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NASA NTRS1992

Self-similar evolution of magnetized plasmas. I - Quasi-static solution

The concept of linear expansion suggested by Wei-Hong (1989 and 1990), describes the self-similar evolution of a magnetic structure. Linear expansion can be represented by a single function which connects the evolving physical parameters of the plasma with their initial values in explicit forms. A general self-similar dynamic equation, therefore, is derived. As the first step toward more general consideration, the quasi-static solution is investigated in this paper. It is shown that a gamma = 4/3 polytrope may evolve through consecutive equilibria if its magnetic field expands self-similarly. The change of the energy everywhere inside the plasma equals the work done by the internal plasma pressure and magnetic field for the expansion. For the special case of an expanding force-free magnetic field, the self-similar expansion is a clean expansion. No free magnetic energy is left anywhere inside the magnetic structure. The approximation in quasi-state modeling of a pressure confined magnetized plasmoid is analyzed.

Yang, Wei-Hong↗

NASA NTRS1993

Formation of the stable auroral arc that intensifies at substorm onset

In a companion paper, we present observational evidence that the stable, growth-phase auroral arc that intensifies at substorm expansion phase onset often forms on magnetic field lines that map to within approximately 1 to 2 R(sub e) of synchronous. The equatorial plasma pressure is 1 to 10 nPa in this region, which can give a cross-tail current greater than 0.1 A/m. In this paper, we propose that the arc is formed by a perpendicular magnetospheric-current divergence that results from a strong dawn-to-dusk directed pressure gradient in the vicinity of magnetic midnight. We estimate that the current divergence is sufficiently strong that a is greater than 1 kV field-aligned potential drop is required to maintain ionospheric-current continuity. We suggest that the azimuthal pressure gradient results from proton drifts in the vicinity of synchronous orbit that are directed nearly parallel to the cross-tail electric field.

Lyons, L. R.↗

NASA NTRS1994

On the specta of X-ray bursters: Expansion and contraction stages

The theory of spectral formation during the explosion and contraction stages of X-ray bursters, which include the effects of Computonization and free-free absorption and emission, is described. Analytical expressions are provided for color ratios, and the spectral shape is given as a function of input parameters, elemental abundance, neutron star mass and radius, and Eddington ratio. An Eulerian calculation is used to determine the photospheric evolution accurately during the Eddington luminosity phase. The developed analytical theory for hydrodynamics of the expansion takes into account the dependence of Compton scattering opacity on electron temperature. An analytical expression is derived from the sonic point position and the value of the sonic velcoity. Using this value as a boundary condition at the sonic point, the velocity, density, and temperature profile are calculated throughout the whole photosphere. It is shown that the atmopsphere radiates spectra having a low-energy power-law shape and blackbody-like hard tail. In the expansion stage the spectra depend strongly on the temperature of the helium-burning zone at the neutron star surface. The X-ray photosheric radius increases to approximately 100 km or more, depending on the condition of the nuclear burning on the surface of the neutron star in the course of the expansion.

Titarchuk, Lev↗

NASA NTRS2003

Interferometer for Measuring Displacement to Within 20 pm

An optical heterodyne interferometer that can be used to measure linear displacements with an error <=20 pm has been developed. The remarkable accuracy of this interferometer is achieved through a design that includes (1) a wavefront split that reduces (relative to amplitude splits used in other interferometers) self interference and (2) a common-optical-path configuration that affords common-mode cancellation of the interference effects of thermal-expansion changes in optical-path lengths. The most popular method of displacement- measuring interferometry involves two beams, the polarizations of which are meant to be kept orthogonal upstream of the final interference location, where the difference between the phases of the two beams is measured. Polarization leakages (deviations from the desired perfect orthogonality) contaminate the phase measurement with periodic nonlinear errors. In commercial interferometers, these phase-measurement errors result in displacement errors in the approximate range of 1 to 10 nm. Moreover, because prior interferometers lack compensation for thermal-expansion changes in optical-path lengths, they are subject to additional displacement errors characterized by a temperature sensitivity of about 100 nm/K. Because the present interferometer does not utilize polarization in the separation and combination of the two interfering beams and because of the common-mode cancellation of thermal-expansion effects, the periodic nonlinear errors and the sensitivity to temperature changes are much smaller than in other interferometers

Zhao, Feng↗

NASA NTRS1988

Analytical approximation of a distorted reflector surface defined by a discrete set of points

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

Acosta, Roberto J.↗

NASA NTRS1983

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Dadfar, M. B.↗

NASA NTRS1982

A facility for the simulation of low orbit atmospheric oxygen bombardment

A molecular beam facility to simulate the space environment of a spacecraft at low orbit was designed with the intent of studying the effect on the properties of optical elements of oxygen atoms impacting at orbital velocity. The four-stage differentially pumped molecular beam facility includes a variety of oxygen atom beam sources which cover a wide range of velocities (1 km/sec to approximately 8 km/sec), in addition to the ultra-clean experimental environmental of an ultra-high vacuum chamber and an optical diagnostic set-up. The primary oxygen atom beam source used to obtain the 8 km/sec O atoms is an arc heated source. It consists of a modified commercially available plasma torch. The modifications include attachments which provide for a nozzle which is used to expand the atomic beam into the vacuum system, and exhaust channels to dispose of excess torch gas. The torch operates in the 'nontransferred' mode of operation, that is the electric arc is confined within the torch. A plasma is formed in helium by a dc arc. A small amount of O2 is injected downstream from the arc where it is thermally dissociated by the hot He into oxygen atoms. The high temperature and isentropic expansion give the oxygen atoms their velocity. Using seeded beam techniques, oxygen atom beams of approximately 3.5 and approximately 1.5 km/sec, respectively, are obtained.

Arnold, G. S.↗

NASA NTRS1993

Vulcanian explosive eruptions: A mechanism for localised pyroclast dispersal on Venus

A model of the mechanisms involved in transient (vulcanian-type) explosive eruptions has enabled us to place constraints on the velocities of blocks ejected during such events on Earth as well as on the excess pressure and concentration of gas in the vent prior to the onset of the explosion. This model, suitably modified, can predict the results of similar eruptions occurring under the differing Venusian environmental conditions. It is found that the much higher atmospheric pressure (approximately 100 bars at the mean planetary radius) dominates the form of the resulting deposit in two main ways: (1) by inhibiting the expansion out of the vent of overpressured gas, hence reducing ejecta velocity; and (2) by retarding the flight of ejected blocks via drag effects. Thus, it is expected that such deposits will typically extend to approximately 200 m on Venus as compared to several km for documented terrestrial deposits.

Fagents, S. A.↗

NASA NTRS1994

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Baumeister, Kenneth J.↗

NASA NTRS1978

Second order approximation of natural frequency constraints in structural synthesis

The paper is concerned with structural optimization problems in which the constraints consist of limits imposed on the natural frequencies of the structure. Improvements in the quality of approximations for the frequency constraints are sought by considering second-order Taylor series expansions. Analysis of the second-order sensitivity of natural frequencies is carried out. As an example, the design of a midplane symmetric aluminum beam of constant depth supporting three nonstructural masses is considered. Web thickness and chord member areas were determined so as to achieve minimum structural mass while maintaining the fundamental frequency at or above 30 Hz.

Miura, H.↗

NASA NTRS1984

A method for computing the kernel of the downwash integral equation for arbitrary complex frequencies

For the design of active controls to stabilize flight vehicles, which requires the use of unsteady aerodynamics that are valid for arbitrary complex frequencies, algorithms are derived for evaluating the nonelementary part of the kernel of the integral equation that relates unsteady pressure to downwash. This part of the kernel is separated into an infinite limit integral that is evaluated using Bessel and Struve functions and into a finite limit integral that is expanded in series and integrated termwise in closed form. The developed series expansions gave reliable answers for all complex reduced frequencies and executed faster than exponential approximations for many pressure stations.

Desmarais, R. N.↗

NASA NTRS1987

A hybrid perturbation Galerkin technique with applications to slender body theory

A two step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

NASA NTRS1986

Studies of electron-molecule collisions - Applications to e-H2O

Elastic differential and momentum transfer cross sections for the elastic scattering of electrons by H2O are reported for collision energies from 2 to 20 eV. These fixed-nuclei static-exchange cross sections were obtained using the Schwinger variational approach. In these studies the exchange potential is directly evaluated and not approximated by local models. The calculated differential cross sections, obtained with a basis set expansion of the scattering wave function, agree well with available experimental data at intermediate and larger angles. As used here, the results cannot adequately describe the divergent cross sections at small angles. An interesting feature of the calculated cross sections, particularly at 15 and 20 eV, is their significant backward peaking. This peaking occurs in the experimentally inaccessible region beyond a scattering angle of 120 deg. The implication of this feature for the determination of momentum transfer cross sections is described.

Brescansin, L. M.↗

NASA NTRS1989

A hybrid perturbation Galerkin technique with applications to slender body theory

A two-step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

NASA NTRS1994

Second-order reconstruction of the inflationary potential

To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, n and n(sub T), and their contributions to the variance of the quadrupole CBR temperature anisotropy, S and T. In addition, there is a 'consistency relation' between these quantities: n(sub T) = (-1/ 7)(T/S). We derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, in terms, of n, n(sub T), S, T, and dn/d ln gamma. We also obtain the second-order consistency relation, n(sub T) = (-1/7)(T/S)(1 + 0.11(T/S) + 0.15(n-1)). As an example we consider the exponential potential, the only known case where exact analytic solutions for the perturbation spectra exist. We reconstruct the potential via Taylor expansion (with coefficients calculated at both first and second order), and introduce the Pade approximate as a greatly improved alternative.

Liddle, Andrew R.↗

NASA NTRS2015

Periodic Density Structures and the Origin of the Slow Solar Wind

The source of the slow solar wind has challenged scientists for years. Periodic density structures (PDSs), observed regularly in the solar wind at 1 AU (Astronomical Unit), can be used to address this challenge. These structures have length scales of hundreds to several thousands of megameters and frequencies of tens to hundreds of minutes. Two lines of evidence indicate that PDSs are formed in the solar corona as part of the slow solar wind release and/or acceleration processes. The first is corresponding changes in compositional data in situ, and the second is PDSs observed in the inner Heliospheric Imaging data on board the Solar Terrestrial Relations Observatory (STEREO)/Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) suite. The periodic nature of these density structures is both a useful identifier as well as an important physical constraint on their origin. In this paper, we present the results of tracking periodic structures identified in the inner Heliospheric Imager in SECCHI back in time through the corresponding outer coronagraph (COR2) images. We demonstrate that the PDSs are formed around or below 2.5 solar radii-the inner edge of the COR2 field of view. We compute the occurrence rates of PDSs in 10 days of COR2 images both as a function of their periodicity and location in the solar corona, and we find that this set of PDSs occurs preferentially with a periodicity of approximately 90 minutes and occurs near streamers. Lastly, we show that their acceleration and expansion through COR2 is self-similar, thus their frequency is constant at distances beyond 2.5 solar radii.

sun: corona↗

NASA NTRS2015

The THS Experiment: Simulating Titans Atmospheric Chemistry at Low Temperature (200K)

In Titan's atmosphere, composed mainly of N2 (95-98%) and CH4 (2-5%), a complex chemistry occurs at low temperature, and leads to the production of heavy organic molecules and subsequently solid aerosols. Here, we used the Titan Haze Simulation (THS) experiment, an experimental setup developed at the NASA Ames COSmIC simulation facility to study Titan's atmospheric chemistry at low temperature. In the THS, the chemistry is simulated by plasma in the stream of a supersonic expansion. With this unique design, the gas is cooled to Titan-like temperature ( approximately 150K) before inducing the chemistry by plasma, and remains at low temperature in the plasma discharge (approximately 200K). Different N2-CH4-based gas mixtures can be injected in the plasma, with or without the addition of heavier precursors present as trace elements on Titan, in order to monitor the evolution of the chemical growth. Both the gas- and solid phase products resulting from the plasma-induced chemistry can be monitored and analyzed using a combination of complementary in situ and ex situ diagnostics. A recent mass spectrometry[1] study of the gas phase has demonstrated that the THS is a unique tool to probe the first and intermediate steps of Titan's atmospheric chemistry at Titan-like temperature. In particular, the mass spectra obtained in a N2-CH4-C2H2-C6H6 mixture are relevant for comparison to Cassini's CAPS-IBS instrument. The results of a complementary study of the solid phase are consistent with the chemical growth evolution observed in the gas phase. Grains and aggregates form in the gas phase and can be jet deposited on various substrates for ex situ analysis. Scanning Electron Microscopy images show that more complex mixtures produce larger aggregates. A mass spectrometry analysis of the solid phase has detected the presence of aminoacetonitrile, a precursor of glycine, in the THS aerosols. X-ray Absorption Near Edge Structure (XANES) measurements also show the presence of imine and nitrile functional groups, showing evidence of nitrogen chemistry. These complementary studies show the high potential of THS to better understand Titan's chemistry and the origin of aerosol formation.

Laboratory↗

NASA NTRS1981

Substorm signatures at synchronous altitude

The signatures of magnetospheric substorms near 6.6 earth radii are statistically examined using data obtained on board ATS 6 by magnetic field and energetic particle measurements. It is confirmed that the configuration change toward a tail-like field in the dusk-to-midnight sector typically begins about one hour before the onset of the expansion phase of a substorm. Configuration changes before the onsets of moderate substorms are characterized by a directional change of magnetic field at magnetic latitude of approximately 10 deg, rather than by a change in the field magnitude. It is found during storm periods that the magnetic field orientation occasionally becomes almost parallel to the magnetic equator before expansion phase onsets. Here, the field magnitude usually increases above background levels. These facts are seen as strongly suggesting that a tail-like configuration is caused by an intensification and earthward motion of the cross-tail current system, often close to 6.6 earth radii, rather than by development of diamagnetic ring current.

Kokubun, S.↗