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NASA NTRS1992

Birkeland currents in an anisotropic, magnetostatic plasma

The paper derives an expression for the parallel current density for a plasma characterized by negligible bulk flow (magnetostatic velocity and a two-component (anisotropic) pressure tensor by expanding the equilibrium Vlasov equation for each species in the adiabatic parameter until such point as a nonvanishing moment j-parallel = integral d-cubed vv-parallel f is identified. The result is a nonlocal one: it relates j-parallel at one point s along a field line to j-parallel at another (reference) point s0 plus an integral function of the pressure and magnetic field between them. The equation derived by Vasyliunas (1970) is generalized and extended to a plasma in which the pressure tensor is comprised of two separate elements, P-perpendicular and P-parallel. This equation follows when P-perpendicular is set equal to P-parallel and s and s0 are taken to be at the ionosphere and the equator. These results are compared to others in the literature.

Birmingham, Thomas J.↗

NASA NTRS1991

Adjoint-operators and non-adiabatic learning algorithms in neural networks

Adjoint sensitivity equations are presented, which can be solved simultaneously (i.e., forward in time) with the dynamics of a nonlinear neural network. These equations provide the foundations for a new methodology which enables the implementation of temporal learning algorithms in a highly efficient manner.

Toomarian, N.↗

NASA NTRS2000

Adiabatic Compression of Oxygen: Real Fluid Temperatures

The adiabatic compression of oxygen has been identified as an ignition source for systems operating in enriched oxygen atmospheres. Current practice is to evaluate the temperature rise on compression by treating oxygen as an ideal gas with constant heat capacity. This paper establishes the appropriate thermodynamic analysis for the common occurrence of adiabatic compression of oxygen and in the process defines a satisfactory equation of state (EOS) for oxygen. It uses that EOS to model adiabatic compression as isentropic compression and calculates final temperatures for this system using current approaches for comparison.

Barragan, Michelle↗

NASA NTRS1972

Modulation of low energy cosmic rays

The power spectrum of the interplanetary magnetic field were tested, as well as the power spectrum-cosmic diffusion ray coefficient relation at low energies. A first order perturbation solution of the Fokker-Planck equation governing the diffusion, convection, and adiabatic deceleration of galactic cosmic rays in the solar medium was found to relate intensity fluctuations of low energy cosmic rays to local changes in the propagation parameters. Diffusion coefficients and their day to day variations were calculated from interplanetary magnetic field data obtained by Pioneer 6 in 1965/1966. These are compared to simultaneous observations by IMP 3 of the proton flux in three energy channels (20 to 40, 40 to 60, 60 to 80 MeV).

Sari, J. W.↗

NASA NTRS1979

Theory of flux anisotropies in a guiding center plasma

Assuming time stationarity of the one-particle distribution function f on the scale of the bounce motion of particles in a magnetic field, the paper expands the Vlasov equation through O(epsilon) in the adiabatic parameter epsilon, which is the ratio of particle gyroradius to scale length of the magnetic field. Since f is directly proportional to particle flux differential in kinetic energy and solid angle, f is in principle measurable in space experiments, and the present analysis is tailored to be explicitly applicable to space problems. It is shown that the usual expression for the electric field which produces plasma corotation in an axisymmetric system such as a dipole also holds for any nonaxisymmetric but rigidly rotating magnetic field pattern, provided the observed magnetic field is used in place of the dipole field. The analysis is applied to the electric field in a rigidly corotating magnetosphere.

Birmingham, T. J.↗

NASA NTRS1981

Analytic solutions of the radial pulsation equation for rotating and magnetic star models

Eddington's (1926) form of wave equation for small-amplitude, radial, adiabatic stellar pulsations of spherically symmetric, gaseous stars is generalized to include the effects of axial rotation and tangled magnetic fields. Equilibrium quantities possessing dimensions are affected, and the relative importance of rotation and magnetism in affecting pulsation characteristics of the models depends on the choices of gamma and the type of model. Solutions are obtained in closed form for adiabatic pulsation periods of fine analytic stellar models, and nonadiabatic stability criteria are determined by means of the one-zone stellar model. Results are discussed for a range of physical parameters such as rotational angular momenta, central condensations, and magnetic energies; and applications are made to the case of classical Cepheids and other variable giant stars.

Stothers, R.↗

NASA NTRS1990

Electron heating in quasi-perpendicular shocks - A Monte Carlo simulation

To study the problem of electron heating in quasi-perpendicular shocks, under the combined effects of 'reversible' motion, in the shock electric potential and magnetic field, and wave-particle interactions a diffusion equation was derived, in the drift (adiabatic) approximation and it was solved by using a Monte Carlo method. The results show that most of the observations can be explained within this framework. The simulation has also definitively shown that the electron parallel temperature is determined by the dc electromagnetic field and not by any wave particle induced heating. Wave-particle interactions are effective in smoothing out the large gradients in phase space produced by the 'reversible' motion of the electrons, thus producing a 'cooling' of the electrons. Some constraints on the wave-particle interaction process may be obtained from a detailed comparison between the simulation and observations. In particular, it appears that the adiabatic approximation must be violated in order to explain the observed evolution of the perpendicular temperature.

Veltri, Pierluigi↗

NASA NTRS1991

Analysis of radiative and phase-change phenomena with application to space-based thermal energy storage

The simplified geometry for the analysis is an infinite, axis symmetric annulus with a specified solar flux at the outer radius. The inner radius is either adiabatic (modeling Flight Experiment conditions), or convective (modeling Solar Dynamic conditions). Liquid LiF either contacts the outer wall (modeling ground based testing), or faces a void gap at the outer wall (modeling possible space based conditions). The analysis is presented in three parts: Part 3 considers and adiabatic inner wall and linearized radiation equations; part 2 adds effects of convection at the inner wall; and part 1 includes the effect of the void gap, as well as previous effects, and develops the radiation model further. The main results are the differences in melting behavior which can occur between ground based 1 g experiments and the microgravity flight experiments. Under 1 gravity, melted PCM will always contact the outer wall having the heat flux source, thus providing conductance from this source to the phase change front. In space based tests where a void gap may likely form during solidification, the situation is reversed; radiation is now the only mode of heat transfer and the majority of melting takes place from the inner wall.

Lund, Kurt O.↗

NASA NTRS1949

Two-Dimensional Motion of a Gas at Large Supersonic Velocities

A large number of papers have been devoted to the problem of integration of equations of two-dimensional steady nonvertical adiabatic motion of a gas. Most of these papers are based on the application of the hodograph method of S. A. Chaplygin in which the plane of the hodograph of the velocity is taken as the region of variation of the independent variables in the equations of motion; the equations become linear in this plane. The exact integration of these equations is, however, obtained in the form of infinite series containing hypergeometric functions. The obtaining of such solutions and their investigation involves extensive computations. As a result, methods have been developed for the approximate integration of the equations of motion first transformed to a linear form. S. A. Chaplygin first pointed out such an approximate method applicable to flows in which the Mach number does not exceed 0.4.

Falkovich, S. V.↗

NASA NTRS1981

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30 degree inclination angle.

Wang, C. R.↗

NASA NTRS2003

An Equation for Moist Entropy in a Precipitating and Icy Atmosphere

Moist entropy is nearly conserved in adiabatic motion. It is redistributed rather than created by moist convection. Thus moist entropy and its equation, as a healthy direction, can be used to construct analytical and numerical models for the interaction between tropical convective clouds and large-scale circulations. Hence, an accurate equation of moist entropy is needed for the analysis and modeling of atmospheric convective clouds. On the basis of the consistency between the energy and the entropy equations, a complete equation of moist entropy is derived from the energy equation. The equation expresses explicitly the internal and external sources of moist entropy, including those in relation to the microphysics of clouds and precipitation. In addition, an accurate formula for the surface flux of moist entropy from the underlying surface into the air above is derived. Because moist entropy deals "easily" with the transition among three water phases, it will be used as a prognostic variable in the next generation of cloud-resolving models (e. g. a global cloud-resolving model) for low computational noise. Its equation that is derived in this paper is accurate and complete, providing a theoretical basis for using moist entropy as a prognostic variable in the long-term modeling of clouds and large-scale circulations.

Tao, Wei-Kuo↗

NASA NTRS1981

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center-line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30-deg inclination angle.

Wang, C. R.↗

NASA NTRS1976

Trajectory Traces of Charged Particles in the Magnetosphere

The characteristic enhancements of ring current particles with energies of about 1 to 100 keV, associated with magnetospheric substorms, were observed by Explorer 45 around the plasmapause in the afternoon to midnight region, and showed the characteristic structure called a 'nose' in the proton spectrograms. The motion of these particles in the equatorial magnetosphere, under a recently proposed convection electric field and a dipole magnetic field is described. Approximate equations of a bounce period, a second adiabatic invariant, and a bounce-average azimuthal velocity are given with inaccuracies less than about 0.001 for all pitch angles. The complete set of flow patterns of 90 deg pitch angle particles is also presented by means of stagnation lines through which radial drifts and/or azimuthal drifts change their directions. The particle tracings in the magnetosphere give a basic concept to explain the observed nose characteristics.

Ejiri, M.↗

NASA NTRS1982

Structure of the magnetopause rotational discontinuity

A model is developed for the rotational discontinuities associated with the reconnection configuration on the dayside magnetopause and the energy transfer process in the tail magnetopause. The model, in which the ion dynamics is described by the fluid equations and electrons are assumed to move adiabatically along the magnetic field lines, is valid for a rotational discontinuity with a thickness greater than a few ion gyroradii. It is shown, by the inclusion of self-consistency for trapped electrons, that (1) the trapped electron density profile is uniquely related to the rate of angular rotation of the magnetic field, and (2) the sense of magnetic field rotation is determined by the ratio of the normal and tangential components of the magnetic field. It is found that the electron polarization of magnetopause rotational discontinuities should be in agreement with satellite observations.

Lee, L. C.↗

NASA NTRS2011

Evolution of the Equatorial Oscillation in Saturn's Stratosphere Between 2005 and 2010 from Cassini/CIRS Limb Data Analysis

We present an analysis of thermal infrared spectra acquired in limb viewing geometry by Cassini/CIRS in February 2010. We retrieve vertical profiles of Saturn's stratospheric temperature from 20 hPa to 10 (exp -2) hPa, at 9 latitudes between 20 deg N and 20 deg S. Using the gradient thermal wind equation, we derive a map of the zonal wind field. Both the temperature and the zonal wind vertical profiles exhibit an oscillation in the equatorial region. These results are compared to the temperature and zonal wind maps obtained from 2005-2006 CIRS limb data, when this oscillation was first reported. In both epochs, strong temperature anomalies at the equator (up to 20K) are consistent with adiabatic heating (cooling) due to a sinking (rising) motion at a speed of 0.1 - 0.2 mm/s. Finally, we show that the altitude of the maximum eastward wind has moved downwards by 1.3 scale heights in 4.2 years, hence with a 'phase' speed of approximately 0.5 mm/s. This rate is consistent with the estimated period of 14.7 years for the equatorial oscillation, and requires a local zonal acceleration of 1.1 x 10(exp -6) m.s(exp -2) at the 2.5 hPa pressure level. This downward propagation of the oscillation is consistent with it being driven by absorption of upwardly propagating waves.

Guerlet, S.↗

NASA NTRS1995

Relativistic hadrons and the origin of relativistic outflows in active galactic nuclei

We examine the hydrodynamic origin of relativistic outflows in active galactic nuclei (AGN). Specifically, we propose that the presence of a population of relativistic hadrons in the AGN 'central engine' and the associated neutron production suffices to produce outflows which under rather general conditions could be relativistic. The main such condition is that the size of the neutron production region be larger than the neutron flight path tau(sub n) approximately 3 x 10(exp 13) cm. This condition guarantees that the mean energy per particle in the proton fluid, resulting from the decay of the neutrons outside their production region, be greater than the proton rest mass. The expansion of this fluid can then lead naturally to a relativistic outflow by conversion of its internal energy to directed motion. We follow the development of such flows by solving the mass, energy as well as the kinetic equation for the proton gas in steady state, taking into account the source terms due to compute accurately the adiabatic index of the expanding gas, and in conjunction with Bernoulli's equation the detailed evolution of the bulk Lorentz factor. We further examine the role of large-scale magnetic fields in confining these outflows to produce the jets observed at larger scales.

Contopoulos, John↗

NASA NTRS1992

Computation of steady and unsteady quasi-one-dimensional viscous/inviscid interacting internal flows at subsonic, transonic, and supersonic Mach numbers

Computations of viscous-inviscid interacting internal flowfields are presented for steady and unsteady quasi-one-dimensional (Q1D) test cases. The unsteady Q1D Euler equations are coupled with integral boundary-layer equations for unsteady, two-dimensional (planar or axisymmetric), turbulent flow over impermeable, adiabatic walls. The coupling methodology differs from that used in most techniques reported previously in that the above mentioned equation sets are written as a complete system and solved simultaneously; that is, the coupling is carried out directly through the equations as opposed to coupling the solutions of the different equation sets. Solutions to the coupled system of equations are obtained using both explicit and implicit numerical schemes for steady subsonic, steady transonic, and both steady and unsteady supersonic internal flowfields. Computed solutions are compared with measurements as well as Navier-Stokes and inverse boundary-layer methods. An analysis of the eigenvalues of the coefficient matrix associated with the quasi-linear form of the coupled system of equations indicates the presence of complex eigenvalues for certain flow conditions. It is concluded that although reasonable solutions can be obtained numerically, these complex eigenvalues contribute to the overall difficulty in obtaining numerical solutions to the coupled system of equations.

Swafford, Timothy W.↗

NASA NTRS1972

Model development of supersonic trough wind with shocks

The time dependent one dimensional hydrodynamic equations describe the evolution of the thermal plasma flow along closed magnetic field lines outside of the plasmasphere. The convection of the supersonic polar wind onto a closed fieldline results in the assumed formation of collisionless plasma shocks. These shocks move earthward as the field line with its frozen-in plasma remains fixed or contracts with time to smaller L coordinates. The high equatorial plasma temperature (of the order of electron volts) produced by the shock process decreases with time if the flow is isothermal but it will increase if the contraction is under adiabatic conditions. Assuming adiabaticity a peak in the temperature forms at the equator in conjunction with a depression in the ion density. After an initial contraction, if the flux tube drifts to higher L coordinates the direction of the shock motion can be reversed so that the supersonic region will expand along the field line towards the state characterizing the supersonic polar wind. A rapid expansion will lower the equatorial density while the temperature decreases with time under adiabatic but not isothermal conditions.

Grebowsky, J. M.↗