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Study of remote probing of inhomogeneous media making use of the known reflection coefficient of the medium as a function of the varied incident angle of the probing plane wave. An analytical method is developed for processing these reflection coefficient data. A critical evaluation of the numerical aspects of the method is presented.
The problem of determining the electric permittivity of an inhomogeneous dielectric medium is considered. Two analytical methods and one numerical method for solving this problem are presented. All these methods utilize the reflection coefficient measured as a function of the angular spectrum variable. This allows measurements at a fixed frequency, and these methods, therefore, can be used when the medium being studied is dispensive. A few examples are provided and some comments are made regarding the stability of solutions obtained using the various methods.
The methods of geometric optics are used to obtain the irradiance and spectral distribution of light scattered by fluctuations in an inhomogeneous fluid. The optical properties of the fluid are assumed to be described by a local dielectric constant that varies monotonically in one direction.
In this paper we treat the multiple scattering theory of radiative transfer in plane-parallel inhomogeneous atmospheres. The treatment presented here may be adopted to model atmospheres characterized by an optical depth dependent coherent scattering phase function. For the purpose of illustration we consider the semi-infinite medium in which the absorption property of the atmosphere is characterized by an exponential function. The methodology employed here is the extension of the case treated previously by the author for homogeneous atmospheres.
Small variations in the properties of an acoustic medium produce cumulative effects that significantly alter wave forms propagating over long distances. To investigate some aspects of these effects, without statistical models, the one-dimensional wave equation with a weak spatially periodic variation in the sound speed is treated. An approximation is developed valid for such weak inhomogeneities over large distances based upon the approximate treatment of a linear differential equation with a periodic coefficient. It is applied to the propagation of an initial step wave and identifies the dispersive nature of the medium which accounts for the cumulative effects.
Work done in several areas to advance the state of the art of magnetic mass spectrometers is described. The calculations and data necessary for the design of inhomogeneous field mass spectrometers, and the calculation of ion trajectories through such fields are presented. The development and testing of solid state ion detection devices providing the capability of counting single ions is discussed. New techniques in the preparation and operation of thermal-ionization ion sources are described. Data obtained on the concentrations of copper in rainfall and uranium in air samples using the improved thermal ionization techniques are presented. The design of a closed system static mass spectrometer for isotopic analyses is discussed. A summary of instrumental aspects of a four-stage mass spectrometer comprising two electrostatic and two 90 deg. magnetic lenses with a 122-cm radius used to study the interaction of ions with solids is presented.
The electrostatic resonance properties of an inhomogeneous plasma column are reported by application of the Rayleigh-Ritz method. A description of the rf equation of motion and pressure term that expresses the system of equations in Euler-Lagrange form is presented. The Rayleigh-Ritz procedure is applied to the corresponding Lagrangian to obtain approximate resonance frequencies and eigenfunctions. An appropriate set of trial coordinate functions is defined, which leads to frequency and eigenfunction estimates.
Some of the basic developments in the theory of electromagnetic field representation in terms of Hertz vectors are reviewed. A solution for the field in an inhomogeneous anisotropic medium is given in terms of the two Hertz vectors. Conditions for presentation of the field in terms of uncoupled transverse electric and transverse magnetic modes, in a general orthogonal coordinate system, are derived when the permeability and permittivity tensors have only diagonal components. These conditions are compared with some known special cases.
Equations are derived for describing the inhomogeneous equilibrium and small deviations from the equilibrium, giving particular attention to systems with trapped particles. An investigation is conducted of periodic systems with a single trapped-particle water bag, taking into account the behavior of the perturbation equations at the turning points. An outline is provided concerning a procedure for obtaining the eigenvalues. The results of stability calculations connected with the sideband effects are considered along with questions regarding the general applicability of the multiple water-bag approach in stability calculations.
The influence of pulse volume dimensions on the accuracy of reflectivity from various clouds is considered. It is shown that due to the spatial averaging and the inhomogeneities of the clouds, the dependence frequently breaks down, which is a cause of lower values of the spatial distribution estimate. Values of the corrections calculated for various conditions are presented.
The article details an inhomogeneous reflecting layer (IRFL) model designed to survey absorption line behavior from a Squires-like cloud cover (which is characterized by convection cell structure). Computational problems and procedures are discussed in detail. The results show trends usually opposite to those predicted by a simple reflecting layer model. Per cent equivalent width variations for the tower model are usually somewhat greater for weak than for relatively strong absorption lines, with differences of a factor of about two or three. IRFL equivalent width variations do not differ drastically as a function of geometry when the total volume of absorbing gas is held constant. The IRFL results are in many instances consistent with observed equivalent width variations of Jupiter, Saturn, and Venus.
The electrostatic resonance properties of an inhomogeneous plasma column are treated by the Rayleigh-Ritz method. In contrast to Parker, Nickel & Gould (1964), who carried out an exact computation, the present treatment uses a description of the RF equation of motion and pressure term that allows one to express the system of equations in Euler-Lagrange form. The Rayleigh-Ritz procedure is then applied to the corresponding Lagrangian, to obtain approximate resonance frequences and eigenfunctions. An appropriate set of trial coordinate functions is defined, which leads to frequency and eigenfunction estimates in excellent agreement with the work of Parker et al. (1964).
The reported method makes it possible to conduct all maser frequency measurements under conditions of low magnetic field intensity for which the hydrogen maser is most stable. Aspects concerning the origin of the magnetic inhomogeneity shift are examined and the available approaches for measuring this shift are considered, taking into account certain drawbacks of currently used methods. An approach free of these drawbacks can be based on the measurement of changes in a parameter representing the difference between the number of atoms in the involved states.
We describe a method for calculating directly the mean integrated intensity in an inhomogeneous Rayleigh scattering atmosphere using a combined variational and iterative technique. This method is particularly useful for computing dissociation rates in aeronomical problems. Simple semi-analytic expressions are derived.
The generalized inhomogeneous wave equation that governs magnetoacoustic, vortical, and thermal motions in compressible fluids and that is applicable to the problem of heating of the solar chromosphere and corona is obtained. The effects of kinematic and bulk viscosity, heat conduction, Joule dissipation, and magnetic diffusivity are included. Under the usual assumptions, the generalized wave equation reduces to the well-known equations of Lighthill, Kulsrud, Phillips, and others. The major problems encountered in applying Lighthill's (1952) mechanism to sound generation in turbulent media are reviewed for both the subsonic and supersonic cases.
Observed profiles of the R branch of Saturn's CH4 3 nu (3) band are compared with synthetic profiles computed from inhomogeneous models which are consistent with Saturn's H2 quadrupole-line equivalent widths. A C/H ratio approximately three times the solar value and a CH4 abundance of about 100 m am are found. Scattering plays a significant role in the formation of manifold profiles below a depth where the H2 abundance is 20-30 km am.
The paper studies thermal microwave emission from an inhomogeneous slab of a random medium, with possible nonuniform absorption, scattering, and temperature profiles, bounded by different dielectrics on both sides. The invariant imbedding method is used to cast the boundary value problem of the radiative transfer equations into an initial value problem at zero slab thickness. As a numerical example, the angular and polarization variations of brightness temperatures for ice over water are considered.
Calculations of the transmission of infrared radiation through the atmosphere must take into account inhomogeneities in the path due to variations of temperature, pressure and absorbing matter. For ozone absorption the method due to Curtis and Godson does not seem to yield results that are sufficiently precise. In this paper an improved approximation is developed that yields an analytic expression for the transmission function and this is compared with the exact results obtained from the Goody random model.