High Harmonic Wave Research Articles

Decomposition of incident and reflected higher harmonic waves using four wave gauges

This study proposes a new technique to separate incident and reflected higher harmonic waves using four or more spatially separated probes. Both the free and locked modes in the higher harmonics of the regular waves can be isolated. The complex waves are decomposed into individual frequency components using the Fourier transform. The least squares method is applied to minimize the error caused by possible signal noise and to obtain the equations for solving the unknown parameters related to the wave amplitudes. Probe spacing condition for preventing singularity in the calculation is provided. The accuracy of this method is verified by applying it to resolve artificial waves with arbitrarily selected amplitudes. The sensitivity of this method to the noise inevitably associated with the experiments is also tested. The free surface elevation data collected from probes located upstream and downstream of a submerged breakwater in a numerical wave tank are analyzed to demonstrate the applicability of this method. The results are compared with those obtained using the methods of Goda and Suzuki [Goda, Y., Suzuki, Y., 1976. Estimation of incident and reflected waves in random wave experiments. Proc. 15th Costal Eng. Conf., ASCE, pp. 828–845] and Mansard and Funke [Mansard, E.P.D., Funke, E.R., 1980. The measurement of incident and reflected spectra using a least squares method. Proc. 17th Costal Eng. Conf., ASCE, pp. 154–172]. The comparison indicated that this method gives exactly the same first harmonic incident and reflected wave amplitudes as the other two methods. The full modes in the higher harmonics can be determined using this method, while the higher harmonics are presumed to be free waves in the other two methods.

Higher-harmonic wave forces and ringing of vertical cylinders

A pronounced secondary load cycle may occur in the force on a vertical circular cylinder exposed to moderately steep transient water wave events. The timing is about one quarter wave period later than the main peak of the force. The load cycle contributes locally to a pronounced higher harmonic wave force. Experimental observations of the phenomenon in small and moderate scale are characterized in terms of the local wave slope of the incoming individual waves, kη m ( k the wavenumber, η m the local maximal wave elevation), and the wavenumber relative to the cylinder radius, kR ( R the cylinder radius). The height of the secondary load cycle is typically up to about 0.1–0.15 times the peak to peak force on the cylinder during a wave event. In the small scale experiments the secondary load cycle occurs when 0.3< kη m and kR<0.33 (registrations are made for 0.1< kR). In the experiments of moderate scale the secondary load cycle occurs for a smaller wave slope than observed in the small scale experiments. This is true in the long wave regime. The secondary load cycle is then observed for a nondimensional wavenumber kR in the range 0.1–0.33 and a Froude number (Fr=ωη m / gD ; ω, the wave frequency; g, the acceleration of gravity; D=2 R) exceeding about 0.4. The important difference between the experiments in moderate and small scale is explained by the effect of flow separation. This effect is weaker in moderate than in small scale. Registrations of pronounced resonant high-frequency ‘ringing’ motions of vertical cylinders and models of offshore structures of moderate scale are compared with the force recordings. Large motion occurs for the same wave parameters as for the pronounced secondary load cycle in the moderate scale experiments. The additional load cycle contributes to a build-up of resonant body responses if the resonance frequency is close to about four times the wave frequency.

High-density plasma production with potential confinement in the GAMMA 10 tandem mirror

The improvement of potential confinement was attained in the GAMMA 10 tandem mirror [Phys. Rev. Lett. 55, 939 (1985); Proceedings of the 13th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Washington, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 2, p. 539] by axisymmetrization of heating systems for the plasma production, heating, and potential formation. A significant increase of the density and diamagnetism by the potential confinement was observed. In the previous experiment, it was difficult to increase the central cell density higher than 2.7×1018 m−3. One of the possible mechanisms is the density clamping due to the eigenmode formation of the ion–cyclotron-range of frequency (ICRF) waves in the axial direction. With high harmonic ICRF waves (RF3), the experiments to overcome this problem have been performed. In preliminary experiments with RF3 and NBI the maximum density of 4×1018 m−3 was attained.

An experimental investigation of higher-harmonic wave forces on a vertical cylinder

First- and higher-harmonic wave loads on a vertical circular cylinder are investigated experimentally in a wave tank of small scale. The incoming waves are (periodic) Stokes waves with wave slope up to 0.24. A large set of waves which are long compared to the cylinder radius is calibrated. The first seven harmonic components of the measured horizontal force on the cylinder are analysed. The higher-harmonic forces are significantly smaller than the first-harmonic force for all wave parameters. The measurements are continued until the wave amplitude is comparable to the cylinder radius, where the second-, third- and fourth-harmonic forces become of comparable size. Comparison with existing perturbation and fully nonlinear models shows, with a few exceptions, an overall good agreement for small and moderate wave amplitude. A fully nonlinear model agrees with the experiments even up to the seventh-harmonic force for part of the amplitude range. For the large amplitudes the models mostly give conservative predictions. It is important that the distance from the wave maker to the cylinder is large in order to avoid parasitic effects in the incoming wave field. The limited width of the wave tank is not important to the results except when close to resonance.

Calculation of the Parameters for Ring-loop Traveling Wave Tube in MMW

The feature of the ring-loop slow wave structure is high coupling impedance and low harmonic wave components. Therefore ring-loop traveling wave tube (TWT) has advantages of high gain, small dimension, higher operating voltage and less danger of the backward wave oscillation. But calculation of the ring-loop is rather difficult. Here on basis of calculation of dispersion and impedance, a fast estimation of interaction efficiency, output power and saturated gain for Ka-band ring-loop TWT are given.

Nonlinear radiated and diffracted waves due to the motions of a submerged circular cylinder

We study the high-harmonic surface wave associated with nonlinear diffraction and radiation of gravity waves by a near-surface circular cylinder. Based on nonlinear potential-flow theory, we show analytically, using a boundary-integral equation method, that: (a) for a circular motion of the cylinder, the leading-order outgoing radiated waves at any harmonic are generated only in one direction; (b) for a cylinder free to respond to regular incident waves, the total leading-order scattered waves at any harmonic are two orders smaller upstream of the body. These theoretical results are substantially confirmed by direct time-domain simulations of the problem.

EXPERIMENTAL INVESTIGATION OF THE DYNAMIC CHARACTERISTICS OF THE DAMPED BLADE

The test facility and measurement system for the investigation of the dynamic characteristics of a damped blade are described. The test results are analyzed, and some important conclusions are drawn. It is found that dry friction between the dampers (or between damper and blade) is a very effective means of reducing the vibration of a blade.The resonance frequency, the response amplitude and the relative damping ratio can all be influenced by dry friction. High harmonic waves on the response of the blade which are caused by dry friction are observed in the test. However, the wave response of the damped blade is still basically harmonic. The normal force acting on the rub surfaces of the damped blade will influence the dynamic characteristics of the blade. Since the damped blade system is non-linear due to dry friction, the external exciting force can also influence the dynamic characteristics of the blade.

A new kind of nonlinear mild-slope equation for combined refraction-diffraction of multifrequency waves

This paper presents the numerical solution of a new nonlinear mild-slope equation governing waves with different frequency components propagating in a region of varying water depth. There are two new nonlinear equations. The linear part of the equations is the mild-slope equation, and one of the models has the same non-linearity as the Boussinesq equations. The new equations are directly applicable to the problems of nonlinear wave-wave interactions over variable depth. The equations are first simplified with the parabolic approximation, and then solved numerically with a finite difference method. The Crank-Nicolson method is used to discretize the models. The numerical models are applied to a set of published experimental cases, which are nonlinear combined refraction-diffraction with generation of higher harmonic waves. Comparison of the results shows that the present models generally predict the measurements better than other nonlinear numerical models which have been applied to the data set.

マイクロ波受電用レクテナの高調波再放射の評価に関する実験的研究

マイクロ波受電用レクテナの高調波再放射の評価に関する実験的研究

Expansion of span-width of an optical frequency comb using a higher harmonic wave modulation

We propose a novel method for expanding the spanwidth of an optical frequency comb that utilizes modulation by a superposition of higher harmonic waves. Based on the calculations, it was found that in the terms up to third-order harmonic wave, the optimum superposition is the one whose power ratio between the fundamental and the third-order harmonic waves is 1:1. The validity of this method was experimentally confirmed at 1.5-/spl mu/m wavelength region. By this optimum modulation with a wave power of 1.0 W, the span-width of OFC was increased to 72 mn (=9.1 THz).

Gyrobroadening of fast ion energy spectrum due to relativistic mass variation

A gyrobroadening process causing the perpendicular energy of fast ions to be broadened by cyclotron instabilities due to the relativistic mass variation of the fast ions in a magnetized plasma is reported. At low cyclotron harmonics, a two-gyro-stream instability can be excited with the involvement of thermal ions if the condition lfwcf < w < lswcs is satisfied. The fast ions can be anomalously thermalized. Their lost energy goes to bulk ion heating. While the fusion produced protons can satisfy the condition, the alphas cannot. The low harmonics are linearly stable for the alphas. Therefore, for low harmonics one has to inject waves to affect the alpha dynamics. However, the alphas can excite high harmonic cyclotron waves in the lower hybrid regime, in which thermal ions respond as cold plasma. The interaction becomes selective. Only alphas with high pitch angle are involved. The implications of this process for fusion ignition and fast ion confinement are assessed

Electromagnetic radiation by parametric decay of upper hybrid waves in ionospheric modification experiments

A nonlinear dispersion relation for the parametric decay of an electrostatic upper hybrid wave into an ordinary mode electromagnetic wave, propagating parallel to the ambient magnetic field, and an electrostatic low frequency wave, being either a lower hybrid wave or a high harmonic ion Bernstein wave, is derived. The coherent and resonant wave interaction is considered to take place in a weakly magnetized and collisionless Vlasov plasma. The instability growth rate is computed for parameter values typical of ionospheric modification experiments, in which a powerful high frequency electromagnetic pump wave is injected into the ionospheric F-region from ground-based transmitters. The electromagnetic radiation which is excited by the decaying upper hybrid wave is found to be consistent with the prominent and commonly observed downshifted maximum (DM) emission in the spectrum of stimulated electromagnetic emission.

Propagation of Impact-Induced Longitudinal Waves in Mechanical Systems With Variable Kinematic Structure

In previous publications by the authors of this paper it was shown that elastic media become dispersive as the result of the coupling between the finite rotation and the elastic deformation. Impact-induced harmonic waves no longer travel, in a rotating rod, with the same phase velocity and consequently the group velocity becomes dependent on the wave number. In this investigation, the propagation of impact-induced longitudinal waves in mechanical systems with variable kinematic structure is examined. The configuration of the mechanical system is identified using two different sets of modes. The first set describes the system configuration before the change in the system topology, while the second set describes the configuration of the system after the topology changes. In the analysis presented in this investigation, it is assumed that collision between the system components occurs first, followed by a change in the system topology. Both events are assumed to occur in a very short-lived interval of time such that the system configuration does not appreciably change. By using the first set of modes, the jump discontinuity in the system velocities is predicted using the algebraic generalized impulse momentum equations. The propagation of the impact-induced wave motion after the change in the system topology is described using the Fourier method. The series solution obtained is used to examine the effect of the topology change on the propagation of longitudinal elastic waves in constrained mechanical systems. It is shown that, while, for a nonrotating rod, mass capture or mass release has no effect on the phase and group velocities, in rotating rods the phase and group velocities depend on the change in the system topology. In particular the phase velocities of low harmonic longitudinal waves are more affected by the change in the system topology as compared to high frequency harmonic waves.

Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities

The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation-theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave–wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the perturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave–wave resonance condition which, in turn, causes the wave amplitude to cease its growth.

Anomalous RF induced steps in resonant Josephson tunnel junctions for voltage standard maintenance

The authors theoretically investigated the current steps in the I-V (current-voltage) characteristics of a long Josephson tunnel junction driven by microwaves at frequencies near its geometrical resonance. They used a numerical algorithm based on a lossy transmission line model of the Josephson tunnel junction to calculate the DC current density distribution. In addition to the fundamental microwave frequency, harmonic contents of the tunneling current are also considered. The calculations show a strong asymmetric behavior of the current steps with respect to the quasi-particle curve. It is suggested that the excitation of higher harmonic waves gives rise to these anomalous microwave-induced steps. Due to the nonuniform DC-tunneling-current density distribution, the amplitudes of these current steps are not usually larger than 10% of the critical current. Since the critical current in long junctions is of the order of milliamperes, these amplitudes are considered relatively large. >

Changes in the cerebrospinal fluid pulse wave spectrum associated with raised intracranial pressure.

The frequency spectrum of the cerebrospinal fluid (CSF) pulse and the amplitude transfer function between arterial and CSF pressures were measured from the cisterna magna of anesthetized, artificially ventilated cats when the intracranial pressure (ICP) was raised by saline infusion. The spectrum of CSF pulsation was composed of a fundamental and three higher harmonic waves. The amplitude and the amplitude transfer function of each spectral component revealed significant positive correlation with ICP and negative correlation with cerebral perfusion pressure (CPP). Both the amplitude and the transfer function of the fundamental CSF pulse wave showed an exponential correlation with ICP and CPP. A distortion factor of the CSF pulse wave, a measure of its difference from a simple sine wave, was calculated from the spectral components. This showed that distortion of the CSF pulse wave was rapidly and progressively reduced as the ICP rose to 50 mm Hg and then was reduced less thereafter.

Reproduction of higher harmonics in irregular waves

The basic features of higher harmonic waves were originally presented by Stokes in 1847 who showed that a 2nd-order regular wave would attain a higher, sharper crest and a flatter trough than the basic linear one. In this paper, these characteristics are investigated for an irregular wave train. This was done to make it possible to reproduce in a laboratory flume a wave train which has the correct profile and rms according to 2nd-order theory. The 2nd-order wave heights and the overall horizontal asymmetries of the wave train were calculated for a 1st-order PM and a Jonswap spectrum. The theoretical predictions show that the traditional wave generation in a laboratory flume which is based on linear theory produces free 2nd-order waves in addition to the bound 2nd-order waves described by Stokes. These free, parasitic waves incorrectly distort the shape of the waves and produce a varying rms as a function of distance from the wave paddle. In the 2nd-order theory presented in this paper, these free (parasitic) waves are calculated for the entire spectrum. Knowing these, they can be eliminated by compensating for them by using a 2nd-order control signal on the wave paddle. This is verified by a series of model tests which show that realistic wave profiles can be generated only by means of 2nd-order control signals. The theory and corresponding paddle control are presented for any type of translating, rotating or combined wave generator.

Refraction-diffraction model for weakly nonlinear water waves

A model equation is derived for calculating transformation and propagation of Stokes waves. With the assumption that the water depth is slowly varying, the model equation, which is a nonlinear Schrödinger equation with variable coefficients, describes the forward-scattering wavefield. The model equation is used to investigate the wave convergence over a semicircular shoal. Numerical results are compared with experimental data (Whalin 1971). Nonlinear effects, which generate higher-harmonic wave components, are definitely important in the focusing zone. Mean free-surface set-downs over the shoal are also computed.

Higher harmonics of electron plasma waves

A model based on nonlinear mixing of dispersive waves is used to predict higher harmonic waves generated by weakly nonlinear electron plasma waves. The total harmonic wave is given by superposition of modes which lie at different points (with the same frequency) in the dispersion diagram. The model well explains the experimental results concerning the harmonic waves produced by externally excited electron plasma waves propagating along a collisionless plasma column.

Elimination of Wavefront Aberration of Optical Elements Used in Phase Difference Amplification

Two holograms are used. A first hologram is recorded by the light that passes through the phase object with an ordinary off-axis holographic system. A second hologram is recorded by the light that passes through the deformed object and is diffracted by the first hologram and processed nonlinearly. Phase difference amplification is performed by the superposition of two higher harmonic waves from the second hologram. In a resultant interferogram of eight-fold phase difference amplification, phase change, due to only the deformation of the object, is amplified; and wavefront aberration, caused by poor quality of an optical system and by inhomogeneity of the object, is completely eliminated.