Order Eigenmodes Research Articles

Generalized Amplitude Transfer Factor for an Analysis of Transversal Modes in Surface Acoustic Wave Resonator-Type Devices

A generalized amplitude transfer factor for analyzing the effect of transversal modes in surface acoustic wave (SAW) resonator-type devices is newly presented, taking the arbitrary transversal source distribution into account. The factor is defined as the ratio of the inner product of G and Ψn to the product of their norms, where G is the source distribution function and Ψn is the n-th order eigenmode function in a ΔV/V waveguide. Several concrete analyses clarify the validity of the factor.

The higher order modal characteristics of circular-rectangular coaxial waveguides

A rigorous analysis combining the orthogonal expansion method and Galerkin method for the higher order eigenmodes in a circular-rectangular (C-R) waveguide is presented in this paper. The Bessel-Fourier series is employed to merge the circular and rectangular coordinate systems used in the analysis. The cutoff frequencies of the higher order modes are determined with the singular value decomposition (SVD) technique. The computed results are in excellent agreement with results obtained using the finite element method. Because of its analytic form, the solution will be useful in the rigorous analysis of many practical microwave components and circuits.

Reduced dynamical models of nonisothermal transitional grooved-channel flow

Reduced dynamical models are derived for transitional flow and heat transfer in a periodically grooved channel. The full governing partial differential equations are solved by a spectral element method. Spontaneously oscillatory solutions are computed for Reynolds number Re⩾300 and proper orthogonal decomposition is used to extract the empirical eigenfunctions at Re=430, 750, 1050, and Pr=0.71. In each case, the organized spatio-temporal structures of the thermofluid system are identified, and their dependence on Reynolds number is discussed. Low-dimensional models are obtained for Re=430, 750, and 1050 using the computed empirical eigenfunctions as basis functions and applying Galerkin’s method. At least four eigenmodes for each field variable are required to predict stable, self-sustained oscillations of correct amplitude at “design” conditions. Retaining more than six eigenmodes may reduce the accuracy of the low-order models due to noise introduced by the low-energy high order eigenmodes. The low-order models successfully describe the dynamical characteristics of the flow for Re close to the design conditions. Far from the design conditions, the reduced models predict quasi-periodic or period-doubling routes to chaos as Re is increased. The case Pr=7.1 is briefly discussed.

Effects of equilibrium on instabilities driven by ion temperature gradients in tokamaks

The consequences of beta driven equilibrium changes on toroidal ion temperature gradient driven instabilities are considered. A semi-analytic method for evaluating the stability of finite aspect ratio, shaped tokamaks at finite beta is presented. The appearance of higher order eigenmodes with relatively high growth rates is observed. Stabilization is achieved at high poloidal beta.