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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

The sensitivity of nonradial p mode eigenfrequencies to solar envelope structure

Eigenfrequencies are calculated for nonradial p mode oscillations in the sun. These frequencies are shown to depend on the adiabat of the solar convective envelope. The frequency dependence is greatest for the p2 and p3 modes described by spherical harmonics with l = 500 to 1000. The solar envelope model includes a realistic representation of the chromosphere out to the base of the corona. For the chromospheric model of Vernazza, Avrett, and Loeser (1976) chromospheric modes with a distinct locus of eigenfrequencies exist near an eigenfrequency of 0.026 Hz. The actual frequencies of these eigenmodes depend on the thickness of the chromosphere. Because of the difference in the dependence of eigenfrequency on l for the chromospheric modes as compared with the p modes, the two types of mode can be distinguished observationally. If detected, the chromospheric modes would provide a good way of determining the thickness of the chromosphere.

Ulrich, R. K.↗
NASA NTRS2001

Determining the Mass Density Along Magnetic Field Lines from Toroida Eigenfrequencies

Toroidal eigenfrequencies can be used to remotely sense the equatorial mass density rho(sub eq) and the density dependence along a magnetic field line. Here we present improvements to the method of Schulz [1996], which allows rho(sub eq) and the power law index alpha (for mass density along a field line proportional to R(sup -alpha), where R is the radial distance from the center of the Earth) to be determined from the y intercept and slope of a plot of toroidal frequency versus toroidal harmonic number n. Our modifications include a model form for eigenfrequencies with a fractional precision of 0.0005 for -6 less than or = alpha less than or = 6 and 2 less than or = L less than or = 8 (accuracy is doubtful beyond L = 5) and an iterative procedure for getting more accurate results than those found using Schulz's method. In addition, we do an analysis of the effect of random measurement errors. Observed frequencies need to be accurate to approx. 6% (3%) of the fundamental frequency in order to determine rho(sub eq) (alpha) to a precision of 30% (unity). We then apply our method to data generated using the Global Core Plasma Model for plasmaspheric mass density; our analysis demonstrates clearly bow the alpha index represents the mass density dependence on the outer part of the field line (R/(LR(sub E)) greater than or approx. 2/3).

Denton, R.↗
NASA NTRS1979

The effect of a radial rotational velocity gradient on p-mode eigenfrequencies

The splitting of p-mode eigenfrequencies due to a depth-dependent solar rotation rate is considered. It is shown that to a first approximation this splitting can be treated as resulting from the translation of the wave pattern across the field of view with a velocity equal the actual velocity at a depth called the effective depth. The effective depths for a model solar envelope with l/H = 3 are presented as a function of position on the (kh, omega)-plane. The combination of omega near 0.025/s and kh near 0 yields the deepest probe of the solar envelope. For this same combination of kh and omega it is possible to resolve individual groups of eigenmodes in frequency but not in spatial wavenumber. Achievement of this resolution observationally may permit a determination of the lifetime of these particular modes.

Ulrich, R. K.↗
NASA NTRS1981

Effect of elastic end rings on the eigenfrequencies of thin cylinders

The effect of elastic end rings on the eigenfrequencies of thin cylindrical shells is studied by using an exact solution of the linear eigenvalue problem. The out-of-plane and torsional rigidities of the rings are responsible for the overall shell stiffness. Considerable mode interaction exists for modes with low circumferential wave numbers when the mass of the ring is comparable with that of the shell. The hypothetical simply supported and clamped boundary conditions are practically impossible to realize with a finite-mass ring for relatively short and thin shells.

El Raheb, M.↗
NASA NTRS1984

The Sensitivity of Solar Eigenfrequencies to the Treatment of the Equation of State

The principal uncertainties in the equation of state involve the treatment of pressure ionization, the Debye-Huckel coulomb corrections, and the treatment of many-particle interaction effects. It is found that, for the lowest degree modes (l between 0 and 3), the terms and procedures used in the equation of state which deal with these uncertainties introduce changes in the frequencies which are less than 4 micro Hz. Recently, Shibahashi, Noels and Gabriel (1983) published solar eigenfrequencies using a theory with an equation of state improved with respect to the theory used earlier by Shibahashi and Osaki (1981). Their comparison between the two sets of results suggested that uncertainties in the frequencies as large as 10 micro Hz could be caused by the equation of state. It is felt that since the entire effect of the uncertain terms is only 4 micro Hz and since the uncertainties are only a fraction of each term, the 10 micro Hz changes found by Shibahashi et al must be a consequence of differences between the earlier and later calculations in areas other than the equation of state.

Ulrich, R. K.↗
NASA NTRS1995

The role of photospheric magnetic fields in the variation of solar oscillation eigenfrequencies

The frequencies of solar oscillations have been found to be higher at the peak of the solar cycle, their variation being consistent with that expected from a change in the solar structure confined to the Sun's outer layers. In this work, a technique is introduced for estimating the effect of the highly inhomogeneous photospheric magnetic field on solar oscillation eigenfrequencies, and its results are compared with the solar data. It is found that the observed steep rise in frequency shift at low frequency and the leveling of or decline at high frequency are well reproduced by the model. The correct order of magnitude for the frequency changes is also reproduced, at least at low frequency. The model implies a particular functional form for the variation of the frequency changes with order and degree, and it is suggested that future advances in observation and theory will therefore allow this model to be confirmed or refuted.

Rosenthal, C. S.↗
NASA NTRS2009

A Technique for Adjusting Eigenfrequencies of WGM Resonators

A simple technique has been devised for making small, permanent changes in the eigenfrequencies (resonance frequencies) of whispering-gallery-mode (WGM) dielectric optical resonators that have high values of the resonance quality factor (Q). The essence of the technique is to coat the resonator with a thin layer of a transparent polymer having an index of refraction close to that of the resonator material. Successive small frequency adjustments can be made by applying successive coats. The technique was demonstrated on a calcium fluoride resonator to which successive coats of a polymer were applied by use of a hand-made wooden brush. To prevent temperature- related frequency shifts that could interfere with the verification of the effectiveness of this technique, the temperature of the resonator was stabilized by means of a three-stage thermoelectric cooler. Measurements of the resonator spectrum showed the frequency shifts caused by the successive coating layers.

Strekalov, Dmitry↗
NASA NTRS1987

An analysis of electromagnetic coupling and eigenfrequencies for microwave electrothermal thruster discharges

This paper discusses the basic approach to developing a comprehensive electromagnetic model for a microwave electrothermal discharge. The discharge and surrounding region are modeled as a section of waveguide loaded with a uniform, cold, lossy plasma. A characteristic equation has been derived describing all possible system modes. In particular the TM(01) mode is numerically solved. Propagation and attenuation constants for the TM(01) mode are found numerically for a given range of electron-neutral collision frequencies and plasma densities. Results are used to interpret a number of experimental observations in helium. Specifically, they are used to explain high coupling efficiencies and ease of cavity tuning at high pressures.

Frasch, L. L.↗
NASA NTRS1990

Eigenfrequencies and horizontal structure of divergent barotropic instability originating in tropical latitudes

A systematic investigation of eigenfunctions of the generalized Laplace tidal equation, for the case of tropical-latitude monotonic mean zonal wind profiles with a single narrow reversed vorticity gradient region, has revealed that, in the limit of low planetary zonal wavenumber, the barotropic instability modes bifurcate into weakly divergent modes of hemispheric scale, on the one hand, and on the other strongly divergent 'internal' modes trapped about the source region. These latter disturbances penetrate into the deep tropics as a Kelvin wave-type phenomenon not previously seen in this context. These results suggest that hemispheric barotropic instability need not be purely nondivergent, and that the growth of weakly divergent modes is preferred.

Dunkerton, Timothy J.↗
NASA NTRS1995

Uncertainties for two-dimensional models of solar rotation from helioseismic eigenfrequency splitting

Observed solar p-mode frequency splittings can be used to estimate angular velocity as a function of position in the solar interior. Formal uncertainties of such estimates depend on the method of estimation (e.g., least-squares), the distribution of errors in the observations, and the parameterization imposed on the angular velocity. We obtain lower bounds on the uncertainties that do not depend on the method of estimation; the bounds depend on an assumed parameterization, but the fact that they are lower bounds for the 'true' uncertainty does not. Ninety-five percent confidence intervals for estimates of the angular velocity from 1986 Big Bear Solar Observatory (BBSO) data, based on a 3659 element tensor-product cubic-spline parameterization, are everywhere wider than 120 nHz, and exceed 60,000 nHz near the core. When compared with estimates of the solar rotation, these bounds reveal that useful inferences based on pointwise estimates of the angular velocity using 1986 BBSO splitting data are not feasible over most of the Sun's volume. The discouraging size of the uncertainties is due principally to the fact that helioseismic measurements are insensitive to changes in the angular velocity at individual points, so estimates of point values based on splittings are extremely uncertain. Functionals that measure distributed 'smooth' properties are, in general, better constrained than estimates of the rotation at a point. For example, the uncertainties in estimated differences of average rotation between adjacent blocks of about 0.001 solar volumes across the base of the convective zone are much smaller, and one of several estimated differences we compute appears significant at the 95% level.

Genovese, Christopher R.↗
NASA NTRS2013

Radio frequency tank eigenmode sensor for propellant quantity gauging

A method for measuring the quantity of fluid in a tank may include the steps of selecting a match between a measured set of electromagnetic eigenfrequencies and a simulated plurality of sets of electromagnetic eigenfrequencies using a matching algorithm, wherein the match is one simulated set of electromagnetic eigenfrequencies from the simulated plurality of sets of electromagnetic eigenfrequencies, and determining the fill level of the tank based upon the match.

Zimmerli, Gregory A.↗
NASA NTRS1981

A diurnal resonance in the ocean tide and in the earth's load response due to the resonant free 'core nutation'

The effects of the oceans, which are subject to a resonance due to a free rotational eigenmode of an elliptical, rotating earth with a fluid outer core having an eigenfrequency of (1 + 1/460) cycle/day, on the body tide and nutational response of the earth to the diurnal luni-tidal force are computed. The response of an elastic, rotating, elliptical, oceanless earth with a fluid outer core to a given load distribution on its surface is first considered, and the tidal sea level height for equilibrium and nonequilibrium oceans is examined. Computations of the effects of equilibrium and nonequilibrium oceans on the nutational and deformational responses of the earth are then presented which show small but significant perturbations to the retrograde 18.6-year and prograde six-month nutations, and more important effects on the earth body tide, which is also resonant at the free core notation eigenfrequency.

Wahr, J. M.↗
NASA NTRS1984

Solar Inverse Theory

Helioseismological inversion, as with the inversion of any other data, is divided into three phases. The first is the solution of the so-called forward problem: namely, the calculation of the eigenfrequencies of a theoretical equilibrium state. The second is an attempt to understand the results, either empirically by determining how those frequencies vary as chosen parameters defining the equilibrium model are varied, or analytically from asymptotic expansions in limiting cases of high order or degree. The third phase is to pose and solve an inverse problem, which seeks to find a plausible equilibrium model of the Sun whose eigenfrequencies are consistent with observation. The three phases are briefly discussed in this review, and the third, which is not yet widely used in helioseismology, is illustrated with some selected inversions of artificial solar data.

Gough, D.↗
NASA NTRS1985

Resistive decay of Alfven waves in a non-uniform plasma

The effect of resistive dissipation on the propagation of an MHD disturbance in a nonuniform plasma is examined. The present analysis, based on a boundary-layer technique, shows the existence of resistive normal modes with complex eigenfrequencies. The real part of the eigenfrequency is associated with an oscillatory behavior and defines the location in space of the layer where resistivity is important. The dissipation mechanism is responsible for the damping of the wave, in contrast with previous works in which the ideal MHD theory was used.

Mok, Y.↗