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Results for “self-consistent field”

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NASA NTRS1978

EUV structure of a small flare

Observations of a small flare are presented using data from the Harvard spectroheliometer on Skylab. The event is discussed in terms of the magnetic structure of the active region as deduced from the EUV observations and from field line extrapolations. The role of emerging flux in the initial flare brightenings is emphasized. A detailed model of one loop is deduced using the EUV data. This self-consistent model indicates initial heating of the loop modeled near its top, and mass flow into the cool core of the loop, with matter preferentially concentrating in a few distinct knots along the loop. Implications for theories of the flare process are discussed.

Levine, R. H.↗

NASA NTRS1973

Classical electromagnetic radiation of the Dirac electron

A wave-function-dependent four-vector potential is added to the Dirac equation in order to achieve conservation of energy and momentum for a Dirac electron and its emitted electromagnetic field. The resultant equation contains solutions which describe transitions between different energy states of the electron. As a consequence it is possible to follow the space-time evolution of such a process. This evolution is shown in the case of the spontaneous emission of an electromagnetic field by an electron bound in a hydrogen-like atom. The intensity of the radiation and the spectral distribution are calculated for transitions between two eigenstates. The theory gives a self-consistent deterministic description of some simple radiation processes without using quantum electrodynamics or the correspondence principle.

Lanyi, G.↗

NASA NTRS1973

A cylindrical shell model of the NASA-MPE barium ion cloud experiment.

A computer model is developed using infinitely long concentric cylindrical shells to represent the neutral atoms, ions and electrons in the barium cloud. The neutral shells are given a distribution of positions and velocities whose parameters are chosen to be consistent with the dynamics of the release. From this distribution, the ion and electron shells are generated at random using the observed time constant for photoionization. The ion and electron shells thus formed are followed using self-consistent equations of motion. Various averages which could be compared with observation of the actual cloud are calculated at regular time intervals. An unexpected result is the predicted very early return of the magnetic field within the cloud to its ambient value.

Grauer, A. D.↗

NASA NTRS1971

Amplitude and polarization asymmetries in a ring laser

Asymmetric amplitude effects between the oppositely directed traveling waves in a He-Ne ring laser are analyzed both theoretically and experimentally. These effects make it possible to detect angular orientations of an inner-cavity bar with respect to the plane of the ring cavity. The amplitude asymmetries occur when a birefringent bar is placed in the three-mirror ring cavity, and an axial magnetic field is applied to the active medium. A simplified theoretical analysis is performed by using a first order perturbation theory to derive an expression for the polarization of the active medium, and a set of self-consistent equations are derived to predict threshold conditions. Polarization asymmetries between the oppositely directed waves are also predicted. Amplitude asymmetries similar in nature to those predicted at threshold occur when the laser is operating in 12-15 free-running modes, and polarization asymmetry occurs simultaneously.

Campbell, L. L.↗

NASA NTRS1976

Can Malin's gravitational-field equations be modified to obtain a viable theory of gravity

Malin's (1975) gravitational theory, which was recently shown by Lindblom and Nester (1975) to be incorrect, is modified by means of a recently proposed method for obtaining viable gravitational theories. The resulting self-consistent theory, which is in effect a Rastall-type modification of the Einstein theory, exhibits nonconservation of momentum, yet agrees with all experimental limits known to date within the post-Newtonian approximation framework.

Smalley, L. L.↗

NASA NTRS1973

Electron avalanche structure determined by random walk theory

A self-consistent avalanche solution which accounts for collective long range Coulomb interactions as well as short range elastic and inelastic collisions between electrons and background atoms is made possible by a random walk technique. Results show that the electric field patterns in the early formation stages of avalanches in helium are close to those obtained from theory based on constant transport coefficients. Regions of maximum and minimum induced electrostatic potential phi are located on the axis of symmetry and within the volume covered by the electron swarm. As formation time continues, however, the region of minimum phi moves to slightly higher radii and the electric field between the extrema becomes somewhat erratic. In the intermediate formation periods the avalanche growth is slightly retarded by the high concentration of ions in the tail which oppose the external electric field. Eventually the formation of ions and electrons in the localized regions of high field strength more than offset this effect causing a very abrupt increase in avalanche growth.

Englert, G. W.↗

NASA NTRS1973

Expansion of an ion cloud in the earth's magnetosphere.

The initial expansion of a barium ion cloud release in the distant earth's magnetosphere is numerically investigated by means of a computer model with self-consistent electric and magnetic interactions. Initial conditions for the calculations are an expanding neutral cloud that is photoionized with a time constant of 20 sec. The results show that after the first 30 sec, the large fluctuations in the magnetic field and in other parameters are damped out and the magnetic field in the central region of the cloud is reduced to near zero. Also, after only 10 sec, a relatively high central ion density has developed and remains for the duration of the calculations.

Hohl, F.↗

NASA NTRS1974

Temperature and density structure of thermal proton flows

Thermal proton flows along magnetic field lines are an important feature of magnetosphere-ionosphere coupling. In this paper we report the results of a theoretical study of the thermal structure of such flows. The adopted steady state model is based upon O+, H+, and electrons with self-consistent solutions for the separate O+, H+, and electron temperatures, the O+ and H+ densities and the H+ drift velocity. Through investigation of a number of parameters affecting the model, it is shown that Joule heating arising from the flow of H+ through O+ preferentially heats H+, so that the H+ temperature is substantially greater than the O+ temperature. Low O+ densities characteristic of the trough region appear to give high H+/O+ temperature ratios. Typical O+ densities characteristic of polar wind flow regions give moderate H+/O3 temperature ratios. The Mach number of H+ outflow is substantially reduced in the present models in comparison with the older fixed temperature calculations.

Banks, P. M.↗

NASA NTRS1978

Helium ion outflow from the terrestrial ionosphere

For situations where ion outflow occurs from the topside ionosphere, steady-state solutions for the He(+) continuity, momentum, and energy equations have been obtained self-consistently, yielding density, velocity, and temperature profiles of He(+) from 200 to 2000 km altitude. The study indicates that the outflowing He(+) has density profiles of similar shape to those of H(+), for basically different reasons; the effect of the perpendicular electric field differs considerably for H(+) and He(+); the fractional heating of He(+) due to the He(+)-O(+) relative flow is not as effective in heating He(+) as the flow is in heating H(+); during magnetospheric disturbances the He(+) peak density decreases only by approximately a factor of 2; and the He(+) escape flux over the winter pole is approximately a factor of 20 greater than the He(+) escape flux over the summer pole. The possibility of interhemispheric He(+) flux from winter to summer on high-latitude closed field lines is considered.

Raitt, W. J.↗

NASA NTRS1973

Precise calculation of the magnetosphere surface for a tilted dipole.

The shape of the magnetosphere has been calculated self-consistently for inclinations of the earth's magnetic dipole from perpendicular to the solar wind. Inclination angles of 0-35 deg have been chosen in steps of 5 deg and various smooth trends in the surface characteristics with increasing inclination angle noted. The surface points and the complete field at the surface points have been calculated for the entire surfaces. The neutral point region has been given precise study in one degree steps and is found to be tangent to the solar wind velocity and to have a smooth continuous curvature.

Choe, J. Y.↗

NASA NTRS1978

Diffuse auroral precipitation

The paper summarizes the development of a plausibly coherent view of the self-consistent coupling of convection in the plasma sheet to auroral particle precipitation and the ionosphere. Attention is given to an understanding of the plasma instabilities responsible for diffuse auroral precipitation. The electrostatic ion and electron cyclotron harmonic loss-cone instabilities seem to be the best candidates, although they depend sensitively upon the cold electron density and temperature deep in space on auroral field lines. However, there is little or no experimental or theoretical information about these parameters. For this reason, further theoretical progress on cyclotron harmonic instabilities will be limited until the cold electron temperature is known. Also necessary are a complete phenomenological understanding of ion harmonic modes and a modeling of the cold electron distribution on auroral field lines.

Ashour-Abdalla, M.↗

NASA NTRS1977

Physical conditions in the solar corona during flarelike events

Soft X-ray images of the sun obtained with the S-056 telescope aboard Skylab are used to investigate physical conditions in the X-ray-emitting coronal plasma during flarelike events. Temporal and spatial variations in the density and temperature of the main X-ray source during a flare are determined along with the total radiative energy emitted by an observed loop system. Models for heat sources and energy balance are analyzed, radiative as well as conductive energy losses are computed, and an attempt is made to develop a self-consistent model of the observed X-ray event. It is concluded that: (1) loop tips constitute the source of the maximum X-ray flux; (2) conductive losses exceed radiative losses by several orders of magnitude; (3) energy (and possibly new matter) is added at loop tips; and (4) the most intense X-ray structures are located in areas where the magnetic field has a small radius of curvature and the axis of a loop sequence changes direction.

Vorpahl, J. A.↗

NASA NTRS1976

Accretion onto magnetized neutron stars - Structure and interchange instability of a model magnetosphere

A self-consistent model is analyzed for the spherical infall of weakly magnetized plasma into the magnetosphere of a slowly rotating, strongly magnetized neutron star. It is shown that spherical infall is probably a good approximation for X-ray sources which accrete from a stellar wind. The location of the standoff shock which halts the hypersonic infall is estimated along with the emission from the shocked layer. The location of the equilibrium magnetopause and the structure of the magnetic field within it are calculated; it is found that the magnetic poles are true cusps and that the entry of gas due to equilibrium flow across a cusp is almost certainly dominated by the interchange instability near the magnetic equator. The energy principle is applied to derive necessary conditions for the occurrence of this instability. The results indicate that the strong magnetic-pressure gradient stabilizes the gas unless moderately strong radiative cooling takes place and that the cooled plasma enters the magnetosphere as long filaments capable of moving between field lines. The rate at which the equilibrium magnetopause can 'absorb' mass and momentum is derived, the validity of the approximations employed is discussed, and the likely evolution of the sinking filaments is outlined to show that the spatial distribution of the plasma is determined mainly by the dynamics and thermodynamics of the filaments rather than the magnetic-field structure.

Arons, J.↗

NASA NTRS1976

Influence of finite-beta effects on the lower-hybrid-drift instability in post-implosion theta pinches

The influence of finite values of the plasma parameter beta on the lower-hybrid-drift instability is investigated, with particular emphasis on the post-implosion theta-pinch configurations. The analysis is carried out in a fully self-consistent manner and includes the finite-beta effects associated with transverse electromagnetic perturbations as well as with resonant and nonresonant electron-orbit modifications. Except in the limit where the ratio of electron and ion temperatures approaches zero, it is found that there is a critical value for the local beta such that the lower-hybrid-drift instability is completely stabilized. For typical post-implosion theta pinches, it is concluded that if the magnetic-field depression is sufficiently large, the interior region of the pinch will be stable to the examined instability but the exterior region will be unstable.

Davidson, R. C.↗

NASA NTRS1972

A two component model of the diurnal variations in the thermospheric composition

A self-consistent, two-dimensional, two-component diffusion model is presented to describe the diurnal component of thermosphere dynamics. In the regions where oxygen and helium are the minor constituents, diffusion is shown to increase the amplitudes of these constituents and to advance the times of their diurnal maxima by several hours with respect to the gas temperature and the major species. Both effects are in basic agreement with satellite observations. The diffusion process is relatively insignificant for temperature, total mass density, and wind fields. The magnitude of the temperature-density phase delay is discussed with respect to its dependence on the electron density distribution.

Mayr, H. G.↗

NASA NTRS1978

Solitons and second harmonic radiation in type III bursts

The emission at the second harmonic of the plasma frequency from self-consistent Langmuir solitons is calculated. The theory predicts, in a natural way, the observed transition from the region where the intensity is linearly proportional to the electron flux to the region where the radio intensity is proportional to the square of the electron flux. A detailed comparison of the radiation observed at the second harmonic for the burst of 18:10 UT March 31, 1976, with the one expected on the assumption of radiation from solitons, using the correlated in situ measurements of the electric fields at the second harmonic, and their spatial structure, provides strong evidence that, for the first time, Langmuir solitons have been observed in space.

Papadopoulos, K.↗

NASA NTRS1976

Diamagnetic boundary layers - A kinetic theory

A kinetic theory is presented for boundary layers associated with MHD tangential 'discontinuities' in a collisionless magnetized plasma, such as those observed in the solar wind. The theory consists of finding self-consistent solutions of Vlasov's equation and Maxwell's equation for stationary one-dimensional boundary layers separating two Maxwellian plasma states. Layers in which the current is carried by electrons are found to have a thickness of the order of a few electron gyroradii, but the drift speed of the current-carrying electrons is found to exceed the Alfven speed, and accordingly such layers are not stable. Several types of layers in which the current is carried by protons are discussed; in particular, cases are considered in which the magnetic-field intensity, direction, or both, changed across the layer. In every case, the thickness was of the order of a few proton gyroradii, and the field changed smoothly, although the characteristics depended somewhat on the boundary conditions. The drift speed was always less than the Alfven speed, consistent with stability of such structures. These results are consistent with observations of boundary layers in the solar wind near 1 AU.

Lemaire, J.↗

NASA NTRS1976

Calculations of molecular ionization energies using a self-consistent-charge Hartree-Fock-Slater method

A numerical-variational method for performing self-consistent molecular calculations in the Hartree-Fock-Slater (HFS) model is presented. Molecular wavefunctions are expanded in terms of basis sets constructed from numerical HFS solutions of selected one-center atomlike problems. Binding energies and wavefunctions for the molecules are generated using a discrete variational method for a given molecular potential. In the self-consistent-charge (SCC) approximation to the complete self-consistent-field (SCF) method, results of a Mulliken population analysis of the molecular eigenfunctions are used in each iteration to produce 'atomic' occupation numbers. The simplest SCC potential is then obtained from overlapping spherical atomlike charge distributions. Molecular ionization energies are calculated using the transition-state procedure; results are given for CO, H2O, H2S, AlCl, InCl, and the Ni5O surface complex. Agreement between experimental and theoretical ionization energies for the free-molecule valence levels is generally within 1 eV. The simple SCC procedure gives a reasonably good approximation to the molecular potential, as shown by comparison with experiment, and with complete SCF calculations for CO, H2O, and H2S.

Rosen, A.↗