the initial fluctuation is very large. A possible way to produce very large initial fluctuations by modifying the equation of state by including gravitational interactions is also examined. It is found that a phase transition can occur at baryonic density of 1 nucleon per cubic Planck length or equivalently, at a time of about 10 to the -43rd power sec. At those early times, the masses allowed by causality requirements are too small to be of interest in galaxy formation.

Adams, P. J.↗
NASA NTRS1975

Interpretation of recent positron-electron measurements between 20 and 800 MeV

Recently measured positron and negatron spectra are discussed with regard to the problem of solar modulation. At energies above 180 MeV, the spherically symmetric Fokker-Planck equation with a diffusion coefficient proportional to particle rigidity provides reasonable fits to both the positron and total electron data. At energies below 180 MeV, the data are consistent with a continuation of the same diffusion coefficient and a local source of negatrons or with a change in the diffusion coefficient to a constant value.

Pellerin, C. J.↗
NASA NTRS1976

Cosmic-ray positron and negatron spectra between 20 and 800 MeV measured in 1974

The flux density of cosmic-ray positrons and electrons was measured by a balloon-borne spark chamber magnetic spectrometer in two flights in an attempt to study the solar modulation of galactic cosmic rays. The total electron flux was found to be about 0.03/cu m/s/sr/MeV between 70 and 800 MeV and to increase toward lower energies, while the positron flux decreased sharply toward lower energies from about 0.008/cu m/s/sr/MeV at 650 MeV and only upper limits were obtained for positrons below 200 MeV. At energies above 180 MeV, the spherically symmetrical Fokker-Planck equation with a diffusion coefficient proportional to the particle rigidity provided a reasonable fit to both positron and total electron data, while at energies below 180 MeV, the data were consistent with a continuation of the same diffusion coefficient and local source of electrons, or a change in the diffusion coefficient to a constant value.

Hartman, R. C.↗
NASA NTRS1976

A quasi-linear kinetic equation for cosmic rays in the interplanetary medium

A kinetic equation for interplanetary cosmic rays is set up with the aid of weak-plasma-turbulence theory for an idealized radially symmetric model of the interplanetary magnetic field. As a starting point, this treatment invokes the Vlasov equation instead of the traditional Fokker-Planck equation. Quasi-linear theory is applied to obtain a momentum diffusion equation for the heliocentric frame of reference which describes the interaction of cosmic rays with convecting magnetic irregularities in the solar-wind plasma. Under restricted conditions, the well-known equation of solar modulation can be obtained from this kinetic equation.

Luhmann, J. G.↗
NASA NTRS1976

Plasma kinetic processes in a strong d.c. magnetic field

Recent results in the kinetic theory of a strongly magnetized plasma are surveyed. Emphasis is on the electrostatic guiding-center plasma in two dimensions, in both the fluid and 'charged rod' descriptions. The basic kinetic description of the plasma is in terms of the statistically-distributed Fourier coefficients associated with the velocity and 'enstrophy' (charge density) fields. It is a universal tendency in such media for enstrophy to flow to shorter wavelengths but for energy to flow to longer wavelengths. A consequence of the energy flow to longer wavelengths is the generation of long-range order in the form of macroscopic vortices. These kinds of structure have been called 'convection cells' and can be extraordinarily efficient in transporting particles transverse to a magnetic field. The tendency to vortex formation can be disrupted by collisions between particles. Modifications of the Fokker-Planck equation for a plasma produced by a strong dc magnetic field are considered in both two and three dimensions.

Montgomery, D.↗
NASA NTRS1976

A method for the analysis of nonlinearities in aircraft dynamic response to atmospheric turbulence

An analytical method is developed which combines the equivalent linearization technique for the analysis of the response of nonlinear dynamic systems with the amplitude modulated random process (Press model) for atmospheric turbulence. The method is initially applied to a bilinear spring system. The analysis of the response shows good agreement with exact results obtained by the Fokker-Planck equation. The method is then applied to an example of control-surface displacement limiting in an aircraft with a pitch-hold autopilot.

Sidwell, K.↗
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 NTRS1977

Flare heating by energetic nonthermal electrons

A model has been developed which includes, in a self-consistent fashion, the energy degradation and attendant bremsstrahlung emission of a high-energy electron beam, heating of a flare plasma by the beam, and subsequent cooling by thermal conduction and radiation. To assist in the interpretation of experimental diagnostics, the model also characterizes the radiative behavior of iron ions present in the flare plasma. Electron deposition is described by the Fokker-Planck equation for an initial power-law particle distribution. Results are presented for the bremsstrahlung radiation emitted by the incident beam as it impinges on the disturbed atmosphere. A comparison is made between direct beam heating and thermal-conduction heating of the flare plasma. The radiation emitted by several selected spectral lines of Fe ions is determined as a function of time during and after deposition

Davis, J.↗
NASA NTRS1977

Spectral radiance calibrations between 165-300 nm - An interlaboratory comparison

The spectral radiance of deuterium lamps calibrated by the Max-Planck-Institut fuer Astronomie (MPI), by the U.S. National Bureau of Standards (NBS), and by the Physikalisch-Technische Bundesanstalt (PTB) are compared to check the agreement of UV radiometric scales. The NBS group used the optically thin continuum radiation from a wall-stabilized hydrogen arc as its fundamental radiometric standard, while the MPI and PTB groups used the synchrotron radiation facility in DESY. It is found that the spectral radiance scales based upon the DESY synchrotron and the NBS hydrogen arc are consistent, at least for one wavelength relative to another.

Bridges, J. M.↗
NASA NTRS1978

Analysis of dynamic system response to product random processes

The response of dynamic systems to the product of two independent Gaussian random processes is developed by use of the Fokker-Planck and associated moment equations. The development is applied to the amplitude modulated process which is used to model atmospheric turbulence in aeronautical applications. The exact solution for the system response is compared with the solution obtained by the quasi-steady approximation which omits the dynamic properties of the random amplitude modulation. The quasi-steady approximation is valid as a limiting case of the exact solution for the dynamic response of linear systems to amplitude modulated processes. In the nonlimiting case the quasi-steady approximation can be invalid for dynamic systems with low damping.

Sidwell, K.↗
NASA NTRS1977

Photon pair production in astrophysical transrelativistic plasmas

Photon pair-production processes in marginally relativistic (transrelativistic) accretion plasmas are investigated in both Planckian and non-Planckian cases. Pair production in a plasma with an equilibrium (Planck) spectrum is reviewed, and pair-concentration calculations are performed for three general non-Planckian situations most relevant to black-hole accretion scenarios: steady-state transrelativistic plasmas of relatively high density characterized by a pure bremsstrahlung spectrum, a comptonized bremsstrahlung spectrum, and an unsaturated Compton scattering spectrum. The results obtained indicate that for transrelativistic temperatures (600 million to 6 billion K) photon pair production is not generally a dominant process for a plasma with a pure bremsstrahlung spectrum, but becomes dominant for plasmas where comptonization is important. It is also shown that photon pair-creation processes in a transrelativistic bremsstrahlung-radiating plasma that is more than marginally optically thick to Compton scattering significantly alter the plasma's spectrum by forcing it to become black-body before it reaches relativistic temperatures. Pair production and instabilities in unsteady-state plasmas are briefly considered

Stoeger, W. R.↗