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Volume 49, Issue 8, 01 August 1978

Relativistic study of electromagnetic waves in the accelerated dielectric medium
View Description Hide DescriptionThe problem of electromagnetic wave propagation in the linearly accelerateddielectric medium is studied by using the extended Maxwell‐Minkowskitheory. First, from the viewpoint of the extended Maxwell‐Minkowskitheory, the well‐known problem of reflection and transmission of electromagnetic waves by the moving dielectric with constant velocity is studied by using the Galilean transformations instead of the Lorentz transformations. It is shown that the problem can be solved and the same results can be obtained as those obtained by using the Lorentz transformations. Then, with the aid of the covariant properties of Maxwell’sequations, a rigorous solution of the electromagnetic wave in a linearly accelerateddielectric is founded. The phenomena of bending of light rays in the accelerated system and the relativistic energy velocity and phase velocity addition law for the acceleratedmotion are derived from the rigorous solution obtained. The problem of reflection and transmission of the electromagnetic wave at normal incidence by a linearly accelerateddielectric interface is solved using the solution obtained. The reflected wave and the transmitted wave are obtained, and their interesting properties concerning the Doppler effect and drag effect are discussed in comparison with the case of constant‐velocity motion.

On the determination of phase and group velocities of dispersive waves in solids
View Description Hide DescriptionA new technique is developed to determine the dispersion relation and the propagational speeds of waves in dispersive solids. The phase spectrum of a broadband pulse is linearly related to the dispersion relation of the dispersive medium. The method is simpler than the continuous‐wave phase comparison technique. Application is made to measure the phase and group velocities of waves in fiber‐reinforced composite materials and in thin wires. This technique is expected to be applicable to measurements of acoustic or electromagnetic wave speeds in other dispersive media.

Infrared fluorescence measurement of equilibrium and vibrational temperatures in laser‐irradiated gases
View Description Hide DescriptionA calibrated two‐color temperature method has been developed for the measurement of time‐dependent temperatures in low‐pressure gases following laser excitation. Ratios of ir fluorescence signals arising from specific vibrational manifolds are used to determine the magnitude of laser heating, the vibrational temperatures of individual modes, and density fluctuations due to gasdynamic expansion following spatially inhomogeneous excitation. This technique has been applied to a prototype system consisting of SF_{6}, SO_{2}, and CH_{3}F exposed to TEA CO_{2} laser excitation of the ν_{3} mode of SF_{6}. Prior to V‐T/R relaxation, this system cannot be described by a single vibrational temperature.

A Fourier‐Bessel solution of an Einzel‐type electrostatic field with rotational symmetry
View Description Hide DescriptionA solution φ (r,z) is given of a rotationally symmetric boundary‐value problem: φ (A,z) =0 for z⩽0 and z⩾L, and φ (A,z) =F (z) for 0⩾z⩾L. A and L are given constants and F (z) is a given function which is symmetrical with respect to the plane z=L/2. The solution is in the form of an infinite Fourier‐Bessel series, the coefficients of which can be found without inverting matrices. It is shown that the given field can be approximated physically by means of two long equipotential cylinders and one or more central electrodes of curved cross sections. Since the electric intensity is also known at all points, the solution allows a precise determination of the electron‐optical properties of a wide variety of electrostatic Einzel lenses with curved electrodes.

Radiant‐energy exchange by small objects using continuum fields
View Description Hide DescriptionIn the emission or absorption of electromagnetic radiation by small objects, generally speaking, the smaller the size‐wavelength ratio and the higher the modal number, the larger will be the ratio of reactive to real power flow. However, if the source is internally lossless and free of constraints, charge‐current relationships may exist which produce combinatory sets of multipolar electric and magnetic moments for any modal number which yields zero net reactive power flow—a resonant condition. The needed reactive energy for resonance to occur decreases with increasing modal number. The radiative Q is very large and will give rise to reactive forces that are quite capable of driving an atomic source to radiate energy h/ω during electronic transition times. When resonance occurs, the resulting radiation has an energy–to–angular‐momentum ratio mω, where m is an integer, and a combinatory set of modal coefficients exists for which the radiation is largely directed in that the ratio of exchanged momentum to exchanged energy is greater than 0.8/c. Other mechanisms may supply the momentum increment needed to make the exchanged ratio be exactly 1/c. This continuum‐field description appears to be adequate to describe the radiative portion of atomic electronic transitions, treated as a boundary‐value problem.

Third‐harmonic generation by a Gaussian electromagnetic beam in a magnetoplasma
View Description Hide DescriptionThis paper presents an investigation of nonlinear third‐harmonic generation in a weakly collisional magnetoplasma due to simultaneous propagation of both the right and left circularly polarized modes, having a Gaussian intensity distribution; self‐focusing has been taken into account. At moderate powers, the self‐focusing is seen to enhance the harmonic output by two orders of magnitude; at high powers, propagation occurs in an almost uniform waveguide devoid of plasma, and the harmonic output is, consequently, decreased. In the vicinity (ω_{ c }/ω=0.7) of the electron cyclotron resonance, the harmonic output of the extraordinary mode is enhanced by an order of magnitude; the present theory is not applicable at resonance.

Efficient coupling of LED and spherical‐ended fiber
View Description Hide DescriptionA model of the coupling of a Lambertian LED and a spherical‐ended fiber is proposed and analyzed by means of geometrical optics. The system of this optical coupling can be regarded as a simple optical system which consists of a light source, a principal plane, and an aperture stop. The model analyzed is that in which a light source and an aperture stop are on the anterior and the posterior focal planes, respectively. The maximum incident angle φ_{ m } into the fiber is determined from the condition that the ray passing through the anterior focal point is not obstructed by the aperture stop, which has the same diameter as the core one. According to the theoretical analysis, the coupling efficiency for the Lambertian LED and the spherical‐ended fiber is sin^{2}φ_{ m } provided that d _{0}?d _{ c } and (d _{ c }/d _{0})^{2} sin^{2}φ_{ m } provided that d _{0}≳d _{ c }, where d _{0} is the emitting diameter and d _{ c } is the critical diameter defined by the critical angle φ_{ c } of the light propagation in the fiber. For two kinds of LED’s with emitting diameters of 35 and 85 μm, the coupling experiment was performed on spherical‐ended fibers which had a numerical apertureNA of 0.14 and a core diameter of 85 μm. The spherical ends of fibers were fabricated to radii r from 75 to 170 μm. A good agreement between the theoretical and experimental results is obtained. In the case that the emitting diameter is 35 μm and the spherical radius is 75 μm, the calculated efficiciency is 6.3%, three times greater than that for a flat‐ended fiber. It is shown that the coupling efficiency can be improved by using the spherical‐ended fiber with the spherical radius less than about d _{1}/(4NA), where d _{1} is the core diameter. It is also shown that the maximum coupling efficiency for the LED with the emitting diameter of d _{0} is obtained by the fiber with the spherical radius less than about d _{0}/(4NA).

Copper acetylacetonate as a source in the 5106‐Å neutral copper laser
View Description Hide DescriptionA copper‐vapor laser utilizing copper acetylacetonate as a copper atom donor in a flowing gas heated discharge tube has been studied. As in the other metal‐vapor laser systems based upon the dissociation of a metal salt, two successive discharges are required to achieve laser action. The output energy of such a system would appear to be comparable to that obtained in the CuCl systems; however, the operating temperature is much lower.

Surface‐wave generation in crystals with high dielectric constant
View Description Hide DescriptionThe generation of surface acoustic waves by interdigital transducers in materials with high and strain‐dependent dielectric constants, which are not necessarily piezoelectric, was studied theoretically using Lamb’s integral‐solution method and the flat‐field approximation of Tseng for the solutions of the wave equation. The influence of the dependence of the dielectric constant on the strain was considered in the approximation given by Pekar and Ogg. As a result, a transducer gain proportional to an applied dc field has been obtained. With respect to the frequency responses, an increased output at higher odd harmonics as compared to transducers on piezoelectric crystals was found. The transducers are shown to be tunable because of a stiffening of the surface‐wave velocity by the applied field. Thus, amplitude modulation and frequency modulation should be possible in a simple manner.

Temperature and stresses in a cylindrical conductor with an alternating current
View Description Hide DescriptionSteady periodic temperature, transient temperature, and stresses produced in an isotropic cylindrical conductor carrying an electric alternating current are calculated. The investigations are made for the small skin effect when the current density is homogeneous.

rf electric fields in an inhomogeneous magnetized plasma column
View Description Hide DescriptionA perturbation method for determining electric fields in an inhomogeneous magnetized plasma column is given that removes restrictions on the wavelengths present in previous treatments. The method is also applicable to finite‐amplitude wave problems.

Optical properties of uranium plasmas
View Description Hide DescriptionThe opacity and radiative‐energy current due to line radiation is calculated for a U^{235}plasma with a temperature range 5000–8000 °K. Also, a variation in the neutron flux of 2×10^{12} to 2×10^{16} neutrons/cm^{2} sec is considered. The plasma forms a cylinder with a diameter and height of 1 m. Because the electron states in uranium lie below 5 eV, recombination is the principal excitation mechanism. At and above 6000 °K, inversions are found and, at all temperatures, the line radiation at line center is greater than the corresponding blackbody radiation. An example of this is the 28763–5762‐cm^{−1} transition in neutral uranium, where the Planck function at 5000 °K is 6.49×10^{−6} ergs/cm^{2}, and the calculated radiative‐energy current is 1.492×10^{−4} ergs/cm^{2}. Negligible changes in the radiative‐energy current are observed for changes in the neutron flux at a given temperature. The opacity at 5000 °K agrees with Parks’s previous calculations, and recombinational excitation explains the variation in the opacity with temperature.

Nonuniform mesh diode simulation code
View Description Hide DescriptionA new version of a diode simulation code has been written which allows for nonuniform zoning in both the r and z directions. This new flexibility enables more accurate treatment of crucial areas in the diode such as near emission surfaces and in target regions. The new code also has the ability to treat slanted surfaces such as that found in a tapered cathode diode. An interesting result of the new code is that a ’’parapotential’’ cathode pinches better than the corresponding flat cathode at the same total current.

Thomson scattering of EM pulses by random fluctuations in plasmas: Effect of self‐focusing
View Description Hide DescriptionIn the present paper the authors have investigated the transient Thomson scattering of the EM pulses (having Gaussian intensity distribution in space and time) from a collisional plasma with random inhomogeneities. Because of a Gaussian intensity distribution of the pulse in a plane transverse to the pulse propagation, the electrons get redistributed and affect the scattering accordingly. When the power of the pulse is greater than the critical power for self‐focusing, the backscattered power is found to exhibit a maximum at a particular time, dependent on the parameters of the pulse and the plasma.

Ionization and radiation dynamics of dense MHD plasmas
View Description Hide DescriptionThe ionization and radiationdynamics of dense magnetohydrodynamicplasmas has been modeled in a fashion suitable for implementation in MHDcomputer simulation codes. It has been shown that more restrictive LTE models such as those based on the Saha equation are inadequate to describe the rapidly varying temperature and density regimes characterizing many such plasmas. Detailed collisional‐radiative models are developed which directly solve the time‐dependent rate equations characterizing atomic processes along with those equations characterizing the hydrodynamic motion of the plasma. These models are applied to analyze high‐density‐helium Z‐pinch and lithium exploding‐wire plasmas, and they are found to yield results which compare quite favorably with experimental data.

High‐power discharge in Na‐Xe vapor
View Description Hide DescriptionHigh‐power (10–100 MW/liter) pulsed discharges in Na‐doped Xe vapor have been studied at Na densities of 10^{15}–10^{16} cm^{−3} and Xe densities of 10^{19}–10^{20} cm^{−3}, as appropriate for excimer‐laser use. Stable steady‐state discharges are obtained for a number of microseconds in a small‐volume cell, without use of preionization or sustainers. This stability is attributed to the observed positive V‐I characteristic. Measured spectra are interpreted to yield Na excited‐state densities, and the implications for a potential excimer laser are discussed.

Ranges of 10–30‐keV deuterons implanted into solids
View Description Hide DescriptionRanges of 10–30‐keV deuterons implanted into amorphous C, and polycrystalline Al, Ni, and Zr have been measured via the D(^{3}He,α)^{1}H nuclear reaction. The finite depth resolution, which has been determined separately, was taken into account in the evaluation of the data. Monte Carlo computer calculations have been carried out for comparison with the experimental results. Generally, good qualitative agreement is observed.

Elastic constants of niobium‐zirconium, hafnium, and tungsten alloys
View Description Hide DescriptionThe adiabatic single‐crystalline elastic constants of pure niobium, Nb‐Zr, Nb‐Hf, and Nb‐W alloys were determined in the temperature range 77–298 °K. An unusual temperature dependence was noted in the Nb‐rich alloys which may be related to the shape of the Fermi surface. Zr and Hf alloying additions decrease the value of C′, which indicates decreasing bcc lattice stability. The values of the elasticanisotropy ratio C _{44}/C′ follow the behavior predicted by Fisher, which indicates that the elastic shear moduli are closely related to the filling of the d band. The Debye temperatures ϑ_{ D } were calculated, and W additions tend to increase ϑ_{ D }, while Zr and Hf lower ϑ_{ D }.

High‐pressure single‐crystal structure determinations for ruby up to 90 kbar using an automatic diffractometer
View Description Hide DescriptionComplete high‐pressure single‐crystal structure determinations have been performed up to 90 kbar on ruby (Al_{2}O_{3} with less than 0.05 wt% Cr_{2}O_{3}) using an automatic diffractometer. The rhombohedral lattice constanta _{ R } is found to decrease linearly within the given error limits from a _{ R }=5.136±0.004 to a _{ R }=5.075±0.005 Å at 90 kbar. The rhombohedral angle α_{ R }=55.30°±0.06° as well as the atom‐position parameters u (Al, Cr) =0.3520±0.0004 for Al (or Cr) and u (0) =0.556±0.003 for oxygen remain constant up to at least 86 kbar. These results are in very good agreement with earlier measurements up to 25 kbar by Schiferl and Jamieson as well as with the Birch and Murnaghan equations of state with the literature values of the isothermal compresssibility K _{0} and its pressure derivative K′.

Physical behavior of the neck‐down region during furnace drawing of silica fibers
View Description Hide DescriptionDuring the drawing of optical fibers, the maintenance of a uniform fiber diameter is a difficult task. Parameters affecting the diameter variations are the temperature and viscosity distributions within the neck‐down region, the neck‐down shape, and the fiber drawing tension. A physical model is presented that predicts the neck shape and temperature distribution within the neck‐down region during the drawing of a high silica rod into a fiber. The model is formulated by an iterative technique to obtain solutions from the coupled equations of momentum and energy for given fiber‐drawing conditions. It is demonstrated that the predicted values of the viscosity, neck shape, and drawing tension agree well with those of measured values.