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A derivation of the equation of transfer is obtained by starting with Maxwell's equations in the 'slowly varying envelope' form. Particular attention is paid to characterizing the intensity that is 'seen' by the atom (which is found to be related to a Wigner distribution of the electric field). The equation of transfer is found to be valid for 'broad-band' slowly varying radiation fields.
A review is presented of Birkeland's outstanding contributions to auroral theory and, in particular, to the foundation of modern magnetospheric physics. Birkeland's first years in research, after a study of mathematics and theoretical physics at the university, were concerned with Maxwell's theory, the investigation of electromagnetic waves in conductors, wave propagation in space, an energy transfer by means of electromagnetic waves, and a general expression for the Poynting vector. Experiments with cathode rays near a magnet in 1895, led Birkeland to the development of an auroral theory. This theory represented the first detailed, realistic explanation of the creation of an aurora. Attention is given to experiments conducted to verify the theory, the discovery of the polar elementary storm, and the deduction of auroral electric currents. Birkeland's background and education is also considered along with his personality.
Using the unabridged Maxwell equations (including vectors D, E and H) new effects in collisionless plasmas are uncovered. In a steady state, it is found that spatially varying energy density of the electric field (E perpendicular) orthogonal to B produces electric current leading, under certain conditions, to the relationship P perpendicular + B(2)/8 pi-epsilon E perpendicular(2)/8 pi = constant, where epsilon is the dielectric constant of the plasma for fields orthogonal to B. In steady state quasi-two-dimensional flows in plasmas, a general relationship between the components of electric field parallel and perpendicular to B is found. These effects are significant in geophysical and astrophysical plasmas. The general conditions for a steady state in collisionless plasma are deduced. With time variations in a plasma, slow compared to ion-gyroperiod, there is a general current, (j-asterisk), which includes the well-known polarization current, given by J-asterisk = d/dt (E x M) + (P x B) x B B(-2) where M and P are the magnetization and polarization vectors respectively.
A numerical modeling technique is utilized to investigate the response of a UH-60A helicopter to both lightning and nuclear electromagnetic pulses (NEMP). The analytical approach involves the three-dimensional time domain finite-difference solutions of Maxwell's equations. Both the external currents and charges as well as the internal electromagnetic fields and cable responses are computed. Results of the analysis indicate that, in general, the short circuit current on internal cables is larger for lightning, whereas the open-circuit voltages are slightly higher for NEMP. The lightning response is highly dependent upon the rise time of the injected current as was expected. The analysis shows that a coupling levels to cables in a helicopter are 20 to 30 dB larger than those observed in fixed-wing aircraft.
In NOAA Active Region 2372 (April 1980), 4 x 10 to the 20th power maxwell of magnetic flux concentrated within a 30" circular area disappeared overnight. Vector magnetograms show that all components of the magnetic field weakened together. If the field had weakened through diffusion or fluid flow, 80% of the original flux would still have been detected by the magnetograph within a suitably enlarged area. In fact there was at least a threefold decrease in detected flux. Evidently, magnetic field was removed from the photosphere. Since the disappearing flux was located in a region of low magnetic shear and low activity, it is unlikely that the field dissipated through reconnection. The most likely possibility is that flux submerged. Observations suggest that even in the growth phase of active regions, submergence is a strong process comparable in magnitude to emergence.
In NOAA Active Region 2372 (April 1980), 4 x 10 to the 20th maxwells of magnetic flux concentrated in an area 30 arcsec across disappeared overnight. Vector magnetograms show that all components of the magnetic field weakened together. If the field had weakened through diffusion or fluid flow, 90 percent of the original flux would still have been detected by the magnetograph within a suitably enlarged area. In fact there was a threefold decrease in detected flux. Evidently, magnetic field was removed from the photosphere. Since the disappearing flux was located in a region of low magnetic shear and low activity in H-alpha and Ly-alpha, it is unlikely that the field dissipated through reconnection. It is argued that the most likely possibility is that flux submerged. The observations suggest that even during the growth phase of active regions, submergence is a strong process comparable in magnitude to emergence.
The constitutive equation for the relaxation behavior of time-dependent, chemically unstable materials developed by Valanis and Peng (1983), which used the irreversible thermodynamics of internal variables in Eyring's absolute reaction theory and yielded a theoretical expression for the effect of chemical crosslink density on the relaxation rate, is presently applied to the creep behavior of a network polymer which is undergoing a scission process. In particular, two equations are derived which may for the first time show the relations between mechanical models and internal variables in the creep expressions, using a three-element model with a Maxwell element.
Binary collision rates for arbitrary scattering cross sections are derived in the case of a beam of particles interacting with a Maxwell-Boltzmann (MB) plasma, or in the case of two MB plasmas interacting at generally different temperatures. The expressions are valid for all beam energies and plasma temperatures, from the nonrelativistic to the extreme relativistic limits. The calculated quantities include the reaction rate, the energy exchange rate, and the average rate of change of the squared transverse momentum component of a monoenergetic particle beam as a result of scatterings with particles of a MB plasma. Results are specialized to elastic scattering processes, two-temperature reaction rates, or the cold plasma limit, reproducing previous work.
The concept of the Maxwell time of a viscoelastic material (4.5) is used in conjunction with calculated thermal profiles to evaluate the significance of tectonic estimates of lithospheric thickness. Thermal lithospheric thicknesses provide fundamental constraints on planetary thermal histories that complement the constraints provided by dateable surface deposits of endogenic origin. Lithospheric constraints are of particular value on the icy satellites where our understanding of both rheology and surface ages is considerably poorer than it is for the terrestrial planets. Certain extensional tectonic features can and have been used to estimate lithospheric thicknesses on Ganymede and Callisto. These estimates, however, refer to the depth of the elastic lithosphere defined by the zone of brittle failure. The relation between the elastic lithosphere and the thermal lithosphere (generally defined by the zone of conductive heat transport) is not straightforward, because the depth of brittle failure depends not only on the thermal profile, but also on rheology and strain rate (or the characteristic time over which stresses build towards failure). Characteristic time considerations are not trivial in this context because stresses generating brittle failure on the icy satellites may be produced by impacts, with characteristic times of seconds to days, or by geologic processes with time scales of hundreds of millions of years.
A kinematic approach to short-term geomagnetism has recently been based upon pre-Maxwell frozen-flux electromagnetism. A complete dynamic theory requires coupling fluid dynamics to electromagnetism. A geophysically plausible simplifying assumption for the vertical vorticity balance, namely that the vertical Lorentz torque is negligible, is introduced and its consequences are developed. The simplified coupled magnetohydrodynamic system is shown to conserve a variety of magnetic and vorticity flux integrals. These provide constraints on eligible models for the geomagnetic main field, its secular variation, and the horizontal fluid motions at the top of the core, and so permit a number of tests of the underlying assumptions.
A covariant relativistic formulation is used for self-consistent dynamics of a guiding-center plasma in an electromagnetic field. The reciprocal interactions appear as a magnetization in Maxwell's equations and as field gradient forces in the guiding-center dynamical equation. The ten local conservation laws corresponding to translational and rotational invariance of the Minkowski space are expressed in terms of a symmetric energy-momentum tensor.
In an axially grooved rectangular waveguide the linearized Vlasov equation is solved to find the perturbed distribution function resulting from the electromagnetic forces on the electrons. The resulting beam current and the propagating electromagnetic waves of the cold tube are used in the inhomogeneous Maxwell's equation to derive the general dispersion equation. This equation is then transformed into the electron beam frame and the resulting linear growth rate of amplification is calculated. By maximizing the linear growth rate, the operational parameters of the gyrotron are then optimized.
Electromagnetic particle simulations solve the full set of Maxwell's equations. They thus include the effects of self-consistent electric and magnetic fields, magnetic induction, and electromagnetic radiation. The algorithms for an electromagnetic code which works directly with the electric and magnetic fields are described. The fields and current are separated into transverse and longitudinal components. The transverse E and B fields are integrated in time using a leapfrog scheme applied to the Fourier components. The particle pushing is performed via the relativistic Lorentz force equation for the particle momentum. As an example, simulation results are presented for the electron cyclotron maser instability which illustrate the importance of relativistic effects on the wave-particle resonance condition and on wave dispersion.
The effects of present-day glacial discharges and the growth of the Antarctic ice sheet on exciting the earth's rotational axis are studied. Glacial forcing could cause a maximum change in J2 of about one-third of the observed amount, for the Maxwell rheology and for Burgers' body models with a long-term, lower-mantle viscosity greater than about 10 to the 23rd P. For transient rheologies the amount of excitation due to glacial melting decreases. Polar wander is not much excited by recent glacial melting for the various types of rheologies examined.
The NASA Kennedy Space Center, (KSC) and the U.S. Air Force are currently operating an extensive network of ground-based electric-field mills in order to detect atmospheric electrical hazards to ground operations, launches, and landings of spacecraft. Over the past 10 years, the University of Arizona has utilized data provided by this network, and other instrumentation, to investigate the electrical structure of thunderstorms and lightning in Florida. Recent analyses have included estimates of the Maxwell current density that thunderstorms produce at the ground and computations of the locations and magnitudes of lightning-caused changes in the cloud charge distribution. This work is reviewed, and an example of how thunderstorm current patterns and lightning charges develop in both space and time is presented.
Researchers determined that lightning can be used to determine the diurnal variations of thunderstorms, i.e., storms that produce audible thunder, and that these variations are also in good agreement with diurnal variations in rainfall and convective activity. Measurements of the Maxwell current density, J sub m, under active thunderstorms show that this physical quantity is quasi-steady between lightning discharges and that lightning does not produce large changes in J sub m. Maps of J sub m show contours of iso-current density that are consistent with the locations of radar echos and the locations of where lightning has altered the cloud charge distribution.
The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation.
The Hypercube Matrix Computation (Year 1986-1987) task investigated the applicability of a parallel computing architecture to the solution of large scale electromagnetic scattering problems. Two existing electromagnetic scattering codes were selected for conversion to the Mark III Hypercube concurrent computing environment. They were selected so that the underlying numerical algorithms utilized would be different thereby providing a more thorough evaluation of the appropriateness of the parallel environment for these types of problems. The first code was a frequency domain method of moments solution, NEC-2, developed at Lawrence Livermore National Laboratory. The second code was a time domain finite difference solution of Maxwell's equations to solve for the scattered fields. Once the codes were implemented on the hypercube and verified to obtain correct solutions by comparing the results with those from sequential runs, several measures were used to evaluate the performance of the two codes. First, a comparison was provided of the problem size possible on the hypercube with 128 megabytes of memory for a 32-node configuration with that available in a typical sequential user environment of 4 to 8 megabytes. Then, the performance of the codes was anlyzed for the computational speedup attained by the parallel architecture.