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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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NASA NTRS1984

Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation

The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.

Moon, H. T.↗
NASA NTRS1984

Basic governing equations for the flight regimes of aeroassisted orbital transfer vehicles

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are given explicitly. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, is derived by solving the system of master equations accounting for the multiple-level transitions.

Lee, J.-H.↗
NASA NTRS1985

Basic Governing Equations for the Flight Regimes of Aeroassisted Orbital Transfer Vehicles

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are explicitly given. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, are derived by solving the system of master equations accounting for the multiple-level transitions.

Lee, Jong-Hun↗
NASA NTRS1993

Parametric instabilities of parallel-propagating Alfven waves: Some analytical results

We consider the stability of a circularly polarized Alfven wave (the pump wave) which propagates parallel to the ambient magnetic field. Only parallel-propagating perturbations are considered, and we ignore dispersive effects due to the ion cyclotron frequency. The dissipationless MHD equations are used throughout; thus possibibly important effects arising from Landau and transit time damping are omitted. We derive a series of analytical approximations to the dispersion relation using A = (Delta B/B(sub O))(exp 2) as a small expansion parameter; Delta B is the pump amplitude, and B(sub O) is the ambient magnetic field strength. We find that the plasma beta (the square of the ratio of the sound speed to the Alfven speed) plays a crucial role in determining the behavior of the parametric instabilities of the pump. If 0 less than beta less than 1 we find the familiar result that the pump decays into a forward propagating sound wave and a backward propagating Alfven wave with maximum growth rate gamma(sub max) varies A(sup 1/2), but beta cannot be too close to 0 or to 1. If beta approx. 1, we find gamma(sub max) varies A(sup 3/4), if beta greater than 1, we find gamma(sub max) varies A(sup 3/2), while if beta approx. 0, we obtain gamma(sub max) varies A(sup 1/3); moreover, if beta approx. 0 there is a nearly purely growing instability. In constrast to the familiar decay instability, for which the backward propagating Alfven wave has lower frequency and wavenumber than the pump, we find that if beta greater than or approx. equal to 1 the instability is really a beat instability which is dominated by a transverse wave which is forward propagating and has frequency and wavenumber which are nearly twice the pump values. Only the decay instability for 0 less than beta less than 1 can be regarded as producing two recognizable normal modes, namely, a sound wave and an Alfven wave. We discuss how the different characteristics of the instabilities may affect the evolution of Alfven waves in the solar wind. However, for a solar wind in which beta approx. 1 the growth times of the instabilities are probably too long for these instabilities to have an appreciable effect inside 1 AU.

Jayanti, V.↗
NASA NTRS1977

Impedance characteristics of coaxial and planar magnetoplasma capacitors

A theory has been developed for the impedance of a homogeneous magnetoplasma enclosed between two specular reflecting coaxial electrodes, with a static magnetic field parallel to the electrode axes. The parallel-plate magnetoplasma capacitor is treated as a sub-case. Starting with the Vlasov equation, an integral equation is derived for the electric field. Solving this equation, and integrating to obtain the voltage, gives the capacitor impedance. This includes a capacitive component, and a resistive component expressing the Landau damping associated with the open orbits of electrons reflected at the electrodes. A direct numerical solution of the field integral equation has been carried out for a range of values of magnetic field, plasma density, and signal frequency. The values of impedance so obtained are compared with the predictions of macroscopic theory, and of an approximate microscopic theory in which open orbits are ignored and solutions are obtained using finite Fourier transform methods. The mathematical relations between these theories are demonstrated.

Harker, K. J.↗
NASA NTRS1990

The effect of random Alfven waves on the propagation of hydromagnetic waves in a finite-beta plasma

Using first-order smoothing theory, Fourier analysis and perturbation methods, the evolution equation of the wave spectrum as well as the nonlinear forces generated by random Alfven waves in a finite-beta plasma with phenomenological Landau-damping effects are obtained. The effect of microscale random Alfven waves on the propagation of large-scale hydromagnetic waves is also investigated by solving the mean-field equations. It is shown that parallel-propagating random Alfven waves are modulationally stable and that obliquely propagating random Alfven waves can be modulationally unstable when the energy of random waves is converted to slow magnetoacoustic waves that can be Landau-damped, providing a dissipation mechanism for the Alfven waves.

Hamabata, Hiromitsu↗
NASA NTRS1988

The rate parameters for coupled vibration-dissociation in a generalized SSH approximation

A theoretical study of vibrational excitations and dissociations of nitrogen undergoing a nonequilibrium relaxation process upon heating and cooling is reported. The rate coefficients for collisional induced vibrational transitions and transitions from a bound vibrational state into a dissociative state have been calculated using an extension of the theory originally proposed by Schwarz (SSH) et al. (1952). High-lying vibrational states and dissociative states were explicitly included but rotational energy transfer was neglected. The transition probabilities calculated from the SSH theory were fed into the master equation, which was integrated numerically to determine the population distribution of the vibrational states as well as bulk thermodynamic properties. The results show that: (1) the transition rates have a minimum near the middle of the bound vibrational levels, causing a bottleneck in the vibrational relaxation and dissociation rates; (2) high vibrational states are always in equilibrium with the dissociative state; (3) for the heating case, only the low vibrational states relax according to the Landau-Teller theory; (4) for the cooling case, vibrational relaxation cannot be described by a rate equation; (5) Park's (1985, 1988) two-temperature model is approximately valid; and (6) the average vibrational energy removed in dissociation is about 30 percent of the dissociation energy.

Sharma, Surendra P.↗
NASA NTRS1987

A new interpretation of plasma-line overshoot phenomena

The temporal evolution of Langmuir waves excited by high-power, high-frequency (HF) radio waves in the ionosphere is studied theoretically. This study is motivated by past observations made with the 450 MHz radar at Arecibo Observatory in Puerto Rico. Two kinds of nonlinear damping to the parametric decay instability are considered in the derivation of the rate equation for the spectral intensity of enhanced Langmuir waves. They are Langmuir wave cascading caused by nonlinear Landau damping and cross-field electron diffusion. The first damping process leads to the saturation of individual unstable Langmuir wave. The second process, which results from the incoherent scattering of electron orbits by the total excited Langmuir waves, yields anomalous damping that applies to each Langmuir wave. Consequently, Langmuir waves with smaller growth rates will be suppressed by those with larger growth rates. Such a mode competition process may cause the overshoot of the HF-enhanced plasma line observed with the Arecibo 430 MHz radar. Favorable agreement is obtained between theory and the Arecibo observations.

Kuo, S. P.↗
NASA NTRS1985

Analytical-numerical methods of calculations of energy and three-dimensional particle distributions in electromagnetic cascades

Analytical and numerical methods of calculation of the energy and three dimensional EPS characteristics are reported. The angular and lateral functions of electrons in EPS have been obtained by the Landau and small angle approximations A and B and compared with earlier data. A numerical method of solution of cascade equations for the EPS distribution function moments has been constructed. Considering the equilibrium rms angle as an example, errors appearing when approximating the elementary process cross sections by their asymptotic expressions are analyzed.

Ivanenko, I. P.↗
NASA NTRS1994

Charge transfer in helium-rich supernova plasma

Charge transfer rate coefficients are estimated using Landau-Zener and modified Demkov approximations. The coefficients, augmented by those available from the literature, are used in statistical equilibrium equations describing the state of helium-rich supernova plasma. Such a plasma may describe both Type Ib and Type Ic supernova ejecta. The hypothesis that extensive mixing of metals with helium in Type Ic supernovae may provide a catalyst for rapid charge transfer that weakens the helium line emission by altering the excitation balance is tested. It is shown that charge transfer as a mechanism for suppressing helium line emission is ineffective unless the metal abundance is comparable to or larger than the helium abundance. This result supports an earlier conclusion that Type Ic supernovae must be helium poor relative to Type Ib events.

Swartz, Douglas A.↗
NASA NTRS1994

Langmuir turbulence in the auroral ionosphere 2: Nonlinear theory and simulations

A theoretical interpretation of sounding rocket measurements of intense Langmuir wave fields (less than or equal to 500 mV/m) driven by a stream of 20 eV to 4 keV electrons in the lower auroral zone is developed. This interpretation is based on the ability of the 10 microseconds sampling rate of the wave detector to temporally resolve the structure of the Langmuir wave field envelope. A modified form of the Zakharov equations is used to numerically study beam-driven Langmuir turbulence in the presence of a moderate magnetic field (OMEGA (sub e) approximately equals Omega (sub pe). Strong Landau damping on observed nonthermal scattered electrons, which is treated in a companion paper (Newman et al., this issue), plays an important role by inhibiting backscatter cascade and the development of strong turbulence. A parameterized model of the linear electron stream-driven wave instability is introduced, which incorporates limited quasilinear plateau formation. A reasonable set of parameters is found that yields semiquantitative agreement between observed properties of the Langmuir fields and the results of Zakharov equation simulations, including the amplitude and characteristic frequency of the electric field envelope modulations.

Newman, D. L.↗
NASA NTRS1985

Whistler damping at oblique propagation - Laminar shock precursors

This paper addresses the collisionless damping of whistlers observed as precursors standing upstream of oblique, low-Mach number terrestrial bow shocks. The linear theory of electromagnetic waves in a homogeneous Vlasov plasma with Maxwellian distribution functions and a magnetic field is considered. Numerical solutions of the full dispersion equation are presented for whistlers propagating at an arbitrary angle with respect to the magnetic field. It is demonstrated that electron Landau damping attenuates oblique whistlers and that the parameter which determines this damping is beta-e. In a well-defined range of parameters, this theory provides damping lengths which are the same order of magnitude as those observed. Thus electron Landau damping is a plausible process in the dissipation of upstream whistlers. Nonlinear plasma processes which may contribute to precursor damping are also discussed, and criteria for distinguishing among these are described.

Gary, S. P.↗
NASA NTRS1993

Statistics of Experiments on Cluster Formation and Transport in a Gravitational Field

Metastable state relaxation in a gravitational field is investigated in the case of non-critical binary solutions. A relaxation description is presented in terms of the time-dependent Ginzburg-Landau formalism for a non-conserved order parameter. A new ansatz for solution of the corresponding partial nonlinear stochastic differential equation is discussed. It is proved that, for the supersaturated solution under consideration, the metastable state relaxation in a gravitational field leads to formation of solute concentration gradients due to the sedimentation of subcritical solute clusters. The pure discussion of the possible methods to compare theoretical results and experimental data related to solute sedimentation in a gravitational field is presented. It is shown that in order to describe these experiments it is necessary to deal both with the value of the solute concentration gradient and with its formation rate. The stochastic nature of the sedimentation process is shown.

Izmailov, Alexander F.↗
NASA NTRS1989

Nonlinear interactions in mixing layers and compressible heated round jets

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Jarrah, Yousef Mohd↗
NASA NTRS1973

Propagation of hydromagnetic waves in the upper F2-region

The theory of hydromagnetic-wave in the upper F2-region, in which electrons are in a transitional regime from collisional to collisionless conditions and ions are in a collisionless state, is examined. Derivation of the governing equations is based on the fact that the isotropic electrons are fluid-like, and the anisotropic ions follow kinetic equations modified by ion-electron collisions. Magneto-acoustic waves of a period of from about 0.2 to 10 sec are dissipated by ion Landau damping and electron thermal conduction and viscosity. Numerical solutions under ionospheric conditions show that the dissipation of hydromagnetic waves is insufficient to modify the large scale heating of the ionosphere.

Hung, R. J.↗
NASA NTRS1993

Application of multigrid methods to the solution of liquid crystal equations on a SIMD computer

We will describe a finite difference code for computing the equilibrium configurations of the order-parameter tensor field for nematic liquid crystals in rectangular regions by minimization of the Landau-de Gennes Free Energy functional. The implementation of the free energy functional described here includes magnetic fields, quadratic gradient terms, and scalar bulk terms through the fourth order. Boundary conditions include the effects of strong surface anchoring. The target architectures for our implementation are SIMD machines, with interconnection networks which can be configured as 2 or 3 dimensional grids, such as the Wavetracer DTC. We also discuss the relative efficiency of a number of iterative methods for the solution of the linear systems arising from this discretization on such architectures.

Farrell, Paul A.↗