Dispersion Curves Of Waveguides Research Articles

Kriging metamodeling approach for predicting the dispersion curves for wave propagating in complex waveguide

This study deals with the prediction and analysis of dispersion curves of waveguides, which are known to be critical steps within structural health monitoring (SHM). Despite using more sophisticated methods, such as wave finite element method (WFEM), the determination of the dispersion curves still presents severe numerical difficulties, which can be manifested by high computation time. Then, this paper proposes the metamodeling approach based on kriging theory to overcome the mentioned difficulties. Therefore, the main aim of the present study is to investigate the effectiveness of kriging metamodels when used to predict the WFEM-defined waveguide dispersion curve. Based on numerical simulations, the strategy, which consists of constructing the learning sets for the kriging metamodels using WFEM representations, is shown to be very promising regarding the convenience of the obtained compromise between the accuracy and the computing time.

On a dispersion curve of a waveguide filled with inhomogeneous substance

The paper discusses the relationship between the modes traveling along the axis of the waveguide and the standing modes of a cylindrical resonator, and shows how this relationship can be explored using the Sage computer algebra system. In this paper, we study this connection and, on its basis, describe a new method for constructing the dispersion curve of a waveguide with an optically inhomogeneous filling. The aim of our work was to find out what computer algebra systems can give when calculating the points of the waveguide dispersion curve. Our method for constructing the dispersion curve of a waveguide with optically inhomogeneous filling differs from those proposed earlier in that it reduces this problem to calculating the eigenvalues of a self-adjoint matrix, i.e., a well-studied problem. The use of a selfadjoint matrix eliminates the occurrence of artifacts associated with the appearance of a small imaginary addition to the eigenvalues. We have composed a program in the Sage computer algebra system that implements this method for a rectangular waveguide with rectangular inserts and tested it on SLE modes. The obtained results showed that the program successfully copes with the calculation of the points of the dispersion curve corresponding to the hybrid modes of the waveguide, and the points found fit the analytical curve with graphical accuracy even when with a small number of basis elements taken into account.

Starting behaviors of the TM-mode gyrotrons

This work shows the derivations and calculations of the starting behaviors using the Laplace method and the numerical method. Calculated results based on these two methods agree well when dealing with a uniform structure, while the numerical method is advantageous for the non-uniform and practical structure. The applicability of the zero-field and the outgoing-wave boundary conditions at the collector end is discussed. These two boundary conditions agree well when the beam-wave resonant line and the waveguide dispersion curve intercept at the backward-wave region but differ significantly at the forward-wave region. The beam-wave coupling strength of the TM-mode gyrotron is found to be strongly correlated with the starting current, which can be utilized to avoid the potential competition from the transverse electric (TE) modes. The starting current of the TM11 gyrotron exhibits an additional operating condition at the low-beam voltage that may facilitate the development of low-cost and tabletop gyrotron systems. The beam-voltage and magnetic-field tunings are investigated for an open-cavity structure with the numerical method. Interestingly, the TM11 gyrotron as well as the TE01 gyrotron exhibits a similar starting behavior, which warrants the potential applications of the TM-mode gyrotrons.

On the Dispersion Curves of Anisotropic Waveguides

Behavior of the dispersion curves of waveguides with anisotropic filling is considered. The existence of backward and complex waves at certain values of the anisotropy coefficients is established. The region of localization of the singular points of the dispersion curves in which the generation of backward waves takes place is found.

Novel Dispersion Curves Extraction Method for Waveguides Affected by Nonuniform Transient Temperature Field

Guided waves sensitivity to environmental and operational conditions, especially temperature fluctuations, is one of the major problems when the method is considered for real engineering applications. The aim of this paper is to propose a novel dispersion curves extraction method for waveguides affected by nonuniform transient temperature field. Essentially, the method is based on a simple and robust approach, consisting in a few series of modal analyses for a representative part of the inspected structure. To consider the effect of temperature, a thermal stress calculation based on finite element method is presented. In this way, for different wave lengths, the mode shapes and corresponding natural frequencies can be obtained by solving some thermal-eigenvalue problems. To test the theoretical thermal effect of the dispersion curves a experiment on an isotropic plate is conducted. Those theoretical dispersion curves, consisting of only dominant modes, are compared with dispersion curves obtained from experiment. Finally, this method is used to extract the dispersion curves of the aero-engine casing considering the nonuniform temperature field. The results not only give us insight to how temperature affects Lamb wave velocities in different frequency ranges but also will help those extracting dispersion curves for waveguides affected by nonuniform transient temperature field.

CALCULATION OF DISPERSION CURVES FOR ARBITRARY WAVEGUIDES USING FINITE ELEMENT METHOD

Dispersion curves for waveguide structures are an important prerequisite for the implementation of guided wave-based nondestructive evaluation (NDE) approach. Although many methods exist, each method is only applicable to a certain type of structures, and also requires complex programming. A Bloch theorem-based finite element method (FEM) is proposed to obtain dispersion curves for arbitrary waveguides using commercial finite element software in this paper Dispersion curves can be obtained for a variety of structures, such as homogeneous plates, multilayered structures, finite cross section rods and honeycomb sandwiches. The propagation of guided waves in honeycomb sandwich plates and beams are discussed in detail. Then, dispersion curves for honeycomb sandwich beams are verified by experiments.

Free electron maser oscillations near waveguide cutoff

In waveguide-based FEMs there are two possible frequency radiation bands corresponding to the two intersections of the beam line with the waveguide dispersion curve. The low-frequency intersection point occurring near the waveguide cutoff frequency was studied by us experimentally. Special modifications of the existing TAU FEM facility were made in order to investigate FEM radiation near cutoff. Some rectangular waveguide components, used for the radiation coupling from the resonator to the detection system, were replaced by components based on a double-ridged waveguide having a lower cutoff frequency and a wider frequency band. FEM operation in the vicinity of the waveguide cutoff frequency was studied in free-running oscillator configuration using a unique experimental setup enabling time-dependent spectral measurements within a single radiation pulse. The observed FEM radiation was of good spectral purity without any significant mode competition.

Modal dispersion curves of an optical waveguide with an annular core cross section separated by two nonconcentric circles from two cladding regions

An optical fiber with an annular cross section bounded by two nonconcentric circles is analytically studied with a view to obtaining the modal characteristics. Using the characteristic equation derived from the matching of fields at the core–cladding boundaries expressed in terms of bipolar coordinates, dispersion curves are obtained on the basis of numerical computations. The curves corresponding to some modes are similar to the standard dispersion curves for waveguides. However, the dispersion curves of other modes show some unexpected behavior; one mode even shows no dispersion at all. These points are qualitatively discussed. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 280–283, 1997.

Pulsating mode in peniotron backward wave oscillations

A sustainable pulsating mode in peniotron backward wave oscillations can be excited if parameters are properly chosen, such that at some instant of time the reduction in beam energy resulting from the electron–wave interaction is to such an extent that its cyclotron harmonic line intersects with the waveguide dispersion curve in the positive kz region. The generation of the forward traveling self-oscillating mode eliminates the residual backward traveling wave, which is very essential in establishing relaxation oscillation. As a result, the time evolution of the output wave becomes self-pulsating.

A kinetic theory for the electron cyclotron maser interaction in a lossy cylindrical waveguide: Mode coupling among all supported waveguide modes

A general dispersion relation is derived assuming all supported empty waveguide modes are included in the electron cyclotron maser interaction within a good conducting cylindrical waveguide. Four energy transfer mechanisms exist of which three are directly related to the beam–wave interaction. The beam modes are shown to be coupled as a consequence of azimuthal asymmetry in the fields. New contributions to the instability terms result. Assuming single mode operation, new contributions to both the instability and the stability terms are obtained. Growth rates are examined. It is explicitly shown that all instability, stability, and coupling contributions due to a particular transverse magnetic mode vanish if a beam dispersion curve just grazes the empty waveguide dispersion curve of that mode. By adjusting the radius of a radially thin beam, the dominant azimuthally symmetric mode of operation can be adjusted.

The interaction of high- and low-frequency waves in a free electron laser

When a free electron laser (FEL) interaction occurs inside a waveguide, there are two possible operating frequencies at the two intersections of the beam line with the waveguide dispersion curve. Using a one-dimensional model valid for a low-gain oscillator, the mode competition between the high- and low-frequency waves is studied. It is found that the low-frequency wave can be nonlinearly suppressed, even when its linear growth rate is positive. When the frequency ratio is two, phase locking occurs and the nonlinear gain of the low-frequency wave can exceed its linear growth rate. >