Efficiency enhancement of high power vacuum BWO's using nonuniformslow wave structures

The Sinus-6, a high-power relativistic repetitively-pulsed electron beam accelerator, is used to drive various slow wave structures in a BWO configuration in vacuum. Peak output power of about 550 MW at 9.45 GHz was radiated in an 8-ns pulse. We describe experiments which study the relative efficiencies of microwave generation from a two-stage nonuniform amplitude slow wave structure and its variations without an initial stage. Experimental results are compared with 2.5 D particle-in-cell computer simulations. Our results suggest that prebunching the electron beam in the initial section of the nonuniform BWO results in increased microwave generation efficiency, Furthermore, simulations reveal that, in addition to the backward propagating surface harmonic of the TM₀₁ mode, backward and forward propagating volume harmonics with phase velocity twice that of the surface harmonic play an important role in high-power microwave generation and radiation     

The surface variational principle applied to an acoustic cavity.

This paper presents the development and application of the Surface Variational Principle (SVP) for the evaluation of axisymmetric interior acoustic domains. The interior form of the SVP is first developed in the same manner as the existing exterior form. Then, the surface pressure and normal velocity are represented with a Ritz expansion using basis functions that span the entire wetted surface of the object of interest. The resultant formulation is used to analyze the interior acoustic response of a harmonically forced, right circular elastic cylinder. This validation model was chosen as both the structural and acoustic responses can be solved analytically. Results are presented for two models: one with a length to radius ratio of 2.4, and another with a ratio of 12.3. The SVP is shown to well reproduce the analytical solution for this geometry, and displays the asymptotic convergence expected of its variational formulation. The SVP formulation developed here is not restricted to right-circular cylindrical geometries, and may, indeed, be readily applied to any axisymmetric body.     

Evaluation of mutual radiation impedances between circular pistons by impulse response and asymptotic methods

A general approach is presented to evaluate the mutual radiation impedance between circular pistons of arbitrary size and spacing in an infinite rigid planar baffle. The impedance is expressed as a Fourier transform of a generalized impulse response which is defined by an integral relationship. Although the integral must, in general, be numerically evaluated, several special cases of interest can readily be evaluated by using asymptotic techniques. Several asymptotic expressions for the mutual radiation impedance are developed and their limitations are noted. Numerical results are then presented for the generalized impulse response and mutual radiation impedance corresponding to pistons of equal size and arbitrary spacing. The time domain characteristics of the generalized impulse responses as a function of spacing are noted and related to the frequency characteristics of the mutual radiation impedances as a function of spacing. In addition, the accuracy of a simple closed form expression for the mutual radiation impedance is presented as a function of normalized frequency and spacing.     

Axisymmetric laser welding of ceramics: comparison of experimental and finite element results

In this paper, we compare experimental data for a laser spot weld on a ceramic to the solution from an adaptive finite element model of the system. Our focus is on validating the finite element model, which necessarily includes numerous simplifications. We assume an axisymmetric geometry and flow profile, with a flat free surface. Buoyancy and surface tension drive the liquid motion in the molten ceramic pool beneath the laser, which is calculated using the axisymmetric forms of the continuity, momentum and energy equations. Latent heat, temperature-dependent material properties and radiation effects are all included in the formulation. These equations are solved with standard finite element techniques utilizing mesh relocation with a movement indicator based on solution gradients. Comparision with experimental data indicates that the numerical techniques used successfully predicted the depth and diameter of the actual ceramic weld pool.     

The influence of backward wave transmission on quantitative ultrasonic evaluation using Lamb wave propagation

In view of the various novel quantitative ultrasonic evaluation techniques developed using Lamb wave propagation, the influence of an important related phenomenon, backward transmission, is investigated in this paper. Using the discrete layer theory and a multiple integral transform method, the surface displacement and velocity responses of isotropic plates and cross-ply laminated composite plates due to the Lamb waves excited by parabolic- and piston-type transmitting transducers are evaluated. Analytical expressions for the surface displacement and velocity frequency response functions are developed. Based on this a large volume of calculations is carried out. Through examining the characteristics of the surface displacement and velocity frequency response functions and, especially, the different propagation modes' contributions to them, the influence of the backward wave transmission related to quantitative ultrasonic nondestructive evaluation applications is discussed and some important conclusions are drawn.     

Real-time near-field acoustic holography for continuously visualizing nonstationary acoustic fields

Near-field acoustic holography (NAH) is an effective tool for visualizing acoustic sources from pressure measurements made in the near-field of sources using a microphone array. The method involving the Fourier transform and some processing in the frequency-wavenumber domain is suitable for the study of stationary acoustic sources, providing an image of the spatial acoustic field for one frequency. When the behavior of acoustic sources fluctuates in time, NAH may not be used. Unlike time domain holography or transient method, the method proposed in the paper needs no transformation in the frequency domain or any assumption about local stationary properties. It is based on a time formulation of forward sound prediction or backward sound radiation in the time-wavenumber domain. The propagation is described by an analytic impulse response used to define a digital filter. The implementation of one filter in forward propagation and its inverse to recover the acoustic field on the source plane implies by simulations that real-time NAH is viable. Since a numerical filter is used rather than a Fourier transform of the time-signal, the emission on a point of the source may be rebuilt continuously and used for other post-processing applications.     

On the forced response of waveguides using the wave and finite element method

The forced response of waveguides subjected to time harmonic loading is treated. The approach starts with the wave and finite element (WFE) method where a segment of the waveguide is modeled using traditional finite element methods. The mass and stiffness matrices of the segment are used to formulate an eigenvalue problem whose solution yields the wave properties of the waveguide. The WFE formulation is used to obtain the response of the waveguide to a convected harmonic pressure (CHP). Since the Fourier transform of the response to a general excitation is a linear combination of the responses to CHPs, the response to a general excitation can be obtained via an inverse Fourier transform process. This is evaluated analytically using contour integration and the residue theorem. Hence, the approach presented herein enables the response of a waveguide to general loading to be found by: (a) modeling a segment of the waveguide using finite element methods and post-processing it to obtain the wave characteristics, (b) using Fourier transform and contour integration to obtain the wave amplitudes and (c) using the wave amplitudes to find the response at any point in the waveguide. Numerical examples are presented.     

An annular superposition integral for axisymmetric radiators

A fast integral expression for computing the nearfield pressure is derived for axisymmetric radiators. This method replaces the sum of contributions from concentric annuli with an exact double integral that converges much faster than methods that evaluate the Rayleigh-Sommerfeld integral or the generalized King integral. Expressions are derived for plane circular pistons using both continuous wave and pulsed excitations. Several commonly used apodization schemes for the surface velocity distribution are considered, including polynomial functions and a "smooth piston" function. The effect of different apodization functions on the spectral content of the wave field is explored. Quantitative error and time comparisons between the new method, the Rayleigh-Sommerfeld integral, and the generalized King integral are discussed. At all error levels considered, the annular superposition method achieves a speed-up of at least a factor of 4 relative to the point-source method and a factor of 3 relative to the generalized King integral without increasing the computational complexity.     

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.     

Transient response of an acoustic medium by an excited submerged spherical shell.

An exact closed-form solution is obtained for the transient response of an acoustic fluid due to an excited submerged spherical shell. Step axisymmetric stress acting on the inner surface of the shell is expanded into modal Fourier components in which for each modal stress systematic exact expressions for modal radial displacement of the shell, fluid pressure, fluid particle velocity and displacement are presented. The superiority of the formulations herein is its applicability to any time and spatial distance in the fluid as well as on the shell. The formulation also does not require additional numerical computations associated with other methods.     

On the sound field of a resilient disk in free space

Radiation characteristics are calculated for a circular planar sound source in free space with a uniform surface pressure distribution, which can be regarded as a freely suspended membrane with zero mass and stiffness. This idealized dipole source is shown to have closed form solutions for its far-field pressure response and radiation admittance. The latter is found to have a simple mathematical relationship with the radiation impedance of a rigid piston in an infinite baffle. Also, a single expansion is derived for the near-field pressure field, which degenerates to a closed form solution on the axis of symmetry. From the normal gradient of the surface pressure, the surface velocity is calculated. The near-field expression is then generalized to an arbitrary surface pressure distribution. It is shown how this can be used as a simplified solution for a rigid disk in free space or a more realistic sound source such as pre-tensioned membrane in free space with non-zero mass and a clamped rim.     

Hydrodynamic impulse in a compressible fluid

A suitable expression for hydrodynamic impulse in a compressible fluid is deduced. The development of appropriate impulse formulation for compressible Euler equations confirms the propriety of the hydrodynamic impulse expression for a compressible fluid given here. Implications of the application of this formulation to a compressible vortex ring are pointed out. Extension of Benjamin's variational characterization of a moving axisymmetric vortex system to a compressible fluid is explored.     

Contouring of artwork surface by fringe projection and FFT analysis

In the present work, we propose a simple optical method to perform profilometry on works of art. The method is based on the projection of a Ronchi grating onto the surface to be analyzed. When viewed at an angle different from the projection angle, the grid pattern appears deformed by the surface shape. This pattern is digitized, by a high-resolution CCD camera, and then processed using a Fourier transform analysis. The technique is free from the errors caused by higher harmonic components of the grating pattern. Furthermore, the method relies on very simple equipment and it is therefore suitable for in situ measurements. Theoretical details and examples of the technique in operation are given.     

Fiber grating synthesis by use of time-frequency representations

We propose a method to reconstruct the grating period in fiber grating structures from the field reflection coefficient or the related impulse response. The method is based on the joint time-frequency signal analysis and uses the Wigner-Ville and the spectrogram distributions. Results show good agreement between exact and reconstructed functions.     

The measurement of the free field impulse response of microphones in a laboratory environment

A method is presented of measuring the free field frequency and impulse response of microphones by using a pulse technique in an ordinary laboratory environment. The pressure transient generated by exciting a loudspeaker with a narrow pulse is detected at some point in the loudspeaker's far field by a “reference” microphone whose response is assumed flat over the frequency range of interest. The microphone to be tested is then substituted in exactly the same position and its response to the transient measured. The outputs of the two microphones are accurately sampled and deconvolved by using a discrete Fourier transform technique to give the magnitude and phase parts of the “test” microphone's frequency response, and hence, via the discrete Fourier transform, its response to a delta function of pressure propagating in the free field. The computed impulse responses are presented and the accuracy of the method discussed.To illustrate the use of the method, the free field frequency response and free field correction curves of a one inch instrumentation microphone are measured. The method is then used to measure the pressure which occurs at the centre of the flat end-face of a long a cylinder when excited by an impulse of acoustic pressure propagating in the free field from various angles of incidence.     

Measurement of the frequency response of a diaphragm-based pressure sensor by use of a pulsed excimer laser

We present a novel method for measuring the frequency response of a diaphragm-based optical fiber Fabry-Perot interferometric pressure sensor. The impulse response of the sensor to the radiation pressure generated by an excimer laser pulse is measured. The Fourier transform of the impulse response yields the frequency response of the pressure sensor. Experimental results show that it is a convenient and efficient method for measurement of the frequency response of diaphragm-based pressure sensors.     

Theory of dispersion in lossless multimode optical fibres

Using the ray propagation model generalized expressions for the impulse response of multimode fibres have been derived. The analysis has been applied to lossless fibres for pulses having both gaussian and lambertian spatial distributions as well as impulse and gaussian temporal distributions. Detailed results are given for output pulse shapes and fibre dispersions for various configurations.     

Time delay spectrometry for hydrophone calibrations below 1 MHz

Knowing the response of miniature ultrasonic hydrophones at frequencies below 1 MHz is important for assessing the accuracy of acoustic pressure pulse measurements in medical ultrasound applications. Therefore, a time delay spectrometry (TDS) system was developed as an efficient means to measure hydrophone sensitivity in this frequency range. In TDS a swept-frequency signal is transmitted. A tracking receiver distinguishes arrivals with different propagation delays by their frequency offset relative to the signal being transmitted, thus eliminating spurious signals such as those reflected from the water surface or tank walls. Two piezoelectric ceramic source transducers were used: a standard planar disk and a disk with varying thickness to broaden the thickness-resonance. This latter design was preferred for its more uniform response without significant sensitivity loss. TDS is not an absolute method, but it was demonstrated to provide efficient, accurate calibrations via comparison with a reference hydrophone using a substitution technique.     

Parametric frequency conversion in layered nonlinear media

Frequency-angular distributions of signal wave intensity are calculated for spontaneous parametric down-conversion and parametric frequency conversion in spatially nonuniform nonlinear media. Wave reflection from interfaces is taken into account, and both regular and irregular nonuniform distributions of second-order nonlinear susceptibility are considered. A unified approach using a scattering matrix and a generalized Kirchhoff law is applied in calculations of spontaneous and stimulated processes in dissipative nonlinear media. Interference of electromagnetic zero-point fluctuations of the vacuum, nonlinear interference, and nonlinear diffraction are examined for media with various absorptive properties. Theoretical foundations are developed for diagnostics of nonuniform distributions of the second-order susceptibility, based on measurement of the line profiles of nonlinear signals.     

Acoustic analysis of a rectangular cavity with general impedance boundary conditions

A Fourier series method is proposed for the acoustic analysis of a rectangular cavity with impedance boundary conditions arbitrarily specified on any of the walls. The sound pressure is expressed as the combination of a three-dimensional Fourier cosine series and six supplementary two-dimensional expansions introduced to ensure (accelerate) the uniform and absolute convergence (rate) of the series representation in the cavity including the boundary surfaces. The expansion coefficients are determined using the Rayleigh-Ritz method. Since the pressure field is constructed adequately smooth throughout the entire solution domain, the Rayleigh-Ritz solution is mathematically equivalent to what is obtained from a strong formulation based on directly solving the governing equations and the boundary conditions. To unify the treatments of arbitrary nonuniform impedance boundary conditions, the impedance distribution function on each specified surface is invariantly expressed as a double Fourier series expansion so that all the relevant integrals can be calculated analytically. The modal parameters for the acoustic cavity can be simultaneously obtained from solving a standard matrix eigenvalue problem instead of iteratively solving a nonlinear transcendental equation as in the existing methods. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current method for various impedance boundary conditions, including nonuniform impedance distributions.