Frequencies Of Higher-order Modes Research Articles

Radial Oscillations in Neutron Stars from Unified Hadronic and Quarkyonic Equation of States

We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M⊙ star criterion. We solve the Sturm–Liouville problem to compute the 20 lowest radial oscillation modes and their eigenfunctions for a neutron star modeled with eight selected unified EoSs from distinct Skyrme–Hartree–Fock, relativistic mean field and quarkyonic models. We compare the behavior of the computed eigenfrequency for an NS modeled with hadronic to one with quarkyonic EoSs while varying the central densities. The lowest-order f-mode frequency varies substantially between the two classes of the EoS at 1.4 M⊙ but vanishes at their respective maximum masses, consistent with the stability criterion ∂M/∂ρc>0. Moreover, we also compute large frequency separation and discover that higher-order mode frequencies are significantly reduced by incorporating a crust in the EoS.

Tuning the higher to lower order resonance frequency ratio and implementing the tunable THz MIMO/self-diplexing antenna

The frequency ratio of higher to lower order mode can be electronically tuned in a terahertz (THz) antenna with metallic radiator using a graphene loop. Antenna is designed with slotted metallic radiator to obtain the dual-band response with fundamental and second order transverse magnetic mode providing the directional and bi-directional radiation pattern in the lower and upper band, respectively. The insertion of graphene loop and varying its chemical potential (μc) provides two resonances until 0.4eV and four resonances for further greater values of μc. The desired impedance matching can be achieved at the frequencies of any two resonances at a time by selecting an appropriate value of μc. Antenna can operate with higher/lower order mode centred at frequency 3.77/3.02 THz and 4.39/2.86 THz for the values of μc as 0.9 and 0.3eV , respectively. The frequency ratio of higher to lower order mode can be tuned within the range of 1.22–1.59 with the variation in μc. Also, application of graphene loop confines the radiated power in a single direction at the frequency of higher order mode making the radiation pattern consistent. Antenna can be utilized in future THz wireless applications which require the utilization of adjacent channels with different frequencies in communication. Also, a two-port antenna is designed which can offer the tunable multi-input–multi-output (MIMO) and self-diplexing capability with pattern diversity. The MIMO parameters; envelope correlation coefficient (ECC) and diversity gain (DG) is evaluated and their values are found within acceptable limits as ECC<0.06 and DG>9.9 in the operating bands.

Frequency equation and semi-empirical mechanical coupling strength of microcantilevers in an array.

A characteristic equation for the frequencies of the T-shaped and overhang-shaped cantilevers is derived for the first time. We show that there are optimum values of the overhang lengths and widths that maximize the frequency and the number of maxima is corresponding to the mode number. The frequency of higher-order modes could be tuned by changing the overhang dimensions. Especially, a semi-empirical formula for the coupling strength between cantilevers in an array is proposed where the strength presents a cubic decrease with the overhang width and a linear increase with the overhang length , . There is a very good agreement between the proposed formula and the values obtained in recent experiments by other researchers.

Vibration isolation performance of simply supported beam installed with a negative stiffness device

A negative stiffness device composed of two horizontal pre-compression springs is proposed to isolate the vibration of the simply supported beam. The nonlinear vibration equation of simply supported beam installed with a negative stiffness device is established by using Hamilton principle first. The lower degree of freedom dynamic equation of the system is derived by using Galerkin truncation approach. The influence of support position and negative stiffness parameters on the natural frequency of the beam are obtained from the modal analysis of the free vibration system. According to the dynamic internal force of the beam, the force transmissibility at the support end is defined and the displacement transmissibility of any point on the beam is also defined to facilitate the analysis of the vibration isolation effect. The influence of negative stiffness support parameters on the amplitude–frequency curve and the transmissibility curve of the simply supported beam is discussed. The results show that the fundamental frequency of the system can be significantly reduced by the negative stiffness device, while the frequencies of high-order modes are changed a little bit only. Increasing the horizontal spring stiffness will reduce the first-order resonance frequency and the initial frequency of vibration isolation. Consequently, the aim of lower frequency vibration isolation for the simply supported beam can be achieved. This paper provides an effective approach to the vibration isolating design of flexible structures.

Equivalent circuit for capacitive micromachined ultrasonic transducers to predict anti-resonances

Equivalent circuit models have been long used to evaluate the dynamics of the capacitive micromachined ultrasonic transducer (CMUT). An important parameter in the characterization of a CMUT is the anti-resonance frequency, which limits the immersion bandwidth. However, there is no equivalent circuit model that can accurately determine the anti-resonance frequency of a membrane. In this work, we present an improved lumped element parametric model for immersed CMUT. We demonstrate that the proposed equivalent circuit model accurately predicts anti-resonance and higher order mode frequencies, in addition to that of the fundamental mode. The proposed circuit model is in good agreement with device characteristics calculated using the finite element method and experimentally measured data.

Directivity Enhancement of a Circular Microstrip Antenna with Shorting Post

A technique of loading shorting posts on the patch has been used to enhance the directivity of a circular microstrip antenna (CMSA) in this paper. The shorting posts connected between the patch and the ground plane, force the electric field to become zero at that point, thereby modifying various modes of the circular patch. The shorting posts, also perturb the surface current distribution on the patch that help to increase its electrical size, which – in turn – enhances directivity at fixed resonance frequency. Investigations on various radii and positions of the shorting posts – to enhance the directivity of a CMSA, have been carried out. A systematic analysis on the performance of the CMSA at a lower order mode, fundamental mode and higher order mode frequencies with the loading of shorting posts has also been presented. The simulated and measured results show that the directivity of CMSA can be enhanced by up to 2 dB using the proposed technique without changing the patch geometry. In addition, the proposed antenna configuration yields, a bandwidth enhancement of almost three times as compared to that of a conventional CMSA. The simulated results of the conventional and shorted CMSA are experimentally validated with good agreement.

Analytical and numerical study of New field emitter processing for superconducting cavities

In this article a scientific prove for a new technology to maximize the accelerating gradient in superconducting cavities by processing on higher order mode frequencies is presented. As dominant energy source the heating of field emitters by an induced rf current (rf-heating) is considered. The field emitter structure is assumed to be a chain of conductive particles, which are formed by attractive forces.

Hybrid silencer transmission loss above a duct’s plane wave region

For large ducts, the removal of low frequency and tonal noise is normally achieved through the use of inefficient dissipative silencers; however, a combination of dissipative and reactive solutions could be more effective. But reactive noise control solutions are rarely applied to large diameter duct systems since it is commonly assumed that the low cut-on frequency of higher order modes severely restricts their efficiency. However, it is possible for a reactive silencer to remain operational outside of the plane wave region, provided the reactive elements are distributed across the cross-section of the duct. Of course, at higher frequencies, the sound field within a duct will have nonplane wave modal content, and the transmission loss is expected to differ compared to the plane wave condition. This effect is investigated here using numerical (FEM) predictions for hybrid dissipative-reactive parallel baffle silencers and the performance of the reactive elements is explored under different excitations. The effects of non-planar fields and individually excited modes are analyzed, and it is found that the frequency range over which quarter wave resonators contribute to transmission loss can be extended above the cut-on frequency of the duct by increasing the number of baffles.

Analysis of coupled-bunch instabilities for the NSLS-II storage ring with a 500 MHz 7-cell PETRA-III cavity

The NSLS-II storage ring is designed to operate with superconducting RF-cavities with the aim to store an average current of 500mA distributed in 1080 bunches, with a gap in the uniform filling for ion clearing. At the early stage of the commissioning (phase 1), characterized by a bare lattice without damping wigglers and without Landau cavities, a normal conducting 7-cell PETRA-III RF-cavity structure has been installed with the goal to store an average current of 25mA. In this paper we discuss our analysis of coupled-bunch instabilities driven by the Higher Order Modes (HOMs) of the 7-cell PETRA-III RF-cavity. As a cure of the instabilities, we apply a well-known scheme based on a proper detuning of the HOMs frequencies based upon cavity temperature change, and the use of the beneficial effect of the slow head–tail damping at positive chromaticity to increase the transverse coupled-bunch instability thresholds. In addition, we discuss measurements of coupled-bunch instabilities observed during the phase 1 commissioning of the NSLS-II storage ring. In our analysis we rely, in the longitudinal case, on the theory of coupled-bunch instability for uniform fillings, while in the transverse case we complement our studies with numerical simulations with OASIS, a novel parallel particle tracking code for self-consistent simulations of collective effects driven by short and long-range wakefields.

Ballistic thermal conductance by phonons through superlattice quantum-waveguides

Ballistic thermal conductances (BTCs) by phonons through superlattice quantum-waveguides are investigated by using the scattering-matrix method and the elastic continuum theory. A comparison for the cylindrical model (CM) and the rectangular model (RM) is addressed. We find that for these two models, the quantum thermal conductance can be observed even when the superlattices exist in quantum-waveguides. At low temperature, BTCs for the CM and the RM present almost the same behaviors regardless of the periodic length of superlattices. However, at higher temperature, BTCs for the RM are larger than those for the CM stemming from lower cutoff frequencies of high order modes for the RM. We also find that BTCs undergo a noticeable transformation from the monotonic decrease to constant with increasing the periodic number of superlattices. A brief analysis of these results is given.

MULTIBAND ANTENNA BASED ON LOADING A CPW-FED MONOPOLE WITH ONE CRLH-TL UNIT CELL

A Coplanar Waveguide (CPW)-fed monopole loaded with Composite Right/Left Handed Transmission Line (CRLH-TL) unit cell is presented in this letter. Multiband is achieved due to the nonlinear dispersion relation of the CRLH-TL unit cell. The CRLH-TL unit cell supports a fundamental LH wave (phase advance) at lower frequencies and a RH wave (phase delay) at higher frequencies. By loading CRLH-TL unit cells with a conventional monopole, the resonant frequency of higher order mode can be decreased, and zeroth-order mode or even negative-order mode can be achieved. As a result, the proposed antenna operates at 1.43GHz, 2.58GHz, 3.31GHz and 4.4GHz. Finally the modifled antenna is fabricated and measured; measurements and EM simulations are in a good agreement that conflrms the proposed theory.

Full three-dimensional approach to the design and simulation of a radio-frequency quadrupole

We have developed a new full 3D approach for the electromagnetic and beam dynamics design and simulation of a radio-frequency quadrupole (RFQ). A detailed full 3D model including vane modulation was simulated, which was made possible by the ever advancing computing capabilities. The electromagnetic (EM) design approach was first validated using experimental measurements on an existing prototype RFQ and more recently on the actual full size RFQ. Two design options have been studied, the original with standard sinusoidal modulation over the full length of the RFQ; in the second design, a trapezoidal modulation was used in the accelerating section of the RFQ to achieve a higher energy gain for the same power and length. A detailed comparison of both options is presented supporting our decision to select the trapezoidal design. The trapezoidal modulation increased the shunt impedance of the RFQ by 34%, the output energy by 15% with a similar increase in the peak surface electric field, but practically no change in the dynamics of the accelerated beam. The beam dynamics simulations were performed using three different field methods. The first uses the standard eight-term potential to derive the fields, the second uses 3D fields from individual cell-by-cell models, and the third uses the 3D fields for the whole RFQ as a single cavity. A detailed comparison of the results from TRACK shows a very good agreement, validating the 3D fields approach used for the beam dynamics studies. The EM simulations were mainly performed using the CST Microwave-Studio with the final results verified using other software. Detailed segment-by-segment and full RFQ frequency calculations were performed and compared to the measured data. The maximum frequency deviation is about 100 kHz. The frequencies of higher-order modes have also been calculated and finally the modulation and tuners effects on both the frequency and field flatness have been studied. We believe that with this new full 3D approach, the enhanced computing capabilities and the calculation precision the electromagnetic design software offer, we may be able to skip the prototyping phase and build the final product at once, although we recognize that prototyping is still needed to establish and validate the fabrication procedure.

Optoelectronic time-domain characterization of a 100 GHz sampling oscilloscope

We have carried out an optoelectronic measurement of the impulse response of an ultrafast sampling oscilloscope with a nominal bandwidth of 100 GHz within a time window of approximately 100 ps. Our experimental technique also considers frequency components above the cut-off frequency of higher order modes of the 1.0 mm coaxial line, which is shown to be important for the specification of the impulse response of ultrafast sampling oscilloscopes. Additionally, we have measured the reflection coefficient of the sampling head induced by the mismatch of the sampling circuit and the coaxial connector which is larger than 0.5 for certain frequencies. The uncertainty analysis has been performed using the Monte Carlo method of Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement’ and correlations in the estimated impulse response have been determined. Our measurements extend previous work which deals with the characterization of 70 GHz oscilloscopes and the measurement of 100 GHz oscilloscopes up to the cut-off frequency of higher order modes.

Analytical study of higher order modes of elliptical cavities using oblate spheroidal eigenvalue solution

The oblate spheroidal shape is close to the commonly used elliptical rf cavity shape employed in accelerators. Here we solve the oblate spheroidal radial and angular wave functions to obtain the frequencies of the axisymmetric TM and TE modes. We develop a semianalytic formalism to calculate the characteristic parameters, such as shunt impedance, of higher order modes (HOMs). Our formulation is applied to calculate the HOM frequencies of the INDUS-2 and ILC cavities, and the agreement with three-dimensional finite element calculations is excellent. Using this formalism we investigate the effect of changing the oblate shape, and predict an optimized range of ${\ensuremath{\xi}}_{0}$ (one of the key parameters to define the geometry), to reduce the number of significant HOMs.

Higher-Order-Mode Analysis of the PEFP Low-Beta Superconducting RF Linac

The low-beta elliptical superconducting RF (SRF) cavity is considered to accelerate a proton beam from 80 MeV to 178.6 MeV at 700 MHz in the linac of the Proton Engineering Frontier Project (PEFP). In order to understand the higher-order-mode (HOM) issues regarding the beam stabilities and the induced power in the PEFP low-beta SRF linac, in this paper, we analyze a normalized HOM-induced voltage, an induced power, and a time-averaged induced power, especially from the TM monopole modes. A HOM trapping possibility has been established by considering a manufacturing deviation of the HOM frequency and by studying the spectra of the monopole, the dipole, and the quadrupole modes in the low-beta SRF cavity. The HOM-induced power in the PEFP cavity has been calculated for different values of Qext. The discussion about beam instabilities shows that beam instabilities are not issues in the PEFP low-beta SRF linac. For the PEFP low-beta cavities, the HOM coupler’s Qext is lower than 3 × 10, reducing the influence of dangerous modes on the beam instabilities and the HOM-induced power.

Beam-breakup instability theory for energy recovery linacs

Here we will derive the general theory of the beam-breakup instability in recirculating linear accelerators, in which the bunches do not have to be at the same RF phase during each recirculation turn. This is important for the description of energy recovery linacs (ERLs) where bunches are recirculated at a decelerating phase of the RF wave and for other recirculator arrangements where different RF phases are of an advantage. Furthermore it can be used for the analysis of phase errors of recirculated bunches. It is shown how the threshold current for a given linac can be computed and a remarkable agreement with tracking data is demonstrated. The general formulas are then analyzed for several analytically solvable cases, which show: (a) Why different higher order modes (HOM) in one cavity do not couple so that the most dangerous modes can be considered individually. (b) How different HOM frequencies have to be in order to consider them separately. (c) That no optics can cause the HOMs of two cavities to cancel. (d) How an optics can avoid the addition of the instabilities of two cavities. (e) How a HOM in a multiple-turn recirculator interferes with itself. Furthermore, a simple method to compute the orbit deviations produced by cavity misalignments has also been introduced. It is shown that the BBU instability always occurs before the orbit excursion becomes very large.

Higher-order-mode (HOM) power in elliptical superconducting cavities for intense pulsed proton accelerators

In linacs for intense pulsed proton accelerators, the beam has a multiple time-structure, and each beam time-structure generates resonance. When a higher-order mode (HOM) is near these resonance frequencies, the induced voltage could be large and accordingly the resulting HOM power, too. In order to understand the effects of a complex beam time-structure on the mode excitations and the resulting HOM powers in elliptical superconducting cavities, analytic expressions are developed, with which the beam-induced voltage and corresponding power are explored, taking into account the properties of HOM frequency behavior in elliptical superconducting cavities. The results and understandings from this analysis are presented with the beam parameters of the Spallation Neutron Source (SNS) superconducting linac.

Exact determination of HOM frequency in storage ring RF cavity

A formula for the determination of higher-order mode (HOM) frequency in an active storage ring RF cavity is derived, which utilizes the frequency tuning mechanism of the low-level RF feedback system. It helps us to understand the behavior of coupled bunch instabilities in a storage ring whenever we change the operating beam current, the cavity gap voltage, and the ring RF frequency as well. This analysis includes the fundamental mode frequency detuning for beam loading and Robinson damping. At any operating conditions of the RF cavity, the HOM frequencies can be precisely calculated with the low-power measurement data of the frequency shift as a function of the tuner position. The formula shows a good agreement with the measurement results.

A variational calculation for higher order mode cutoff frequencies of a symmetrical strip line by conformal mapping

AbstractThe cutoff frequencies of higher order modes in a symmetrical strip line are calculated using the variational finite‐element method combined with conformal mapping. Conformal mapping is used to improve the modeling of the infinite transverse extents of a strip line. Then the finite‐element method is employed to solve the variational equation in the transformed finite region. Comparisons with numerical results found in the literature validate the presented method. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 32: 449–452, 2002.

Control of Deep-Hysteresis Aeroengine Compressors1

Frequencies of higher-order modes of fluid dynamic phenomena participating in aeroengine compressor instabilities far exceed the bandwidth of available (affordable) actuators. For this reason, most of the heretofore experimentally validated control designs for aeroengine compressors have been via low-order models—specifically, via the famous Moore-Greitzer cubic model (MG3). While MG3 provides a good qualitative description of open-loop dynamic behavior, it does not capture the main difficulties for control design. In particular, it fails to exhibit the so-called “right-skew” property which distinguishes the deep hysteresis observed on high-performance axial compressors from a small hysteresis present in the MG3 model. In this paper we study fundamental feedback control problems associated with deep-hysteresis compressors. We first derive a parametrization of the MG3 model which exhibits the right skew property. Our approach is based on representing the compressor characteristic as a convex combination of a usual cubic polynomial and a nonpolynomial term carefully chosen so that an entire family of right-skew compressors can be spanned using a single parameter ε. Then we develop a family of controllers which are applicable not only to the particular parametrization, but to general Moore-Greitzer type models with arbitrary compressor characteristics. For each of our controllers we show that it achieves a supercritical (soft) bifurcation, that is, instead of an abrupt drop into rotating stall, it guarantees a gentle descent with a small stall amplitude. Two of the controllers have novel, simple, sensing requirements: one employs only the measurement of pressure rise and rotating stall amplitude, while the other uses only pressure rise and the mass flow rate (1D sensing). Some of the controllers which show excellent results for the MG3 model fail on the deep-hysteresis compressor model, thus justifying our focus on deep-hysteresis compressors. Our results also confirm experimentally observed difficulties for control of compressors that have a high value of Greitzer’s B parameter. We address another key issue for control of rotating stall and surge—the limited actuator bandwidth—which is critical because even the fastest control valves are often too slow compared to the rates of compressor instabilities. Our conditions show an interesting trade-off: as the actuator bandwidth decreases, the sensing requirements become more demanding. Finally, we go on to disprove a general conjecture in the compressor control community that the feedback of mass flow rate, known to be beneficial for shallow-hysteresis compressors, is also beneficial for deep-hysteresis compressors. [S0022-0434(00)03101-4]