Three-wave interaction in a beam-plasma system
Coupling coefficient derived for three-wave interaction in beam plasma system
Hopman, H. J.↗
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Observation of a quadrupole interaction for cubic imperfections exhibiting a dynamic Jahn-Teller effect.
The observation and interpretation of weak EPR transitions, identified as 'forbidden' transitions, establish the existence of a new type of quadrupole interaction for cubic-symmetry imperfections. This interaction is simply a consequence of the ground-vibronic-state degeneracy. The signs as well as the magnitudes of the quadrupole-coupling coefficients are determined experimentally. These data agree well with the predictions of crystal field theory modified to account for a weak-to-moderate vibronic interaction (i.e., a dynamic Jahn-Teller effect).
Herrington, J. R.↗
Polyatomic molecule vibrations
Polyatomic molecule vibrations are analyzed as harmonic vibrations along normal coordinates. The energy eigenvalues are found for linear and nonlinear symmetric triatomic molecules for valence bond models of the potential function with arbitrary coupling coefficients; such models can usually be fitted to observed energy levels with reasonably good accuracy. Approximate normal coordinates for the H2O molecule are discussed. Degenerate vibrational modes such as occur in CO2 are analyzed and expressions for Fermi resonance between close-lying states of the same symmetry are developed. The bending modes of linear triatomic molecules are expressed in terms of Laguerre polynomials in cylindrical coordinates as well as in terms of Hermite polynomials in Cartesian coordinates. The effects of large-amplitude bending such as occur in the C3 molecule are analyzed, along with anharmonic effects, which split the usually degenerate bending mode energy levels. Finally, the vibrational frequencies, degeneracies, and symmetry properties of XY3, X2Y2, and XY4 type molecules are discussed.
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Bragg interactions in periodic media
The interaction of electromagnetic waves of wavelength lambda with periodic structures of spatial period lambda are studied. The emphasis of the work is on Bragg interactions where lambda approximately equal to 2 lambda/N and the Bragg order N takes on the values 1, 2,.... An extended coupled waves (ECW) theory is developed for the case N greater or equal to 2 and the results of the theory are found to compare favorably with the exact results of Floquet theory. Numerous numerical results are displayed as Brillouin diagrams for the first few Bragg orders. Moreover, explicit expressions for coupling coefficients, bandgap shifts and bandgap widths are derived for singly periodic media. Particular note is taken of phase speeding effects.
Jaggard, D. L.↗
Floquet and coupled-waves analysis of higher-order Bragg coupling in a periodic medium
The paper considers wave propagation in longitudinally periodic media near the first- and higher-order Bragg resonances. An extended coupled-waves (ECW) approach is applied to media with single or multiharmonic periodicities and is numerically compared with the Floquet theory. The ECW approach predicts coupling coefficients that vary as the magnitude of the perturbation raised to the power of the Bragg order. Explicit expressions are also given for the band-gap width and band-gap shift for all Bragg orders. A number of applications are discussed.
Jaggard, D. L.↗
Magnetostrictive ultrasonic probes
The principles underlying the design and use of magnetostrictive ultrasonic probes is illustrated by oscillograms and sketches. Attention is given to such concepts as magnetostrictive transduction, broadband pulse shaping, guided wave propagation, wave impedance, reflection, transmission, and attenuation coefficients, coupling methods, and impulse-induced resonance. A number of applications of such probes are discussed including the measurement of elastic moduli, temperature, and acoustic emission and resonance studies.
Lynnworth, L. C.↗
Nonlinear Landau damping in the ionosphere
A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.
Kiwamoto, Y.↗
Symmetry and selection rules for wave-wave interactions
Selection rules for nonlinear three-wave interactions are derived on the basis of the symmetry of the background medium and the waves themselves. The process described bypasses the formal derivation of the coupling coefficient itself. The primary concern is with the effect of the polarization of the waves on the selection rules. Although consideration is limited to three-wave interactions, the method is easily generalized to more waves. Results are derived for these examples: three waves with parallel propagation vectors in an unmagnetized medium, and three waves propagating parallel, and then perpendicular, to a static magnetic field.
Harker, K. J.↗
Nonlinear Landau damping in the ionosphere
A model which explains the nonresonant waves which produce the diffuse resonance observed near 3/2 f(H) by the Alouette and Isis topside sounders, where f(H) is the ambient electron cyclotron frequency, is presented. These waves are the result of plasma wave instabilities driven by anisotropic electron velocity distributions initiated by the high-power short-duration sounder pulse. Calculations of the nonlinear wave-particle coupling coefficients show that the diffuse resonance wave can be maintained by nonlinear Landau damping of the sounder-stimulated 2f(H) wave which is observed with a time duration longer than that of the diffuse resonance wave. The time duration of the diffuse resonance is determined by the transit time of the instability-generated and nonlinearly maintained diffuse resonance wave from the remote short-lived hot region back to the antenna. The model is consistent with the Alouette/Isis observations and it demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.
Kiwamoto, Y.↗
Coupled wave model for large magnet coils
A wave coupled model based on field theory is evolved for analysis of fast electromagnetic transients on superconducting coils. It is expected to play a useful role in the design of protection methods against damage due to high voltages or any adverse effects that might arise from unintentional transients. The significant parameters of the coil are identified to be the turn to turn wave coupling coefficients and the travel time of an electromagnetic disturbance around a single turn. Unlike circuit theoretic inductor, the coil response evolves in discrete steps having durations equal to this travel time. It is during such intervals that high voltages are likely to occur. The model also bridges the gap between the low and high ends of the frequency spectrum.
Gabriel, G. J.↗
HF-induced parametric decay in presence of field-aligned irregularities
A nonlinear theory for the saturation of the HF-induced parametric decay instability is formulated in terms of the normal modes of a field-aligned plasma wave duct. Coupling coefficients between modes are derived, and a saturation spectrum is computed numerically for a typical irregularity. The computed spectrum shows that unstable waves may propagate at larger angles to the magnetic field than would be the case in a regular medium. The relevance of this work to the experiment of Muldrew and Showen (1977), concerning the height of the HF-induced plasma line at Arecibo, is discussed. A possible explanation is also found for the 'decay line' feature in comparison with the 'broad bump' in the observed backscatter spectrum.
Rypdal, K.↗
On the complex state of the interplanetary medium of 28-29 July 1977
Observations of plasma and magnetic field variations in the near-Earth solar wind are discussed. Both a corotating stream and a driven shock are present. The driver gas seems to be enveloped in the rising speed phase of this stream; this appearance is attributed to a convoluted surface separating the two plasma domains. The magnetic field in the post shock flow (0030-1230 UT of July 29) has a large and geoeffective southward component at times; the energy coupling coefficient reaches approximately 5.4 x 10 to the 19th power ergs/s. In the driver gas (1230 UT of July 29 to 0110 of July 30) the magnetic field is dominantly northward. The density and dynamic pressure decrease by almost two orders of magnitude (100 to 2 cm/3) from just behind the interplanetary shock to approximately 3 hours into the driver gas flow. The dominant magnetic field variation in the driver gas is modeled by a cloud-like structure. Significant plasma parameter variations within the driver gas are attributed to structure in the parent solar mass ejection event and to interplanetary kinematics.
King, J. H.↗
Macroscopic Lagrangian description of warm plasmas. II Nonlinear wave interactions
A macroscopic Lagrangian is simplified to the adiabatic limit and expanded about equilibrium, to third order in perturbation, for three illustrative cases: one-dimensional compression parallel to the static magnetic field, two-dimensional compression perpendicular to the static magnetic field, and three-dimensional compression. As examples of the averaged-Lagrangian method applied to nonlinear wave interactions, coupling coefficients are derived for interactions between two electron plasma waves and an ion acoustic wave, and between an ordinary wave, an electron plasma wave, and an ion acoustic wave.
Kim, H.↗
Theory of high-harmonic rectangular gyrotron for TE(mn) modes
In this paper, the linearized relativistic Vlasov equation is solved and a dispersion relation is calculated for the interaction between a relativistic electron beam and the electromagnetic fields of a rectangular waveguide supporting TE(mn) modes. The dispersion relation is simplified to the special case of a frame of reference moving with the electrons and the resulting coupling coefficient epsilon(mn)super l is calculated for various TE(mn) modes. The dependence of epsilon(mn)super l on the parity of the harmonic number l and various mn modes of the waveguide are discussed.
Ferendeci, A. M.↗
Optical digital logic operations by two-beam coupling in photorefractive material
The nonlinear phenomena of signal beam saturation, pump beam depletion, and optically controlled coupling coefficient of two-beam interaction in photorefractive materials are analyzed. Applications of these phenomena to digital logic operations is discussed and supported by experimental results obtained in photorefractive BaTiO3.
Fainman, Y.↗
The generation of capillary instabilities on a liquid jet
The coupling between imposed disturbances and capillary instabilities on a liquid jet is examined. It is shown that in most physical situations the forcing produces neutral waves, which can then turn into growing waves as the profile relaxes or may be amplified nonlinearly by a mechanism of the type considered by Akylas and Benney (1980). The effectiveness of the coupling is expressed quantitatively by numerically computed values of the 'coupling coefficient'.
Leib, S. J.↗
Investigation of beamed-energy ERH thruster performance
The objective of this study was to determine the performance of an External Radiation Heated (ERH) thruster. In this thruster, high intensity laser energy is focused to ignite either a Laser Supported Combustion (LSC) wave or a Laser Supported Detonation (LSD) wave. Thrust is generated as the LSC or LSD wave propagates over the thruster's surface, or in the proposed thruster configuration, the vehicle afterbody. Thrust models for the LSC and LSD waves were developed and simulated on a computer. Performance parameters investigated include the effect of laser intensity, flight Mach number, and altitude on mean-thrust and coupling coefficient of the ERH thruster. Results from these models suggest that the ERH thruster using LSC/LSD wave ignition could provide propulsion performance considerably greater than any propulsion system currently available.
Myrabo, Leik N.↗
Theory of beat-resonant coupling of electrostatic modes
A general expression is derived for the beat-resonant coupling electrostatic modes in a Vlasov plasma. The result for the coupling of two modes has a simple structure: the appropriate momentum gradient of the equilibrium particle distribution is weighted by a positive coupling coefficient and averaged over the resonance surface in momentum space. The contributions of all the resonance surfaces are then summed. This basic structure had been previously exhibited only for specific homogeneous plasma models. The present theory, which unifies and greatly simplifies these individual treatments, is based on a variational formulation of the Vlasov-Poisson equations. Using Lie transforms, the variational principle is reexpressed in oscillation-center variables, and then the nonlinear wave dynamics are obtained from the independent variations of the wave phase and the wave amplitude. The power of the method is then applied to a strongly magnetized, strongly inhomogeneous, non-neutral plasma model.
Crawford, John David↗