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NASA NTRS1987

A one-dimensional time-dependent model of the magnetized ionosphere of Venus

The behavior and time evolution of the large-scale magnetic fields and plasma of the dayside Venus ionosphere are studied using a one-dimensional model. The coupled continuity, momentum, and Maxwell's equations are solved simultaneously for O(+), O2(+), and H(+), and the magnetic field. The calculated magnetic field profiles are in good agreement with Pioneer Venus orbiter magnetometer observations. The magnetic field structure is quasi-steady for slow changes of the solar wind dynamic pressure. The peak at 165 km is maintained by downward convection from higher altitudes. The time scale for the decay of the field by the pure one-dimensional vertical diffusion/convection process is several hours unless the flux is resupplied from the top of the ionosphere.

Shinagawa, H.↗

NASA NTRS1987

Power and charge dissipation from an electrodynamic tether

The Plasma Motor-Generator project utilizes the influence of the geomagnetic field on a conductive tether attached to a LEO spacecraft to provide a reversible conversion of orbital energy into electrical energy. The behavior of the current into the ionospheric plasma under the influence of the geomagnetic field is of significant experimental and theoretical interest. Theoretical calculations are reviewed which start from Maxwell's equations and treat the ionospheric plasma as a linear dielectric medium. These calculations show a charge emitting tether moving in a magnetic field will generate electromagnetic waves in the plasma which carry the charge in the direction of the magnetic field. The ratio of the tether's speed to the ion cyclotron frequency which is about 25 m for a LEO is a characteristic length for the phenomena. Whereas for the dimensions of the contact plasma much larger than this value the waves are the conventional Alfven waves, when the dimensions are comparable or smaller, diffraction effects occur similar to those associated with Fresnel diffraction in optics. The power required to excite these waves for a given tether current is used to estimate the impedance associated with this mode of charge dissipation.

Hite, Gerald E.↗

NASA NTRS1987

Current to the ionosphere following a lightning stroke

A simple analytical expression for calculating the total current waveform to the ionosphere after a lightning stroke is derived. The validity of this expression is demonstrated by comparison with a more rigorous computer solution of Maxwell's equations. The analytic model demonstrates that the temporal variation of the current induced in the ionosphere and global circuit and the corresponding return current in the earth depends on the conductivity profile at intervening altitudes in the middle atmosphere. A conclusion is that capacitative coupling may provide tighter coupling between the lower atmosphere and the ionosphere than usually considered, in both directions, which may help to explain observations which seem to indicate that magnetospheric phenomena may in some instances trigger lightning.

Hale, L. C.↗

NASA NTRS1988

Lightning-related fields in the ionosphere

Lightning-related transient electric fields and conduction current densities due to the redistribution of charge by the return stroke, but not directly associated with the high-intensity current channel, are investigated via a simulation of Maxwell's equations. The investigation presents evidence to suggest that the lightning-related charge redistribution and subsequent relaxation, rather than the high intensity current, is the source of the major component of the transient field and energy coupled to the ionosphere. A time domain finite element analysis is employed in the simulation, using a conductivity profile obtained simultaneously with electric field measurements which agree, in general terms, with the simulations. It is concluded that prior depictions of these phenomena underestimate the fraction of the total energy that couples to and dissipates within the ionosphere and magnetosphere.

Baginski, M. E.↗

NASA NTRS1986

Generalized three-dimensional experimental lightning code (G3DXL) user's manual

Information concerning the programming, maintenance and operation of the G3DXL computer program is presented and the theoretical basis for the code is described. The program computes time domain scattering fields and surface currents and charges induced by a driving function on and within a complex scattering object which may be perfectly conducting or a lossy dielectric. This is accomplished by modeling the object with cells within a three-dimensional, rectangular problem space, enforcing the appropriate boundary conditions and differencing Maxwell's equations in time. In the present version of the program, the driving function can be either the field radiated by a lightning strike or a direct lightning strike. The F-106 B aircraft is used as an example scattering object.

Kunz, Karl S.↗

NASA NTRS1990

Theory of circular dielectric waveguide with anisotropic sheet cover

A circular dielectric waveguide consisting of an isotropic core covered with a thin anisotropic sheet is considered. The sheet is represented as a jump immittance and Maxwell's equations are applied. Solution of the boundary value problem yields the characteristic equation, or dispersion relation, which is then solved numerically. The results are verified for the step-index fiber and circular, metallic waveguides. Finally, examples are included to investigate the effects of the anisotropic sheet.

Kish, Jerome Thomas↗

NASA NTRS1990

CFD spinoff - Computational electromagnetics for radar cross section (RCS) studies

A finite-volume discretization procedure derived from proven CFD methods is used to solve the conservation form of the time-domain Maxwell's equations, in order to compute EM scattering from layered objects. This time-domain approach handles both single-frequency/continuous wave and broadband-frequency/pulse incident excitation. Arbitrarily shaped objects are modeled by means of a body-fitted coordinate transformation; complex internal/external structures with many material layers are treated through the implementation of a multizone framework capable of handling any type of zonal boundary condition. Results are presented for various two- and three-dimensional problems.

Shankar, Vijaya↗

NASA NTRS1991

Collisionless reconnection in two-dimensional magnetotail equilibria

A two-dimensional particle simulation model based on the Darwin approximation to Maxwell's equations for studying collisionless reconnection in the magnetotail has been developed. Simulations of the pure ion tearing mode in a thin current sheet with normal B(z) field component demonstrate that in this limit this mode grows more slowly than expected based on previous analytic estimates. The saturation level of the tearing instability greatly surpasses estimates based on a simple trapping argument. The effect of the normal field component on the evolution of the tearing instability is considered. It is found that a normal field of even a few percent on axis strongly inhibits the growth of the instability.

Pritchett, P. L.↗

NASA NTRS1992

Modeling Characteristics Of Surfaces For Radar Polarimetry

Paper reviews mathematical models of polarimetric radar backscattering characteristics of various types of terrain; forests, grasslands, and lava fields. Represents approach to imaging radar polarimetry in which one accumulates models predicting realistic polarization signatures and represent distinct scattering processes, without attempting full vector solutions of Maxwell's equations in all cases. Idea to develop ability to invert models to identify unknown terrain depicted in polarimetric radar images. Describes models, major scattering characteristics predicted by models, and interpretation of characteristics in terms of dominant scattering mechanisms. Models predict realistic polarization signatures.

Van Zyl, Jakob J.↗

NASA NTRS1992

Field quantization and squeezed states generation in resonators with time-dependent parameters

The problem of electromagnetic field quantization is usually considered in textbooks under the assumption that the field occupies some empty box. The case when a nonuniform time-dependent dielectric medium is confined in some space region with time-dependent boundaries is studied. The basis of the subsequent consideration is the system of Maxwell's equations in linear passive time-dependent dielectric and magnetic medium without sources.

Dodonov, V. V.↗

NASA NTRS1989

Nonlinear triggered lightning models for use in finite difference calculations

Two nonlinear triggered lightning models have been developed for use in finite difference calculations. Both are based on three species of air chemistry physics and couple nonlinearly calculated air conductivity to Maxwell's equations. The first model is suitable for use in three-dimensional modeling and has been applied to the analysis of triggered lightning on the NASA F106B Thunderstorm Research Aircraft. The model calculates number densities of positive ions, negative ions, and electrons as a function of time and space through continuity equations, including convective derivative terms. The set of equations is closed by using experimentally determined mobilities, and the mobilities are also used to determine the air conductivity. Results from the model's application to the F106B are shown. The second model is two-dimensional and incorporates an enhanced air chemistry formulation. Momentum conservation equations replace the mobility assumption of the first model. Energy conservation equations for neutrals, heavy ions, and electrons are also used. Energy transfer into molecular vibrational modes is accounted for. The purpose for the enhanced model is to include the effects of temperature into the air breakdown, a necessary step if the model is to simulate more than the very earliest stages of breakdown. Therefore, the model also incorporates a temperature-dependent electron avalanche rate. Results from the model's application to breakdown around a conducting ellipsoid placed in an electric field are shown.

Rudolph, Terence↗

NASA NTRS1992

Computational modeling of nonlinear electromagnetic phenomena

A new algorithm has been developed that permits, for the first time, the direct time integration of the full-vector nonlinear Maxwell's equations. This new capability permits the modeling of linear and nonlinear, instantaneous and dispersive effects in the electric polarization material media. Results are presented of first-time calculations in 1D of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier.

Goorjian, Peter M.↗

NASA NTRS1992

A modeling study of the time-averaged electric currents in the vicinity of isolated thunderstorms

A thorough examination of the results of a time-dependent computer model of a dipole thunderstorm revealed that there are numerous similarities between the time-averaged electrical properties and the steady-state properties of an active thunderstorm. Thus, the electrical behavior of the atmosphere in the vicinity of a thunderstorm can be determined with a formulation similar to what was first described by Holzer and Saxon (1952). From the Maxwell continuity equation of electric current, a simple analytical equation was derived that expresses a thunderstorm's average current contribution to the global electric circuit in terms of the generator current within the thundercloud, the intracloud lightning current, the cloud-to-ground lightning current, the altitudes of the charge centers, and the conductivity profile of the atmosphere. This equation was found to be nearly as accurate as the more computationally expensive numerical model, even when it is applied to a thunderstorm with a reduced conductivity thundercloud, a time-varying generator current, a varying flash rate, and a changing lightning mix.

Driscoll, Kevin T.↗

NASA NTRS1992

Solar wind-magnetosphere interaction as simulated by a 3-D EM particle code

We present here our first results of simulating the solar wind-magnetosphere interaction with a new three-dimensional electromagnetic particle code. Hitherto such global simulations were done with MHD codes while lower-dimensional particle or hybrid codes served to account for microscopic processes and such transport parameters as have to be introduced ad hoc in MHD. Our kinetic model attempts to combine the macroscopic and microscopic tasks. It relies only on the Maxwell curl equation and the Lorentz equation for particles, which are ideally suited for computers. The preliminary results shown here are for an unmagnetized solar wind plasma streaming past a dipolar magnetic field. The results show the formation of a bow shock and a magnetotail, the penetration of energetic particles into cusp and radiation belt regions, and dawn-dusk asymmetries.

Buneman, Oscar↗

NASA NTRS1993

Calculations and experiments concerning lifting force and power in TEMPUS

A critical comparison is reported between the theoretically predicted and experimentally measured values for the electromagnetic lifting force and the heating rates which may be achieved, under simulated microgravity conditions, using the TEMPUS electromagnetic levitation device. The experiments involved the suspending of a metallic sample from one arm of a recording balance, such that it was carefully positioned between the heating and the positioning coils of the levitation device. The net force exerted by the sample was measured as a function of position, the coil currents, and the nature of the sample. Some calculations are also reported regarding the power absorption by the sample. The theoretical predictions, based on the numerical solution of Maxwell's equations using the volume integral technique, were found to be in excellent agreement with the measurements. For the idealized case of a spherical sample, analytical solutions describing the lifting force were also found to agree very well with the computed results.

Zong, J. H.↗

NASA NTRS1993

Shape optimization for aerodynamic efficiency and low observability

Field methods based on the finite-difference approximations of the time-domain Maxwell's equations and the potential-flow equation have been developed to solve the multidisciplinary problem of airfoil shaping for aerodynamic efficiency and low radar cross section (RCS). A parametric study and an optimization study employing the two analysis methods are presented to illustrate their combined capabilities. The parametric study shows that for frontal radar illumination, the RCS of an airfoil is independent of the chordwise location of maximum thickness but depends strongly on the maximum thickness, leading-edge radius, and leadingedge shape. In addition, this study shows that the RCS of an airfoil can be reduced without significant effects on its transonic aerodynamic efficiency by reducing the leading-edge radius and/or modifying the shape of the leading edge. The optimization study involves the minimization of wave drag for a non-lifting, symmetrical airfoil with constraints on the airfoil maximum thickness and monostatic RCS. This optimization study shows that the two analysis methods can be used effectively to design aerodynamically efficient airfoils with certain desired RCS characteristics.

Vinh, Hoang↗

NASA NTRS1993

Interaction with the lower ionosphere of electromagnetic pulses from lightning - Heating, attachment, and ionization

A Boltzmann formulation of the electron distribution function and Maxwell's equations for the EM fields are used to simulate the interaction of lightning radiated EM pulses with the lower ionosphere. Ionization and dissociative attachment induced by the heated electrons cause significant changes in the local electron density, N(e). Due to 'slow' field changes of typical lightning EM pulses over time scales of tens of microsec, the distribution function follows the quasi-equilibrium solution of the Boltzmann equation in the altitude range of interest (70 to 100 km). The EM pulse is simulated as a planar 100 microsec long single period oscillation of a 10 kHz wave injected at 70 km. Under nighttime conditions, individual pulses of intensity 10-20 V/m (normalized to 100 km horizontal distance) produce changes in N(e) of 1-30 percent while a sequence of pulses leads to strong modification of N(e) at altitudes less than 95 km. The N(e) changes produce a 'sharpening' of the lower ionospheric boundary by causing a reduction in electron density at 75-85 km (due to attachment) and a substantial increase at 85-95 km (due to ionization) (e.g., the scale height decreases by a factor of about 2 at about 85 km for a single 20 V/m EM pulse). No substantial N(e) changes occur during daytime.

Taranenko, Y. N.↗

NASA NTRS1993

Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗