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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

A FORMALISM FOR COVARIANT POLARIZED RADIATIVE TRANSPORT BY RAY TRACING

We write down a covariant formalism for polarized radiative transfer appropriate for ray tracing through a turbulent plasma. The polarized radiation field is represented by the polarization tensor (coherency matrix) N{sup {alpha}{beta}} {identical_to} (a{sup {alpha}}{sub k} a*{sup {beta}}{sub k}), where a{sub k} is a Fourier coefficient for the vector potential. Using Maxwell's equations, the Liouville-Vlasov equation, and the WKB approximation, we show that the transport equation in vacuo is k{sup {mu}}{nabla}{sub {mu}} N{sup {alpha}{beta}} = 0. We show that this is equivalent to Broderick and Blandford's formalism based on invariant Stokes parameters and a rotation coefficient, and suggest a modification that may reduce truncation error in some situations. Finally, we write down several alternative approaches to integrating the transfer equation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Second harmonic generation of q-Gaussian laser beam in preformed collisional plasma channel with nonlinear absorption

This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on a numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

NUMERICAL SIMULATION OF FAST-MODE MAGNETOSONIC WAVES EXCITED BY PLASMOID EJECTIONS IN THE SOLAR CORONA

The Atmospheric Imaging Assembly instrument on board the Solar Dynamics Observatory has directly imaged the fast-propagating magnetosonic waves (FMWs) successively propagating outward along coronal magnetic funnels. In this study we perform a numerical investigation of the excitation of FMWs in the interchange reconnection scenario, with footpoint shearing flow being used to energize the system and drive the reconnection. The modeling results show that as a result of magnetic reconnection, the plasma in the current sheet is heated up by Joule dissipation to ∼10 MK and is ejected rapidly, developing the hot outflows. Meanwhile, the current sheet is torn into plasmoids, which are shot quickly both upward and downward. When the plasmoids reach the outflow regions, they impact and collide with the ambient magnetic field there, which consecutively launches FMWs. The FMWs propagate outward divergently away from the impact regions, with a phase speed of the Alfvén speed of ∼1000 km s{sup –1}. In the k – ω diagram of the Fourier wave power, the FMWs display a broad frequency distribution with a straight ridge that represents the dispersion relation. With the WKB approximation, at the distance of 15 Mm from the wave source region, we estimate the energy flux of FMWs to be E ∼ 7.0 × 10{sup 6} erg cm{sup –2} s{sup –1}, which is ∼50 times smaller than the energy flux related to the tube-channeled reconnection outflow. These simulation results indicate that energetically and dynamically the outflow is far more important than the waves.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Varying constants quantum cosmology

We discuss minisuperspace models within the framework of varying physical constants theories including Λ-term. In particular, we consider the varying speed of light (VSL) theory and varying gravitational constant theory (VG) using the specific ansätze for the variability of constants: c(a) = c{sub 0} a{sup n} and G(a)=G{sub 0} a{sup q}. We find that most of the varying c and G minisuperspace potentials are of the tunneling type which allows to use WKB approximation of quantum mechanics. Using this method we show that the probability of tunneling of the universe ''from nothing'' (a=0) to a Friedmann geometry with the scale factor a{sub t} is large for growing c models and is strongly suppressed for diminishing c models. As for G varying, the probability of tunneling is large for G diminishing, while it is small for G increasing. In general, both varying c and G change the probability of tunneling in comparison to the standard matter content (cosmological term, dust, radiation) universe models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

The splitted laser beam filamentation in interaction of laser and an exponential decay inhomogeneous underdense plasma

The splitted beam filamentation in interaction of laser and an exponential decay inhomogeneous underdense plasma is investigated. Based on Wentzel-Kramers-Brillouin (WKB) approximation and paraxial/nonparaxial ray theory, simulation results show that the steady beam width and single beam filamentation along the propagation distance in paraxial case is due to the influence of ponderomotive nonlinearity. In nonparaxial case, the influence of the off-axial of {alpha}{sub 00} and {alpha}{sub 02} (the departure of the beam from the Gaussian nature) and S{sub 02} (the departure from the spherical nature) results in more complicated ponderomotive nonlinearity and changing of the channel density and refractive index, which led to the formation of two/three splitted beam filamentation and the self-distortion of beam width. In addition, influence of several parameters on two/three splitted beam filamentation is discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Formation and evolution of flapping and ballooning waves in magnetospheric plasma sheet

By adopting Lembége & Pellat’s 2D plasma-sheet model, we investigate the flankward flapping motion and Sunward ballooning propagation driven by an external source (e.g., magnetic reconnection) produced initially at the sheet center. Within the ideal MHD framework, we adopt the WKB approximation to obtain the Taylor–Goldstein equation of magnetic perturbations. Fourier spectral method and Runge–Kutta method are employed in numerical simulations, respectively, under the flapping and ballooning conditions. Studies expose that the magnetic shears in the sheet are responsible for the flapping waves, while the magnetic curvature and the plasma gradient are responsible for the ballooning waves. In addition, the flapping motion has three phases in its temporal development: fast damping phase, slow recovery phase, and quasi-stabilized phase; it is also characterized by two patterns in space: propagating wave pattern and standing wave pattern. Moreover, the ballooning modes are gradually damped toward the Earth, with a wavelength in a scale size of magnetic curvature or plasma inhomogeneity, only 1–7% of the flapping one; the envelops of the ballooning waves are similar to that of the observed bursty bulk flows moving toward the Earth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Growth of ring ripple in a collisionless plasma in relativistic-ponderomotive regime and its effect on stimulated Raman backscattering process

A theoretical and numerical study has been made of the propagation of a ring rippled laser beam in collisionless plasma with dominant relativistic ponderomotive nonlinearity and its effect on the excitation of electron plasma wave and stimulated Raman backscattering process. The growth of ring ripple, riding on an intense Gaussian laser beam in plasma has also been studied. A paraxial-ray and WKB approximation has been invoked to understand the nature of propagation of the ring rippled Gaussian laser beam in plasma, electron plasma wave and back reflectivity under the influence of both nonlinearities. The growth rate and focusing of a ring rippled beam is found to be considerably affected by the power of the main beam and the phase angle between the electric vectors of the main beam and the ring ripple. It has also been observed that the focusing is released by the coupling of relativistic and ponderomotive nonlinearities, which significantly affected the dynamics of the excitation of electron plasma wave and back reflectivity of stimulated Raman scattering (SRS). Due to the strong coupling between ring rippled laser beam and the excited electron plasma wave, back reflectivity of SRS is enhanced. It has been observed from the computational results that the effect of the increased intensity leads to suppression of SRS back reflectivity. The results have been presented for established laser and plasma parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Plasma interface of the EC waves to the LHD peripheral region

In order to realize an efficient ECRH and also to reduce stray radiation due to non-absorbed power during ECRH, it is necessary to excite a wave that is absorbed well near the electron cyclotron resonance. In the normal fusion magnetic field confinement machine and in the electron cyclotron frequency range, WKB approximation is valid almost all the way from antenna to the absorption region due to the large scale-length of the plasma density λ{sub n} and the magnetic shear τ{sub s} as compared with the local wavelength λ{sub 0}. In these situation, it is well known that the O/X mode propagates as O/X mode if τ{sub s} ≫ λ{sub 0}. Even in these situation, if τ{sub s} and λ{sub n} are comparable and |1/λ{sub O}−1/λ{sub X}|τ{sub s} ≪ 1, there still remains the question from where ”X” - or ”O” - mode become ”X” - or ”O” mode at the peripheral region. In order to simulate this situation, one dimensional full wave calculation code which solve electromagnetic wave equation under arbitrary magnetic field configuration and arbitrary density profile for a given polarization state are developed and incorporated in the upgraded ray tracing code LHDGauss. It is tried to find the density and shear scale lengths region where the mode mixing effect is not negligible.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

CALCULATING ROTATING HYDRODYNAMIC AND MAGNETOHYDRODYNAMIC WAVES TO UNDERSTAND MAGNETIC EFFECTS ON DYNAMICAL TIDES

To understand magnetic effects on dynamical tides, we study the rotating magnetohydrodynamic (MHD) flow driven by harmonic forcing. The linear responses are analytically derived in a periodic box under the local WKB approximation. Both the kinetic and Ohmic dissipations at the resonant frequencies are calculated, and the various parameters are investigated. Although magnetic pressure may be negligible compared to thermal pressure, the magnetic field can be important for the first-order perturbation, e.g., dynamical tides. It is found that the magnetic field splits the resonant frequency, namely the rotating hydrodynamic flow has only one resonant frequency, but the rotating MHD flow has two, one positive and the other negative. In the weak field regime the dissipations are asymmetric around the two resonant frequencies and this asymmetry is more striking with a weaker magnetic field. It is also found that both the kinetic and Ohmic dissipations at the resonant frequencies are inversely proportional to the Ekman number and the square of the wavenumber. The dissipation at the resonant frequency on small scales is almost equal to the dissipation at the non-resonant frequencies, namely the resonance takes its effect on the dissipation at intermediate length scales. Moreover, the waves with phase propagation that is perpendicular to the magnetic field are much more damped. It is also interesting to find that the frequency-averaged dissipation is constant. This result suggests that in compact objects, magnetic effects on tidal dissipation should be considered.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗
DOE OSTI2017

Tunneling-assisted transport of carriers through heterojunctions.

The formulation of carrier transport through heterojunctions by tunneling and thermionic emission is derived from first principles. The treatment of tunneling is discussed at three levels of approximation: numerical solution of the one-band envelope equation for an arbitrarily specified potential profile; the WKB approximation for an arbitrary potential; and, an analytic formulation assuming constant internal field. The effects of spatially varying carrier chemical potentials over tunneling distances are included. Illustrative computational results are presented. The described approach is used in exploratory physics models of irradiated heterojunction bipolar transistors within Sandia's QASPR program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

Tunneling near the peaks of potential barriers - Consequences of higher-order Wentzel-Kramers-Brillouin corrections

The quantum-mechanical tunneling transmission coefficient is derived for energies near the peak of a general potential barrier, to fourth order in the WKB approximation, using a method based on an eighth-order Taylor expansion of the potential near the peak. The result agrees with contour-integral formulations of WKB tunneling. For the Poeschl-Teller potential the WKB series converges rapidly to the known exact transmission coefficient. Higher-order WKB corrections may be important in attempts to determine the internuclear potential by inversion using low-energy fusion cross-section data.

Will, Clifford M.↗
DOE OSTI2021

WKB Estimate of Bilayer Graphene’s Magic Twist Angles

We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which we obtain analytically. Our analytic flatband twist angles correspond closely to those determined numerically in previous work.

36 MATERIALS SCIENCE↗
NASA NTRS1973

Alfven waves in spiral interplanetary field

A theoretical study is presented of the Alfven waves in the spiral interplanetary magnetic field. The Alfven waves under consideration are arbitrary, large amplitude, non-monochromatic, microscale waves of any polarization. They superpose on a mesoscale background flow of thermally anisotropic plasma. Using WKB approximation, an analytical solution for the amplitude vectors is obtained as a function of the background flow properties: density, velocity, Alfven speed, thermal anisotropy, and the spiral angel. The necessary condition for the validity of the WKB solution is discussed. The intensity of fluctuations is calculated as a function of heliocentric distance. Relative intensity of fluctuations as compared with the magnitude of the background field has its maximum in the region near l au. Thus outside of this region, the solar wind is less turbulent.

Whang, Y. C.↗
NASA NTRS1994

Time-dependent variational approach in terms of squeezed coherent states: Implication to semi-classical approximation

A general framework for time-dependent variational approach in terms of squeezed coherent states is constructed with the aim of describing quantal systems by means of classical mechanics including higher order quantal effects with the aid of canonicity conditions developed in the time-dependent Hartree-Fock theory. The Maslov phase occurring in a semi-classical quantization rule is investigated in this framework. In the limit of a semi-classical approximation in this approach, it is definitely shown that the Maslov phase has a geometric nature analogous to the Berry phase. It is also indicated that this squeezed coherent state approach is a possible way to go beyond the usual WKB approximation.

Tsue, Yasuhiko↗
NASA NTRS1987

Approximate penetration factors for nuclear reactions of astrophysical interest

The ranges of validity of approximations of P(l), the penetration factor which appears in the parameterization of nuclear-reaction cross sections at low energies and is employed in the extrapolation of laboratory data to even lower energies of astrophysical interest, are investigated analytically. Consideration is given to the WKB approximation, P(l) at the energy of the total barrier, approximations derived from the asymptotic expansion of G(l) for large eta, approximations for small values of the parameter x, applications of P(l) to nuclear reactions, and the dependence of P(l) on channel radius. Numerical results are presented in tables and graphs, and parameter ranges where the danger of serious errors is high are identified.

Humblet, J.↗
NASA NTRS1979

The adiabatic semiclassical perturbation theory for vibrationally inelastic scattering. I - Collinear calculations. II - Three-dimensional treatment

A semiclassical approximation to treat vibrationally inelastic scattering is developed. The vibrational basis set used is adiabatic with respect to a reference potential which is chosen to be as close as possible to the true potential and also gives easily obtainable solutions to the vibrational wave equation. The radial wave functions are obtained using the WKB approximation, and the coupled Schroedinger equations are solved by a first-order perturbation method to yield a phase shift matrix which is exponentiated to give the full scattering matrix. Results were obtained for all the cases computed by Secrest and Johnson and by Clark and Dickinson, and the agreement is better than 10% for half of the cross-sections and rarely off by more than a factor of 2.

Cross, R. J., Jr.↗
NASA NTRS1985

Black hole normal modes - A semianalytic approach

A new semianalytic technique for determining the complex normal mode frequencies of black holes is presented. The method is based on the WKB approximation. It yields a simple analytic formula that gives the real and imaginary parts of the frequency in terms of the parameters of the black hole and of the field whose perturbation is under study, and in terms of the quantity (n + 1/2), where n = 0, 1, 2,... and labels the fundamental mode, first overtone mode, and so on. In the case of the fundamental gravitational normal modes of the Schwarzschild black hole, the WKB estimates agree with numerical results to better than 7 percent in the real part of the frequency and 0.7 percent in the imaginary part, with the relative agreement improving with increasing angular harmonic. Carried to higher order the method may provide an accurate and systematic means to study black hole normal modes.

Schutz, B. F.↗