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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

The general Lie group and similarity solutions for the one-dimensional Vlasov-Maxwell equations

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multispecies case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution for a one-species, one-dimensional plasma is one of the general similarity solutions.

Roberts, D.↗
NASA NTRS1987

Particle paths and phase plane for time-dependent similarity solutions of the one-dimensional Vlasov-Maxwell equations

The phase trajectories of particles in a plasma described by the one-dimensional Vlasov-Maxwell equations are determined qualitatively, analyzing exact general similarity solutions for the cases of temporally damped and growing (sinusoidal or localized) electric fields. The results of numerical integration in both untransformed and Lie-group point-transformed coordinates are presented in extensive graphs and characterized in detail. The implications of the present analysis for the stability of BGK equilibria are explored, and the existence of nonlinear solutions arbitrarily close to and significantly different from the BGK solutions is demonstrated.

Roberts, Dana Aaron↗
NASA NTRS1990

Algorithm development for Maxwell's equations for computational electromagnetism

A new algorithm has been developed for solving Maxwell's equations for the electromagnetic field. It solves the equations in the time domain with central, finite differences. The time advancement is performed implicitly, using an alternating direction implicit procedure. The space discretization is performed with finite volumes, using curvilinear coordinates with electromagnetic components along those directions. Sample calculations are presented of scattering from a metal pin, a square and a circle to demonstrate the capabilities of the new algorithm.

Goorjian, Peter M.↗
NASA NTRS1990

Submillimeter observations of the sun from the James Clerk Maxwell Telescope

The first submillimeter solar observations from the 15 m James Clerk Maxwell Telescope (JCMT) on Mauna Kea are reported. The JCMT submillimeter heterodyne receiver is used to observe the sun in 850 micron radiation. These are the first submillimeter observations of features on the size scale of the chromospheric supergranular network and of sunspots. A comparison is made between 850 micron images and calcium K line images of the chromospheric supergranular network in the quiet sun and in plage. Images of sunspots are given, noting that their 850 micron brightness is comparable to, or somewhat greater than, that of the quiet sun.

Lindsey, Charles A.↗
NASA NTRS1991

Evaluating lightning hazards to building environments using explicit numerical solutions of Maxwell's equations

The objective here is to describe the lightning hazards to buildings and their internal environments using advanced formulations of Maxwell's Equations. The method described is the Three Dimensional Finite Difference Time Domain Solution. It can be used to solve for the lightning interaction with such structures in three dimensions with the inclusion of a considerable amount of detail. Special techniques were developed for including wire, plumbing, and rebar into the model. Some buildings have provisions for lightning protection in the form of air terminals connected to a ground counterpoise system. It is shown that fields and currents within these structures can be significantly high during a lightning strike. Time lapse video presentations were made showing the electric and magnetic field distributions on selected cross sections of the buildings during a simulated lightning strike.

Collier, Richard S.↗
NASA NTRS1991

Gravitational spreading of Danu, Freyja and Maxwell Montes, Venus

The potential energy of elevated terrain tends to drive the collapse of the topography. This process of gravitational spreading is likely to be more important on Venus than on Earth because the higher surface temperature weakens the crust. The highest topography on Venus is Ishtar Terra. The high plateau of Lakshmi Planum has an average elevation of 3 km above mean planetary radius, and is surrounded by mountain belts. Freyja, Danu, and Maxwell Montes rise, on average, an additional 3, 0.5, and 5 km above the plateau, respectively. Recent high resolution Magellan radar images of this area, east of approx. 330 deg E, reveal widespread evidence for gravity spreading. Some observational evidence is described for gravity spreading and the implications are discussed in terms of simple mechanical models. Several simple models predict that gravity spreading should be an important process on Venus. One difficulty in using remote observations to infer interior properties is that the observed features may not have formed in response to stresses which are still active. Several causes of surface topography are briefly examined.

Smrekar, Suzanne E.↗
NASA NTRS1991

A Fourier collocation time domain method for numerically solving Maxwell's equations

A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

Shebalin, John V.↗
NASA NTRS1992

Divergence preserving discrete surface integral methods for Maxwell's curl equations using non-orthogonal unstructured grids

Several new discrete surface integral (DSI) methods for solving Maxwell's equations in the time-domain are presented. These methods, which allow the use of general nonorthogonal mixed-polyhedral unstructured grids, are direct generalizations of the canonical staggered-grid finite difference method. These methods are conservative in that they locally preserve divergence or charge. Employing mixed polyhedral cells, (hexahedral, tetrahedral, etc.) these methods allow more accurate modeling of non-rectangular structures and objects because the traditional stair-stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided. Numerical results demonstrating the accuracy of these new methods are presented.

Madsen, Niel K.↗
NASA NTRS1992

Pulsed plane wave analytic solutions for generic shapes and the validation of Maxwell's equations solvers

Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.

Yarrow, Maurice↗
NASA NTRS1993

Fourier analysis of numerical algorithms for the Maxwell equations

The Fourier method is used to analyze the dispersive, dissipative, and isotropy errors of various spatial and time discretizations applied to the Maxwell equations on multi-dimensional grids. Both Cartesian grids and non-Cartesian grids based on hexagons and tetradecahedra are studied and compared. The numerical errors are quantitatively determined in terms of phase speed, wave number, propagation direction, gridspacings, and CFL number. The study shows that centered schemes are more efficient than upwind schemes. The non-Cartesian grids yield superior isotropy and higher accuracy than the Cartesian ones. For the centered schemes, the staggered grids produce less errors than the unstaggered ones. A new unstaggered scheme which has all the best properties is introduced. The study also demonstrates that a proper choice of time discretization can reduce the overall numerical errors due to the spatial discretization.

Liu, Yen↗
NASA NTRS1993

Finite-surface method for the Maxwell equations in generalized coordinates

A finite-surface technique for the Maxwell equations in generalized nonorthogonal coordinates is developed. It directly applies the integral Faraday's and Ampere's laws to faces of primary and secondary grid cells, respectively. The technique features an accurate treatment of matching conditions at a material interface, grid singularities, and radiation conditions at outer boundaries.

Vinokur, Marcel↗
NASA NTRS1993

Direct time integration of Maxwell's equations in two-dimensional dielectric waveguides for propagation and scattering of femtosecond electromagnetic solitons

We present what are to our knowledge first-time calculations from vector nonlinear Maxwell's equations of femtosecond soliton propagation and scattering, including carrier waves, in two-dimensional dielectric waveguides. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and the nonlinear convolution accounts for two quantum effects, the Kerr and Raman interactions. By retaining the optical carrier, the new method solves for fundamental quantities - optical electric and magnetic fields in space and time - rather than a nonphysical envelope function. It has the potential to provide an unprecedented two- and three-dimensional modeling capability for millimeter-scale integrated-optical circuits with submicrometer engineered inhomogeneities.

Joseph, Rose M.↗
NASA NTRS1994

Finite-surface method for the Maxwell equations with corner singularities

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

Vinokur, Marcel↗
NASA NTRS1993

Direct time integration of Maxwell's equations in two-dimensional dielectric waveguides for propagation and scattering of femtosecond electromagnetic solitons

Solution of 2D vector nonlinear Maxwell's equations is described for material media with linear and nonlinear instantaneous and Lorentz dispersion effects in the electric polarization. Finite difference time domain method is used in the analysis. The method discussed here achieves robustness by enforcing vector-field boundary conditions at all interfaces of dissimilar media.

VECTOR FIELDS↗
NASA NTRS1995

Comparisons of the Maxwell and CLL Gas/Surface Interaction Models Using DSMC

Two contrasting models of gas-surface interactions are studied using the Direct Simulation Monte Carlo (DSMC) method. The DSMC calculations examine differences in predictions of aerodynamic forces and heat transfer between the Maxwell and Cercignani-Lampis-Lord (CLL) models for flat plate configurations at freestream conditions corresponding to a 140 km orbit around Venus. The size of the flat plate is that of one of the solar panels on the Magellan spacecraft, and the freestream conditions are one of those experienced during aerobraking maneuvers. Results are presented for both a single flat plate and a two-plate configuration as a function of angle of attack and gas-surface accommodation coefficients. The two plate system is not representative of the Magellan geometry, but is studied to explore possible experiments that might be used to differentiate between the two gas surface interaction models.

Hedahl, Marc O.↗
NASA NTRS1995

The Singularity Mystery Associated with a Radially Continuous Maxwell Viscoelastic Structure

The singularity problem associated with a radially continuous Maxwell viscoclastic structure is investigated. A special tool called the isolation function is developed. Results calculated using the isolation function show that the discrete model assumption is no longer valid when the viscoelastic parameter becomes a continuous function of radius. Continuous variations in the upper mantle viscoelastic parameter are especially powerful in destroying the mode-like structures. The contribution to the load Love numbers of the singularities is sensitive to the convexity of the viscoelastic parameter models. The difference between the vertical response and the horizontal response found in layered viscoelastic parameter models remains with continuous models.

Fang, Ming↗
NASA NTRS1999

A Non-Dissipative Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell's Equations

We consider a divergence-free non-dissipative fourth-order explicit staggered finite difference scheme for the hyperbolic Maxwell's equations. Special one-sided difference operators are derived in order to implement the scheme near metal boundaries and dielectric interfaces. Numerical results show the scheme is long-time stable, and is fourth-order convergent over complex domains that include dielectric interfaces and perfectly conducting surfaces. We also examine the scheme's behavior near metal surfaces that are not aligned with the grid axes, and compare its accuracy to that obtained by the Yee scheme.

Yefet, Amir↗