Number Of Resonant Modes Research Articles

Cylindrical coils near self-resonance.

We present a model of birdcage resonator operation when the size of the resonator approaches a quarter wave length resulting in significant phase shifts along the current conducting elements. In the model resonators are treated as generalized transmission lines. Line termination determines whether the resonator is of the low pass or high pass type. The model correctly describes the dependence of resonant frequency on resonant mode number as well as the distribution of current along the length of the resonator.

Cold tests of open coaxial resonators in the range 9–17 GHz

A study of selective properties of coaxial open cylindrical resonators have been conducted experimentally and compared with theory. The resonator consists of an inner circular cylinder symmetrically located inside an outer weakly irregular open waveguide. Several fundamental TE modes were identified over the range 9 to 17 GHz through measurements of the resonant frequencies and the associated loaded quality factors. It has been verified that the structure and the number of resonant modes are both strongly dependent on the diameter of the coaxial insert. Such an electrodynamical system proves to be useful in guided wave applications requiring, for example, filters, frequency-tunable resonators and devices for analyzing the modal composition of a signal.

Multi-mode resonant gradient coil circuit for ultra high speed NMR imaging

A multi-mode resonant gradient circuit is described for use in ultra high speed imaging techniques like echo-planar and echo-volumar imaging. The circuit behaves overall in a series resonant manner, but at a fixed number of discrete frequencies. By choosing the number of resonant modes, the circuit can be used to generate approximations to a square wave or a trapezoidal waveform. It it shown that trapezoidal waveforms of a given rise time may be described by a more convergent series expansion involving fewer harmonic components. Because the circuit exploits energy conserving principles, much faster current rise times can be achieved with a given driver amplifier and gradient coil than can be achieved by direct coil drive. Expressions are given for the choice of passive circuit components required to accommodate all odd harmonics up to seventh order.

Influence of the nature of the interface on the spin wave resonance spectra of single-crystal nickel films

Observations and associated analyses of the microwave resonance absorption of single-crystal nickel films are described in this paper. NaF films evaporated prior to and/or after nickel deposited onto various crystalline substrates were used to investigate the nature of the asymmetries in several nickel interfaces prepared under various deposition conditions by means of spin wave resonance (SWR) experiments. The angular dependence of SWR spectra obtained for some films provides evidence for the existence of quasi-localized surface (QLS) modes lying within those of the bulk mode manifold. The QLS mode transforms into an acoustic surface mode as the magnitude of the surface pinning parameter is changed. The results also indicate that while the acoustic surface mode disappears from the spectrum at a certain angle, the QLS mode first transforms to an acoustic surface mode and then disappears at a larger angle. All this occurs as the static magnetic field is rotated from the perpendicular to parallel orientation with respect to the film normal. These observations are consistent with the predictions given by Puszkarski's models (H. Puszkarski, Prog. Surf. Sci., 9 (1979) 191; Solid State Commun., 33 (1980) 757). The effect of stress on the SWR spectra indicates that, for the same film, the number of resonance modes and their intensities in strain-free films are less than in strained films. This feature suggests that pinning at the film-substrate interface dominates over that at the film-air interface.

Thick film YBCO microstrip resonators

The authors present results on a microstrip resonator made from thick film YBCO. A number of resonant modes of this structure have been measured in the frequency range 4-12 GHz and results for the centre frequency and Q of these modes are presented.

Planar analysis of radial-line power dividers

The resonant mode field expansion technique presented in previous papers to analyse one- or two-port microstrip structures of different geometrical shapes is now applied to multiport radial lines. In particular, a radial-line n-way power divider is considered. This device allows, under certain hypotheses, an equiphase and equiamplitude splitting of an input signal. The Z matrix formulation has been derived and utilized to obtain the scattering parameters for the circuit. The numerical results are in good agreement with both experimental and theoretical data presented in the literature. The low number of resonant modes required to obtain satisfactory numerical convergence allows a substantial reduction of the computing time with respect to other more complicated approaches.

Spacetime representation of global electrocortical activity

A model for global electrocortical activity is developed by considering telencephalonic structures as mass of linked oscillators generating activity with a number of resonant modes. Equations for the signals are written in the comoving frame and then transformed into the laboratory frame. The state transition matrix is obtained in the presence of electric and magnetic fields.

Three-dimensional simulation of free electron lasers with planar wigglers

The nonlinear evolution of a free electron laser (FEL) amplifier is investigated for a configuration in which an electron beam propagates through an overmoded rectangular waveguide in the presence of a planar wiggler with parabolically tapered pole pieces. The analysis is fully three-dimensional and describes the evolution of an arbitrary number of resonant TE and/or TM modes of the rectangular guide as well as the trajectories of an ensemble of electrons. The theory is found to be in good agreement with the 35 GHz amplifier experiment performed by Orzechowski and co-workers, in which the TE01, TE21, and TM21 modes were observed.

Multimode nonlinear analysis of free-electron laser amplifiers in three dimensions.

The nonlinear evolution of a free-electron laser (FEL) amplifier is investigated for a configuration in which an electron beam propagates through an overmoded rectangular waveguide in the presence of a planar wiggler with parabolically tapered pole pieces. The analysis is fully three dimensional and describes the evolution of an arbitrary number of resonant TE and/or TM modes of the rectangular guide as well as the trajectories of an ensemble of electrons. Numerical simulations are conducted for parameters consistent with the 35-GHz amplifier experiment performed by Orzechowski and co-workers (Phys. Rev. Lett. 54, 889 (1985); 57, 2172 (1986)), in which the TE/sub 01/, TE/sub 21/, and TM/sub 21/ modes were observed. The theory is found to be in good agreement with the experiment. Surprisingly, comparison with a single-mode analysis shows that the enhancement of the efficiency of the TE/sub 01/ mode obtained by means of a tapered wiggler is significantly greater (as well as being in substantial agreement with the experiment) when the TE/sub 21/ and TM/sub 21/ modes are included in the simulation.

The Whittier Narrows, California Earthquake of October 1, 1987—Preliminary Assessment of Strong Ground Motion Records

More than 250 strong-motion accelerograph stations were triggered by the Whittier Narrows, California, earthquake of 1 October 1987. Considering the number of multichannel structural stations in the area of strong shaking, this set of records is one of the more significant in history. Three networks, operated by the U.S. Geological Survey, the California Division of Mines and Geology, and the University of Southern California produced the majority of the records. The excellent performance of the instruments in these and the smaller arrays is attributable to the quality of the maintenance programs and their funding and personnel requirements. Readiness for a magnitude 8 event is directly related to these maintenance programs. Prior to computer analysis of the analog film records, a number of important structural resonant modes can be identified, and frequencies and simple mode shapes have been scaled. The structural records form a basic performance measurement for comparison with larger earthquake response in the future.

A linear theory for global electrocortical activity and its control by the lateral hypothalamus.

A linear model for electrocortical waves and their control by the lateral hypothalamus is proposed. It is argued that such a linear model is not in contradiction to non-linearity of neural elements on the microscopic scale. Telencephalic structures are treated as a mass of linked oscillators generating activity with a number of resonant modes. The lateral hypothalamus is regarded as controlling damping of activity in the telencephalic mass, and therefore exerting a specific parametric control over all signal processing in the cortical networks. An initial test is proposed to assess the constancy of telencephalic natural frequencies, with variation in lateral hypothalamic damping.

Helicopter airframe vibration transmission modeling using statistical energy analysis (SEA)

Predicting helicopter cabin noise is a complex issue. It involves sources which are both acoustic/aerodynamic and vibratory in nature as well as a compact, highly interconnected airframe structure. Energy transmits to the cabin via both airframe structureborne and airborne paths. Since a large number of resonant structural and acoustic modes are excited, a statistical approach, which treats the response of the modes collectively in groups, is desirable. The method described for modeling the helicopter airframe and cabin interior is Statistical Energy Analysis (SEA). An SEA model, funded by a NASA Langley Research Center contract, is presented for the Sikorsky S‐76 (a4‐13 passenger commercial helicopter). This overall source‐to‐receiver modeling approach allows for evaluation of various noise control measures in the conceptual design stage. Expressions have been developed for SEA parameters and the coupling loss factor has been related to the more familiar vibration transmission coefficient. A full scale measurement program was conducted on the Sikorsky S‐76. Data are presented showing the SEA parameters and comparisons with the analytic model. These data include vibration transmission along the beam/panel structure and transmission through intermediate acoustic spaces connected by both resonant and nonresonant conditions. In addition, data are presented concerning the effects of coherent and noncoherent source excitations at distant response points. [Work supported by NASA Langley.]

Theory of ferromagnetic resonances in thin wires

A phenomenological theory of ferromagnetic resonances in a ferromagnetic metallic cylinder magnetized along its axis is based on the simultaneous solution of the equation of motion and Maxwell's equations. A general relaxation term in the equation of motion is used. The boundary conditions correspond to the dynamic surface anisotropy with the preferred direction parallel to the static magnetization. It is shown that the solution yields an infinite number of resonance modes of different spatial symmetry. Formulas for the surface impedance and the relative absorption of individual modes are derived. The effect of the finite radius of the cylinder on the resonance, antiresonance and spin wave resonance behaviour is discussed.

Estimates of power coupling two beams

Davies and Wahab have recently reported extensive precise calculations of the average power coupling the two parts of a beam held by three simple supports, averages being taken over frequency bands and an interval of the ratio of lengths of the two parts [J. Sound Vib. 77, 311 (1981)]. Those results are discussed and compared with prior studies based on one or another statistical hypothesis, including Statistical Energy Analysis. Principal results are (1) for small loss factor η (η ≲ 1/Nπ, where N is average resonant mode number), the new and old results agree very closely; this is the tightly coupled regime where half the power input to each subsystem is dissipated in the other; (2) agreement is less good for larger η; in this regime reverberation is slight since round‐trip attenuation is large; coupling power varies with the source location within each subsystem; (3) for the particular structure, where the wave energy transmission coefficient of the coupling is large (0.5), there is no regime that is bo...

Cavity resonances and mutual coupling in concave waveguide arrays

A method is presented for the mutual coupling analysis of concave, circular cylindrical or spherical waveguide arrays. The array is considered as a set of waveguides that are coupled through a prefectly conducting, lossless cavity, which leads to an equivalent multiport network. The corresponding scattering matrix is obtained by matching the cavity and waveguide fields over the guide apertures and solving the resulting equation by Galerkin's method. In particular the complications are discussed, which arise from the possibly large number of degenerate, resonant cavity modes. A result obtained is the general condition that at a resonance the total aperture field (for all waveguide apertures) must be orthogonal to the set of degenerate, resonant cavity modes. This leads, with certain exceptions, to zero coupling between the guides whenever the total number of aperture modes (for all waveguides) is less than or equal to the number of resonant cavity modes.

Using SEA to model vibration transmission in engine structure

Understanding the vibration characteristics of engine structures is an important aspect of the overall effort to reduce engine noise. Recent advances have been made in the measurement and modeling of the vibration characteristics of the individual components in an engine structure for the purpose of developing an analytical model which predicts the vibration transmission of the complete structure. For components with a small number of resonant modes of vibration in the frequency range of interest, lumped parameter models can be developed which match the vibration response function quite accurately. However, for components with a large number of resonant modes in the frequency range of interest, it is more useful to employ Statistical Energy Analysis to model the average vibration response. This paper demonstrates the comparability of these two types of models and shows some examples of the use of a complete vibration model in identifying component design changes which will result in engine noise reductions. [Work supported by EPA/ONAC.]

Ferrimagnetic resonance spectra of magnetic bubble films at low microwave frequencies

Magnetic bubble films exhibit a number of ferrimagnetic resonance modes due to the spatial variation of the anisotropy. The resonance frequencies have been measured as a function of the applied bias fieldH 0. In the lower field range the magnetization of the transient layer, which has negative anisotropy, is not yet parallel toH 0. In this range the resonance frequencies are shifted to higher values due to pinning effects. In films grown by the vertical dipping method an additional layer on top of the transient layer is observed within which the magnetization rotates from the direction in the transient layer to that of the bulk of the film. In films grown by horizontal dipping no such layer could be detected. Each ferrimagnetic resonance mode excites transverse elastic waves in the film due to the magnetoelastic interaction and thus gives rise to elastic resonances of the whole crystal, film and substrate. These elastic resonances lead to a fine-structure of the ferrimagnetic resonances. The observed fine-structure vanishes periodically with frequency and from this behaviour the thickness of the magnetic film and of the transient layer has been determined.

Frequency control and mode selectivity in the acoustoelectric oscillator

A method of reducing the number of resonant modes in an acoustoelectric oscillator is proposed and experimentally investigated using CdS oscillators. It involves the deposition of an evaporated grid of aluminium strips on to the CdS, which produces an acoustically coupled dual-cavity system. The resonant frequency of the composite cavity is effectively independent of the CdS and is a function of the mechanical properties of the aluminium. Significant improvements in the performance of the oscillator are observed particularly in relation to mode ambiguity and frequency range.

Geometriefaktoren von Hohlraumresonatoren zur Elektronendichte-, Dichteprofil- und Stoßfrequenzmessung von Plasmen

Geometry factors of cavity resonators for the determination of plasma electron density, density profile, and collision frequency Geometry factors of a number of cylindrical TEimn and TMimn cavity resonance modes are cal-culated as a function of the ratio of plasma and cavity radius and as a function of the radial electron density profile. In axial direction homogeneous and sinusoidal density profiles are assumed. Resonance modes with a small index l are suitable for the measurement of electron densities in narrow and dilute plasma columns; modes with an index l ≧ 2 are specially advantageous for measuring the density profile. Results of measurements of the electron density, density profile, and collision frequency in nitrogen are given.

Multimode Degeneracy in a Cavity Resonator

The problem of a resonator having a number of resonant modes at the same frequency is investigated. For this purpose a circular cylindrical cavity with conducting posts symmetrically arranged along a circle and joining the opposite lids of the cylinder is considered. The dependence of the resonant frequencies of the TM modes on the diameter and relative spacings of the conducting posts are studied and conditions are derived for obtaining multimode degeneracy.