Elliptical Cavity Research Articles

Potential Coupling Through a Slot Backed by an Elliptical Cavity: Neumann and Dirichlet Boundary Conditions

Exact, closed-form expressions are presented for the solution to Laplace's equation everywhere in a specific cavity-backed aperture problem. A symmetrically placed slot enables the static field in a half-space above a hard or soft ground plane to penetrate into the interior of an elliptically shaped cavity. Separation-of-variables in elliptic coordinates yields a summable series, whereupon the aperture field or its normal derivative appears naturally as a series of edge-condition weighted Chebyshev polynomials in the Cartesian coordinates. Analytic coefficients explicitly display simple dependence upon the cavity and point-source geometry.

RF characterization of elliptical prototype copper cavity and the power coupler

The present paper describes in detail the RF measurement carried out on a prototype elliptical cavity made up of copper. The measured resonant frequency and Q0 were 1051.17 MHz and 14982 respectively. The dipole mode frequencies were 1469.3 MHz and 1470.6 MHz. The R/Q of the monopole and dipole mode was measured which was 9.404 Ω, 3.34 Ω and 4.32 Ω respectively. Also the external Q of the coaxial power coupler was measured.

Analysis of Soil Disturbance Associated with Mandrel-Driven Prefabricated Vertical Drains Using an Elliptical Cavity Expansion Theory

The installation of mandrel-driven prefabricated vertical drains and resulting disturbance of soft saturated clays are analyzed with a new elliptical cavity expansion theory. This formulated theory accounts for a concentric progression of elliptical cavities in an undrained condition and the large-strain effects in the plastic zone incorporating the modified Cam clay parameters. The total and effective stresses and excess pore water pressure in the soils surrounding the mandrel are predicted taking into account the mandrel installation rate, mandrel dimensions and the time factor. The theoretical variation of excess pore pressure is then compared with the results of large-scale consolidometer tests, which show that the estimated and measured pore pressures are almost the same. The plastic shear strain normalized by the rigidity index is then used to identify the zone of disturbance around the vertical drains. This formulation has been applied to a case history from the Muar clay region in Malaysia, and th...

Effect of crack opening and orientation on dispersion and attenuation of antiplane coherent wave

SUMMARY Propagation of antiplane coherent wave in solids containing randomly and uniformly distributed cracks is studied by calculating the associated effective wave number. Attention is focused on the influence of crack opening and orientation. Strip-like cracks or empty elliptical cavities are either mutually parallel or randomly oriented, and their surfaces are stress-free. Different multiple-scattering formulations for the effective wave number, in terms of the farfield displacement scattered by a single crack in the matrix, are compared for various crack systems. They coincide at low crack density and show similar trends when the crack density increases. Simple analytical estimates enable a direct evaluation of the crack density from the speed and attenuation of the coherent wave. In the low- and high-frequency ranges, the effective wave speed and attenuation appear to be mainly governed by the projection of cracks on the incident plane wave front.

Maximizing TEM 00 solar laser power by a light guide assembly-elliptical cavity

For maximizing TEM 00 solar laser power, a modified light guide assembly-elliptical cavity pumping approach is proposed. By observing refractive and total internal reflection principles, highly concentrated solar radiations from a primary parabolic mirror are firstly collected by a near-hexagonal input face and then transmitted, at low propagation angles, to a near-rectangular output end of the modified assembly. A sharp elliptical pump cavity with an intervening optics is utilized to further couple and concentrate the radiations from the assembly to a thin Nd:YAG rod. Optimum pumping parameters are found through ZEMAX™ non-sequential ray-tracing and LASCAD™ laser cavity analysis. Compared with the output performances of the parallel-packed light guide assembly-elliptical-cylindrical cavity, 45% increase in TEM 00, 10% in multimode solar laser powers are attained by the proposed approach. Experimental results on both the enhanced transmission efficiency of the assembly and the improved focusing capacity of the elliptical cavity with are finally provided.

Homogeneous solutions of the electroelasticity equations for piezoceramic layers in R 3

We present a procedure for the derivation of homogeneous solutions for piezoceramic layers within the framework of electroelasticity. The proposed approach simplifies considerably the Lurie (J Appl Math Mech 6:151–169, 1942) method. Two cases of mechanical boundary-conditions for piezoceramic layers are examined, namely, when the bases are (a) built in, and (b) free from the influence of forces. In both cases, the bases of the layer are assumed to be covered by grounded electrodes. It is shown that in the case of boundary conditions of the first type and for the symmetric, with respect to the mid-surface of the layer, electro-elastic state, the homogeneous solutions do not contain any biharmonic terms. We also calculate the distribution of the characteristic values of the corresponding spectrum problems for every given type of boundary conditions. The derived homogeneous solutions can be used for solving boundary-value problems for piezoceramic cylinders and layers within the framework of electroelasticity. We illustrate our approach through a practical example considering an oblique-symmetric boundary-value problem for layers which weaken due to a side to side elliptic cavity.

Fast Nonlinear Eigenvalues Analysis of Arbitrarily Shaped Substrate Integrated Waveguide (SIW) Resonators

In this paper, the problem of evaluating resonant frequencies of arbitrarily shaped substrate integrated waveguide resonators is considered. Resonances are found regarding them as nonlinear eigenvalues of the operator describing the scattering by metallic posts in a parallel plate waveguide. Nonlinear eigenvalues are usually computed by singular value decomposition. In order to save computational time, we propose an alternative approach derived by some general consideration on the theory of nonlinear eigenvalue problems in the discrete case. Results on rectangular, circular, and elliptical cavities are presented and compared with High Frequency Structure Simulator software package simulations. It is shown that the proposed method is efficient and accurate.

A Simple Approach for Enhancing the Output Performance of Solar‐Pumped Solid‐State Lasers

A simple truncated fused silica elliptical cavity is proposed to enhance the output performance of solar‐pumped solid‐state lasers. The imaging property of the truncated elliptical cavity ensures an enhanced absorption distribution within an Nd:YAG rod. Optimum pumping parameters are found through ZEMAX nonsequential ray‐tracing and LASCAD laser cavity analyses. Compared with the output laser performance of a 3D‐compound parabolic concentrator‐2D‐compound parabolic concentrator (3D‐CPC‐2D‐CPC) cavity, the truncated cavity provides 11% more multimode and 72.7% more TEM00 laser powers. A laser beam of high beam quality can be produced efficiently. The standard tracking error for multimode laser power is also reduced to only 4.0% by the truncated cavity.

The plane strain theory for one-dimensional hexagonal quasicrystals in aperiodical plane

Considering the plane elastic problem of one-dimensional hexagonal quasicrystals with point group 6mm, the theory about plane strain parallel to aperiodic direction is proposed and established. As an application of this theory, the analytic solutions of elastic fields of the quasicrystals with an elliptical cavity perpendicular to quasi-periodical direction are given in the form of general complex variable. In the limit case, our solutions degenerate into the ones of crack problems.

CW and Q-switched performance of end-pumped Yb:YAG laser with elliptical mode geometry

We report the high beam quality diode end-pumped Q-switched Yb:YAG laser operating at 1030 nm wavelength with elliptical cavity mode conguration operating at 1n100 kHz repetition rates. We have performed measurements of highly astigmatic thermal lens in laser active element by means of ShacknHartmann wavefront sensor that provides necessary data for laser cavity design. With optimized laser cavity the output beam quality parameter M 2 does not exceed 1.2 value even at maximum pump power of 50 W.

CONSTRUCTAL THEORY APPLIED TO THE GEOMETRIC OPTIMIZATION OF ELLIPTICAL CAVITIES INTO A SOLID CONDUCTING WALL

This work reports, according to Bejan’s Constructal theory, the geometric optimization of an elliptical cavity that intrudes into a solid conducting wall. The objective is to minimize the global thermal resistance between the solid and the cavity. There is uniform heat generation on the solid wall. The cavity is optimized for two sets of thermal conditions: isothermal cavity and cavity bathed by a steady stream of fluid. The solid conducting wall is isolated on the external perimeter. The total volume and the elliptical cavity volume are fixed while the geometry of the cavity is free to vary. The results show that the optimized geometrical shapes are relatively robust, i.e., insensitive to changes in some of the design parameters: the cavity shape is optimal when penetrates the conducting wall almost completely.

RF properties of 700 MHz, β = 0.42 elliptical cavity for high current proton acceleration

BARC is developing a technology for the accelerator-driven subcritical system (ADSS) that will be mainly utilized for the transmutation of nuclear waste and enrichment of U233. Design and development of superconducting medium velocity cavity has been taken up as a part of the accelerator-driven subcritical system project. We have studied RF properties of 700 MHz, β = 0.42 single cell elliptical cavity for possible use in high current proton acceleration. The cavity shape optimization studies have been done using SUPERFISH code. A calculation has been done to find out the velocity range over which this cavity can accelerate protons efficiently and to select the number of cells/cavity. The cavity’s peak electric and magnetic fields, power dissipation P c , quality factor Q and effective shunt impedance ZT 2 were calculated for various cavity dimensions using these codes. Based on these analyses a list of design parameters for the inner cell of the cavity has been suggested for possible use in high current proton accelerator.

Benchmark for poroelastic and thermoelastic numerical codes

Using the method of complex potentials we present the closed form of analytical solution for the stresses and displacements around an elliptical cavity filled with fluid in the permeable poroelastic medium. The far-field pore pressure is different from the pressure inside cavity. The fluid is allowed to diffuse through the cavity’s wall towards surrounding medium. The two-dimensional plane-strain and plane-stress models are considered with steady-state distribution of diffusive pore-fluid pressure. The diffusion of fluid is coupled to the deformation of a medium using a linear theory of poroelasticity. Since in the static case the diffusion of pore fluid is controlled by an ordinary Laplace equation, the problem is reduced to elastic problem with distribution of volume forces (known as seepage forces) along gradients of pore pressure. Due to similarity between poroelasticity and thermoelasticity, the present solution is applicable both to the poroelastic and thermoelastic problems with a steady-state distribution of pore pressure and temperature, respectively. Since it is getting more common to model the deformation coupled to Darcy-flow in geosciences and no clear criteria has been suggested for verification of numerical codes, we discuss the possible application of the analytical solution as the benchmark for testing of poroelastic and thermoelastic numerical codes. To stimulate a wider use of the solution for stresses, displacements and pore-fluid pressure around an elliptical cavity are implemented in MATLAB and can be downloaded from the web.

Influence of mechanical stresses on partial discharge in a piezoelectric solid containing cavities

For a piezoelectric solid with an air-filled elliptic cavity, the two-dimensional problems of partial discharge inside the cavity are studied when the solid is subjected to combined mechanical stress and electric field. Based on the law of Paschen, the influence of mechanical stress on partial discharge is discussed. It is shown from the obtained results that the applied mechanical stress can retard or enhance the occurrence of partial discharge, which is dependent on the signs of applied electric fields. It is also found that for a mathematical crack (with zero initial width), partial discharge may not happen even when the significantly high mechanical and electric loadings are applied within the range of practical interest.

Some elasticity problems of a general anisotropic solid subjected to anti-plane loadings

Plane elasticity problems of a general anisotropic material subjected to both in-plane and anti-plane loadings are formulated based on Lekhnitskii’s complex variable approach. Some useful solutions to half-plane problems and elliptical cavity problems are derived for cases involving anti-plane loadings. Asymptotical crack-tip elastic fields are reviewed and comparisons are made for crack problems and slender elliptical cavity problems. Specifically, it is shown that the stress state at a rounded crack tip can be characterized by a stress rounding factor and the stress intensity factor of the associated slit crack. An important conclusion is that, for a fixed loading condition and a fixed shape of the cavity, the influence of the shape of the cavity on the stress concentration factor can be separated from the influence of the material properties.

Enhancement of Oxidation Processes of Cellular Microbial Substrate, Using UV Radiation in Resonant Elliptic Cavity

The improvement of disinfection efficiency for different contaminated fluid fluxes is related to the enhancement of oxidation processes at cellular level, developing original disinfection equipment. The construction of developed equipment is based on the amplification and focalization of UV germicide and bactericide radiation (wavelength l = 253.65 nm), using an elliptic cylinder shaped reflector and building up a resonant cavity for these radiations. Some theoretical considerations concerning the experimental device construction are described in the paper. The resonant elliptic cavity is used in LASER technique, as the �optic pumping� and this idea was involved in the developing of our equipment. Two TUV-60 lamps made by Philips Company were placed in the focal points of the elliptic cylinder (made by anodized aluminium) and a central quartz tube (symmetrical disposed between these lamps) was used as plug-and-flow photo-chemical reactor, through the fluid fluxes were passed. In these conditions the syntheses of chemical species with high oxidation capacity (hydroxyl radicals, ozone, etc.) can contribute to the advanced oxidation process of cellular microbian substrate. Distillated water and respectively an air flux contaminated with four types of pathogenic microorganisms (E.coli, Streptococcus sp., Salmonella sp., Pseudomonas aeruginosa) were used in all experiments. The best results were recorded in the case of gas flux due to synchrony of UV/Ozone effects when all pathogenic microorganisms were destroyed. In case of water flux were obtained the similar results, for E.coli and Pseudomonas aeruginosa. Salmonella sp. and Streptococcus, were still found in water after desinfection, as refractar pathogens in 34.3 % and respectivly 7.8 % in raport with initial CFU (104 colony formatting unities/mL).

Structural properties of 1050 MHz, β = 0.49 single cell elliptical cavity for high current proton acceleration

A single cell 1050 MHz, β = 0.49 elliptical cavity has been designed for possible use in High Current Proton Accelerator. The structural behavior of the single cell superconducting elliptical cavity has been studied by finite element structural analysis code. The max. Von MISES stress and cavity wall displacements were calculated under the vacuum load for various wall thickness. Both niobium and copper have been considered as cavity material. The RF resonant frequency shift due to the static Lorentz force has been calculated for 3 mm wall thickness. Structural properties of the 1050 MHz, β = 0.49 cavity have been compared with the 700 MHz, β = 0.42 single cell elliptical cavity. It was found that from structural point of view 1050 MHz, β = 0.49 cavity is more suitable for high current proton accelerator.

Quasilinear infiltration from an elliptical cavity

We develop analytic solutions to the linearized steady-state Richards equation for head and total flowrate due to an elliptic cylinder cavity with a specified pressure head boundary condition. They are generalizations of the circular cylinder cavity solutions of Philip [Philip JR. Steady infiltration from circular cylindrical cavities. Soil Sci Soc Am J 1984;48:270–8]. The circular and strip sources are limiting cases of the elliptical cylinder solution, derived for both horizontally- and vertically-aligned ellipses. We give approximate rational polynomial expressions for total flowrate from an elliptical cylinder over a range of sizes and shapes. The exact elliptical solution is in terms of Mathieu functions, which themselves are generalizations of and computed from trigonometric and Bessel functions. The required Mathieu functions are computed from a matrix eigenvector problem, a modern approach that is straightforward to implement using available linear algebra libraries. Although less efficient and potentially less accurate than the iterative continued fraction approach, the matrix approach is simpler to understand and implement and is valid over a wider parameter range.

RF properties of 1050 MHz, β = 0.49 Elliptical cavity for High Current Proton Acceleration

BARC is developing technology for the accelerator driven subcritical system (ADSS) that will be mainly utilized for the transmutation of nuclear waste and enrichment of U233. Design and development of superconducting medium velocity cavity has been taken up as a part of the accelerator driven subcritical system project. We have studied RF properties of 1050 MHz, β = 0.49 single cell Elliptical cavity for possible use in High Current Proton Accelerator. Cavity shape optimization studies have been done by means of 2D cavity tuning code SUPERFISH and 3D High Frequency Simulation code CST Microwave Studio. The cavity peak electric and magnetic fields, power dissipation Pc, quality factor Q and effective shunt impedante ZT2 were calculated for various cavity dimensions using these codes. Based on these analyses a list of design parameter for the inner cell of the cavity has been suggested for possible use in high current proton accelerator.

Status of the SNS Superconducting Linac and Future Plan

The use of superconducting radiofrequency (SRF) cavities in particle accelerator is becoming more widespread. Among the projects that make use of that technology is the Spallation Neutron Source, where H- ions are accelerated to about 1 GeV, mostly making use of niobium elliptical cavities. SNS generates neutrons by the spallation reaction with the accelerated short (about 700 ns) sub-bunches of protons, which will in turn allow probing structural and magnetic properties of new and existing materials. The SNS superconducting linac is the largest application of RF superconductivity to come on-line in the last decade and has been operating with beam for almost two years. As the rst operational pulsed superconducting linac, many of the aspects of its performance were unknown and unpredictable. A lot of experiences and data have been gathered on the pulsed behavior of cavities and cryomodules at various repetition rates and at various temperatures during the commissioning of its components and beam operations. This experience is of great value in determining future optimizations of SNS as well in guiding in the design and operation of future pulsed superconducting linacs. The testing of the superconducting cavities, the operating experience with beam, the performance of the superconducting linac andmore » the future plans will be presented.« less