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NASA NTRS1981

High frequency scattering by a thin dielectric slab

The geometrical theory of diffraction (GTD) is applied to the problem of a source in the presence of a three-dimensional thin dielectric slab. It is assumed that the reflection and transmission properties of the slab are known, and the slab is not lossy and/or multilayered. Two-dimensional thin dielectric layer scattering is analyzed when diffraction emanates from a single point, the source is not near the slab, and random energy approaching tangentially due to transmission is negligible. Coefficients are obtained for the scattering and the GTD solution is extended to the three dimensional case after development of a ray fixed coordinate system. The results are applied to a half wavelength dipole mounted above a square polystyrene covered ground plane.

Burnside, W. D.↗

NASA NTRS1983

Analytical and Numerical Solution for a Solidifying Liquid Alloy Slab

Numerical and analytical solutions are presented for the temperature and concentration distributions during the solidification of a binary liquid alloy slab. The slab is taken to be of a finite depth but infinite in the horizontal direction. The solidification process is started by withdrawing a fixed amount of heat from the lower surface of the slab. The upper surface of the slab is subjected to both radiation and convective conditions. The solution gives the concentration and temperature profiles and the interface position as a function of time. Due to the smallness of the mass diffusion coefficient in the solid, the numerical solution method breaks down whenever the ratio of the diffusivities in the solid and the liquid falls below a certain value. An analytical method is developed which gives accurate solution for any value of the diffusivity ratio.

Antar, B. N.↗

NASA NTRS1983

Reduced thermal focusing and birefringence in zig-zag slab geometry crystalline lasers

The present investigation is concerned with interferometric measurements of the thermally induced optical effects in laser crystals, taking into account crystals cut in both the zig-zag slab and the conventional rod geometries. The measurements conducted demonstrate the significant advantages obtained by replacing the rod in a Nd:YAG laser with a slab. A description is provided of simple measures designed to eliminate end and edge effects, and efficiency and threshold data for the Nd:YAG slab and the rod it replaced are presented. The only disadvantage is a small increase in cost due to the more difficult fabrication of the slab and the greater amount of Nd:YAG which is needed to allow the ends to be unpumped.

Kane, T. J.↗

NASA NTRS1992

Analysis of surface wave propagation in a grounded dielectric slab covered by a resistive sheet

Both parallel and perpendicular polarized surface waves are known to propagate on lossless and lossy grounded dielectric slabs. Surface wave propagation on a grounded dielectric slab covered with a resistive sheet is considered. Both parallel and perpendicular polarizations are examined. Transcendental equations are derived for each polarization and are solved using iterative techniques. Attenuation and phase velocity are shown for representative geometries. The results are applicable to both a grounded slab with a resistive sheet and an ungrounded slab covered on each side with a resistive sheet.

Shively, David G.↗

NASA NTRS1991

Waveform effects of a metastable olivine tongue in subducting slabs

Velocity models of subducting slabs with a kinetically-depressed olivine to beta- and gamma-spinel transition are constructed, and the effect that such structures would have on teleseismic P waveforms are examined using a full-wave finite-difference method. These 2D calculations yielded waveforms at a range of distances in the downdip direction. The slab models included a wedge-shaped, low-velocity metastable olivine tongue (MOTO) to a depth of 670 km, as well as a plausible thermal anomaly; one model further included a 10-km-thick fast layer on the surface of the slab. The principal effect of MOTO is to produce grazing reflections at wide angles off the phase boundary, generating a secondary arrival 0 to 4 seconds after the initial arrival depending on the take-off angle. The amplitude and timing of this feature vary with the lateral location of the seismic source within the slab cross-section.

Vidale, John E.↗

NASA NTRS1981

On the compensation of geoid anomalies due to subducting slabs

Candidate models of the forces which oppose the sinking of slabs are all constrained to produce results consistent with the following observation: relative geoid highs, which one assumes are due to slabs, characteristically occur over subduction zones. Certain models which are otherwise plausible, such as those based on a Newtonian half-space mantle, yield geoid lows instead of highs. This study has extended a published model of viscous corner flow in subduction zones in order to demonstrate that it can, in certain cases, produce the requisite geoid highs. Specifically the relative geoid highs are produced if mantle flow is distinctly non-Newtonian (stress exponent n 2). Results in the form of deflection on vertical (or geoid slope) profiles are computed for typical values of the slab parameters; they are compared with a representative profile of geoid slopes derived from Seasat altimeter data in order to show qualitative similarities. It is concluded that the effect of non-Newtonian flow as opposed to Newtonian, is to spread out the induced surface deformation, thereby stretching out the regional compensation to wavelengths, (transverse to the trench) of several thousand kilometers.

Mcadoo, D. C.↗

NASA NTRS1984

The distribution of earthquakes with depth and stress in subducting slabs

The global variation of Benioff zone seismicity with depth and the orientation of stress axes of deep and intermediate earthquakes is explained using numerical models of subducting slabs. Models that match the seismicity and stress require a barrier to flow at the 670 km seismic discontinuity. The barrier may be a viscosity increase of at least an order of magnitude or a chemical discontinuity. Instantaneous flow is subparallel to the slabs for models with a viscosity increase but contorted for models with a chemical barrier. Log N (number of earthquakes) decreases linearly to 250-300 km depth and increases thereafter. Stress magnitude in the models shows the same pattern, in accord with experiments showing N proportional to e(k-sigma), with k a constant and sigma the stress magnitude. The models predict downdip compression in the slabs at depths below 300-400 km, as observed for earthquake stress axes.

Vassiliou, M. S.↗

NASA NTRS1986

62-dB-gain multiple-pass slab geometry Nd:YAG amplifier

A flash-lamp-pumped slab Nd:YAG laser amplifier with 62 dB of gain is demonstrated. The amplifier remains linear for energy extraction up to 12 mJ, and the beam spatial quality remains good at repetition rates up to 10 Hz. The slab geometry provides for gain averaging in the zigzag dimension, thus eliminating the undesirable effects of nonuniform pumping. This averaging and the necessity for only a single compact gain element are valuable attributes that may allow for eventual laser-diode array pumping of the slab Nd:YAG amplifier.

Kane, T. J.↗

NASA NTRS1987

Thermally induced phase changes, lateral heterogeneity of the mantle, continental roots, and deep slab anomalies

Factors which influence the lateral heterogeneity in density and seismic velocity with depth in the upper earth mantle are discussed. It is emphasized that most of the increases in density and seismic velocity with depth are caused by pressure-induced solid-solid phase changes in the high-density high-velocity phases of mineral assemblage, due to variations in temperature. In particular, the ilmenite form of MgSiO3 and the gamma-spinel form of Mg2SiO4 have broad stability fields in cold mantle and are not stable in hotter mantle. It is emphasized that the density and velocity anomalies associated with temperature-induced phase changes in mineral assemblage must be taken into account in the thermal models of the slabs; when these effects are accounted for, the geoid and seismic anomalies associated with subducted slabs are consistent with slab confinement to the upper mantle and with layered models of mantle convection.

Anderson, Don L.↗

NASA NTRS1991

Diffraction by a multilayer slab recessed in a ground plane via generalized impedance boundary conditions

The diffraction problem associated with a multilayer material slab recessed in a perfectly conducting ground plane is formulated and solved via the generalized scattering matrix formulation in conjunction with the dual integral equation approach. The multilayer slab is replaced by a surface obeying a generalized impedance boundary condition to facilitate the computation of the pertinent Wiener Hopf split functions and their zeros. Both Ez and Hz polarizations are considered, and a number of scattering patterns are presented, some of which are compared to exact results available for a homogeneous recessed slab.

Ricoy, M. A.↗

NASA NTRS1993

Deformation of a weak subducted slab and variation of seismicity with depth

Numerical simulations of slab evolution are used here to show that a weak slab model is consistent with seismic observations. Assuming that earthquakes occur at a rate proportional to deformation rate, the observed variation with depth of seismicity rate and focal mechanisms is reproduced along with the cessation of seismicity at 670 km depth. Provided that sinking material encounters resistance at depth, the pattern of seismicity can be explained by any mechanism for deep earthquakes in which the rate of seismicity is proportional to strain rate in the slab.

Tao, Winston C.↗

NASA NTRS1993

Surface waves on a grounded dielectric slab covered by a resistive sheet

This paper examines surface wave propagation in a grounded dielectric slab covered with a resistive sheet. Transcendental equations are derived for each polarization and are solved using iterative techniques. Attention and phase velocity are shown for a representative geometry. The results are applicable to both a grounded slab covered with a resistive sheet and an ungrounded slab covered on each side with a resistive sheet.

Shively, David↗

NASA NTRS1995

Dynamical consequences on fast subducting slabs from a self-regulating mechanism due to viscous heating in variable viscosity convection

We have studied 2-D time-dependent convection for a rheology which is both non-Newtonian and temperature-dependent. Strong effects associated with viscous heating are found in the downwelling sheets, which are heated on both sides with an intensity around O(100) times the chondritic value. The magnitude of viscous heating increases strongly with the subduction speed. The slab interior is weakened by viscous heating and slab breakoff then takes place. This process provides a self-regulating mechanism for governing the speed of intact slabs able to reach the deep mantle. Timescales associated with viscous heating are quite short, a few million years. Internal heating by radioactivity decreases the amount of shear heating.

Larsen, Tine B.↗

NASA NTRS2000

Convection in Slab and Spheroidal Geometries

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

Porter, David H.↗

NASA NTRS1969

Parametric excitation in a plasma slab.

Parametric excitation theory involving Langmuir and ion-acoustic waves for homogeneous plasma slab with specular particle reflection at slab walls

Goldman, R.↗

NASA NTRS1972

Scattering of electromagnetic waves from a turbulent plasma slab.

Scattering of electromagnetic waves from a turbulent plasma slab is studied. Part of the effects of the multiple scattering is taken into account. The reflection coefficient is found to be increased and its variation with respect to the slab thickness is smoothed out by the random scattering.

Liu, C. H.↗

NASA NTRS1973

The slab thickness of the mid-latitude ionosphere.

The thickness of the peak of the ionosphere depends primarily on the temperature T sub n of the neutral gas, and corresponds approximately to an alpha-Chapman layer at a temperature of 0.87T sub n. The overall slab thickness, as given by Faraday rotation measurements, is then tau = 0.22T sub n + 7 km. Expansion of the topside ionosphere, and changes in the E- and F1-regions increase tau by about 20 km during the day in summer. Near solar minimum, tau is increased by a lowering of the O(+)/H(+) transition height; if the neutral temperature T sub n is estimated, this height can be obtained from observed values of tau. Hourly values of slab thickness were determined over a period of 6 yr at 34 and 42 S. Near solar maximum the nighttime values were about 260 km in all seasons. The corresponding neutral temperatures agree with satellite drag values; they show a semiannual variation of 14% and a seasonal change of 5%. Daytime values of tau were about 230 km in winter and 320 km in summer, implying a seasonal change of 30% in T sub n.

Titheridge, J. E.↗

NASA NTRS1975

Energy transfer by radiation in non-grey atomic gases in isothermal and non-isothermal slabs

A multiband model for the absorption coefficient of atomic hydrogen-helium plasmas is constructed which includes continuum and line contributions. Emission from 28 stronger lines of 106 that have been screened is considered, of which 21 are from hydrogen and 7 belong to helium, with reabsorption due to line-line, line-continuum overlap accurately accounted for. The model is utilized in the computation of intensities and fluxes from shock-heated slabs of 85% H2-15% He mixtures for slab thicknesses from 1 to 30 cm, temperature from 10,000 to 20,000 K, and for different densities. In conjunction with the multiband model, simple numerical schemes have been devised which provide a quick and comprehensive way of computing radiative energy transfer in nonisothermal and nongrey gases.

Poon, P. T. Y.↗