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Ambipolar diffusion is discussed for the case of a weakly-ionized, multicomponent plasma. Shortcomings of some of the previous formulations of this problem are pointed out. In particular, it is shown that the polarization electrostatic field acts to couple the motion of the various ions with the result that the diffusion velocity of each ion depends on the density gradients of all the ions.
We consider the resistive diffusion of a force-free magnetic field in a tenuous compressible medium, which is free to move to accommodate the changing magnetic-field configuration. This process is nonlinear, contrary to the usual magnetic field diffusion in a fixed medium. We show that the force-free magnetic field may evolve slowly for an extended period of time, whereupon it abruptly develops steep gradients and passes into an explosive phase. We suggest that it is this process that sets the stage for the onset of solar flares.
A new correlation method for binary gaseous diffusion coefficients from very low temperatures to 10,000 K is proposed based on an extended principle of corresponding states, and having greater range and accuracy than previous correlations. There are two correlation parameters that are related to other physical quantities and that are predictable in the absence of diffusion measurements. Quantum effects and composition dependence are included, but high-pressure effects are not. The results are directly applicable to multicomponent mixtures.
Knowledge of the probability distribution of photon path lengths for diffuse reflection in the continuum from a planetary atmosphere greatly simplifies computation of the shape and strength of absorption lines formed under conditions of multiple scattering. Graphs of this probability distribution are presented for diffuse reflection from a semiinfinite conservative atmosphere for both isotropic and forward-directed scattering, and for several angles of incidence and reflection. Graphs showing distributions for the case of absorption in the continuum are also discussed. The distributions are obtained from an analytic expression for the path-length distribution for nth-order scattering and a tabulation of nth-order intensities. It is found that te shape of the probability distribution depends markedly on the degree of forward scattering due to the phase function. The results are compared with those obtained by a Monte Carlo computation of the sort which might be used if tabulated nth-order intensities were not available.
We have investigated a new approach to deriving a diffusion equation for charged particles in a static, random magnetic field. Our method incorporates essential effects of the magnetic fluctuations in the lowest order particle orbits. Significant corrections to the usual quasilinear diffusion coefficient for cosmic rays with pitch angles near 90 deg are a consequence. Monte Carlo results bear out the validity of our theory.
Within the quasi-linear approximation, the existence of the parallel diffusion coefficient for cosmic rays in a random magnetic field (homogeneous, isotropic), despite the slow decay of the interaction between particles and random field, is demonstrated. As an example, the results of a numerical calculation of the parallel diffusion coefficient for a Gaussian random-field correlation function are presented. The numerical results are corroborated by asymptotic analysis and are compared to those of other theories.
Low-speed wind tunnel tests were conducted to study the influence of sweep angle on the pressure distributions of an ogee-tip configuration with relation to the effectiveness of the ogee tip in diffusing a line vortex. In addition to the pressure data, performance and flow-visualization data were obtained in the wind tunnel tests to evaluate the application of the ogee tip to aircraft configurations. The effect of sweep angle on the performance characteristics of a conventional-tip model, having equivalent planform area, was also investigated for comparison with the ogee-tip configuration. Results of the investigation generally indicate that sweep angle has little effect on the characteristics of the ogee in diffusing a line vortex.
A near-Lambertian diffuser is described which transmits and reflects ultraviolet light. An ultraviolet grade fused silica substrate is coated with vaporized fuse silica. The coating thickness is controlled, one thickness causing ultraviolet light to diffuse and another thickness causing ultraviolet light to reflect a near Lambertian pattern.
The mutual diffusion of two reacting gases is examined which takes place in a bath of inert gas atoms. Solutions are obtained between concentric spheres, each sphere acting as a source for one of the reactants. The calculational model is used to illustrate severe number density gradients observed in absorption experiments with alkali vapor. Severe gradients result when sq root k/D R is approximately 5 where k, D, and R are respectively the second order rate constant, the multicomponent diffusion constant, and the geometrical dimension of the experiment.
Diffusion bonding studies have been conducted on IN 718, VM 350 and the dissimilar alloy couple, IN 718 to maraging steel. The experimental processing parameters critical to obtaining consistently good diffusion bonds between IN 718 and VM 350 were determined. Interrelationships between temperature, pressure and surface preparation were explored for short bending intervals under vacuum conditions. Successful joining was achieved for a range of bonding cycle temperatures, pressures and surface preparations. The strength of the weaker parent material was used as a criterion for a successful tensile test of the heat treated bond. Studies of VM-350/VM-350 couples in the as-bonded condition showed a greater yielding and failure outside the bond region.
We have investigated a new approach to deriving a diffusion equation for charged particles in a static, random magnetic field. Our approach differs from the usual, quasi-linear one, in that we replace particle orbits in the average field by particle orbits in a partially averaged field. In this way, the fluctuating component of the field significantly modifies the particle orbits in those cases where the orbits in the average field are unrealistic. This method allows us to calculate a finite value for the pitch angle diffusion coefficient for particles with a pitch angle of 90 deg rather than the divergent or ambiguous results obtained by quasi-linear theories.
The motion of charged particles in a stochastic magnetic field is considered via a generalized quasi-linear expansion of Liouville's equation. The result is an equation relating cosmic-ray scintillations to particle gradients and to magnetic-field fluctuations (or diffusion coefficient). The resulting theory may be regarded as an example of a fluctuation-dissipation phenomenon, in which the diffusion coefficient plays the role of the dissipative parameter. The resonant interaction between particles and the random interplanetary magnetic field is considered explicitly, and it is shown that observed scintillations of high-energy (about 1 GeV) cosmic rays may be reasonably explained by the model.
Two different plasma wave instabilities have been invoked in earlier models for the generation of top side ionogram diffuse resonances. Arguments are presented that support the model based on the Harris instability, i.e., the instability resulting from a sounder-stimulated anisotropic electron velocity distribution. Two modifications to this model are also presented. First, it is only necessary for the instability mechanism to operate for a period of the order of milliseconds (rather than tens of milliseconds) in order to explain the observations. Second, the wave associated with the second harmonic of the electron cyclotron frequency, which enters into the nonlinear wave-wave interaction process included in the model, comes from the side bands of the transmitted sounder pulse rather than from the turbulent state of the plasma caused by the pulse. The second modification provides an explanation for the variation of the time duration observed among the members of the sequence of diffuse resonances.
The detailed effects of a magnetic field on the equilibrium surface abundances of Ap stars as well as on the diffusion velocity are considered. The equivalent widths of the magnetic null lines are shown to be functions of the magnetic field strength. Furthermore, null lines can be used to help distinguish between inhomogeneities in abundance and in magnetic field strength and to determine ionization temperatures. The results of the diffusion mechanism with magnetic fields are used to interpret the phenomenon of spectrum variability. A review of the observational aspects of null lines in the magnetic Ap stars is presented.
Diffused optical waveguides are studied using the modal and the ray tracing approach, with an emphasis on the case of a hollow waveguide with diffuse cladding. The properties of the guided modes are investigated in detail. The applications of these structures to optical circuits, integrated optics lasers and capillary gas lasers are discussed.
Transport mechanisms of zinc atoms in molten zinc were investigated by radiotracer techniques in unit and in near-zero gravity environments. Each melt in the Skylab flight experiments was maintained in a thermal gradient of 420 C to 790 C. Similar tests were performed in a unit gravity environment for comparison. After melting in the gradient furnace followed by a thermal soak period (the latter was used for flight samples only), the samples were cooled and analyzed for Zn-65 distribution. All samples melted in a unit gravity environment were found to have uniform Zn-65 distribution - no concentration gradient was observed even when the sample was brought rapidly to melting and then quenched. Space-melted samples, however, showed textbook distributions, obviously the result of diffusion. It was evident that convection phenomena were the dominant factors influencing zinc transport in unit gravity experiments, while diffusion was the dominant factor in near-zero gravity experiments.
Solutions are given for the diffusion of trapped particles in a planetary magnetic field in which the first and second adiabatic invariants are preserved but the third is not, using as boundary conditions a fixed density at the outer boundary (the magnetopause) and a zero density at an inner boundary (the planetary surface). Losses to an orbiting natural satellite are included and an approximate evaluation is made of the effects of the synchrotron radiation on the energy of relativistic electrons. Choosing parameters appropriate to Jupiter, the electrons required to produce the observed synchrotron radiation are explained. If a speculative mechanism in which the diffusion is driven by ionospheric wind is the true explanation of the electrons producing the synchrotron emission it can be concluded that Jupiter's inner magnetosphere is occupied by an energetic proton flux that would be a serious hazard to spacecraft.
The modulation of galactic cosmic rays is studied by the magnetic heterogeneities stream on the assumption that the diffusion coefficient is reduced whereas the solar wind velocity is increased with the growth of the angle between the sun's rotation axis and the direction of solar plasma motion. The stationary plane problem of isotropic diffusion is solved as it applies to two cases: (1) with due account of particle retardation by the antiphermium mechanism; and (2) without an account of the above mechanism. This problem is solved by the grid method in the polar coordinate system. The results of the calculations are followed by a discussion of the method of solution and of the errors.