Higher Harmonics Induced by Waves Propagating over A Submerged Obstacle in the Presence of Uniform Current

To investigate higher harmonics induced by a submerged obstacle in the presence of uniform current, a 2D fully nonlinear numerical wave flume（NWF） is developed by use of a time-domain higher-order boundary element method（HOBEM） based on potential flow theory. A four-point method is developed to decompose higher bound and free harmonic waves propagating upstream and downstream around the obstacle. The model predictions are in good agreement with the experimental data for free harmonics induced by a submerged horizontal cylinder in the absence of currents. This serves as a benchmark to reveal the current effects on higher harmonic waves. The peak value of non-dimensional second free harmonic amplitude is shifted upstream for the opposing current relative to that for zero current with the variation of current-free incident wave amplitude, and it is vice versa for the following current. The second-order analysis shows a resonant behavior which is related to the ratio of the cylinder diameter to the second bound mode wavelength over the cylinder. The second-order resonant position slightly downshifted for the opposing current and upshifted for the following current.

Theory of higher harmonics imaging in tapping-mode atomic force microscopy

The periodic impact force induced by tip-sample contact in a tapping mode atomic force microscope （AFM） gives rise to the non-harmonic response of a micro-cantilever. These non-harmonic signals contain the full characteristics of tip-sample interaction. A complete theoretical model describing the dynamical behaviour of tip-sample system was developed in this paper. An analytic formula was introduced to describe the relationship between time-varying tip-sample impact force and tip motion. The theoretical analysis and numerical results both show that the timevarying tip-sample impact force can be reconstructed by recording tip motion. This allows for the reconstruction of the characteristics of the tip-sample force, like contact time and maximum contact force. It can also explain the ability of AFM higher harmonics imaging in mapping stiffness and surface energy variations.

Design of a higher harmonic cavity for the SSRF storage ring

Higher harmonic cavity used in the third generation synchrotron light source increases the Touschek lifetime. The higher harmonic cavity of Shanghai Synchrotron Radiation Facility （SSRF） is a 1.5 GHz passive superconducting cavity. Its higher order modes （HOM） are extracted by a ferrite HOM damper out of the cryostat. Multi-cell cavity is chosen concerning the voltage. The harmonic cavity dynamics, beam dynamics with passive harmonic cavity and the design of single cell cavity are included in this paper.

Higher harmonic voltage analysis of magnetic-alloy cavity for CSNS/RCS upgrade project

Background A rapid cycling synchrotron(RCS)in China Spallation Neutron Source(CSNS)would be upgraded,and the proton beam power will reach 200-500 kW.Three RF cavities loaded by magnetic-alloy(MA)material will be added in RCS tunnel to form a dual-harmonic RF system with eight ferrite-loaded cavities in RCS.The bandwidth of the MA cavity is wide because of its intrinsic Q value of less than 1.Higher harmonics can be excited in MA cavities,because the RF power is directly fed into the MA cavity from the final stage of the RF power amplifier.The distortion of voltage in the cavity gap caused by higher harmonics may deteriorate the beam quality.The influence of the higher harmonics to beam needs to be evaluated and the amplitude of higher harmonics should to be suppressed.Methods We built a mathematical model with two functions based on the RF bucket acceptance and bunch factor to evalu-ate this influence.Groups of harmful amplitudes and phases of higher harmonics were found according to the mathematical model by using multi-objective particle swarm optimization(MOPSO).Conclusion The dual-harmonic RF system with higher harmonics in CSNS/RCS and a suitable harmonic suppression for MA cavities was discussed according to the results of MOPSO and the beam dynamics simulations.

Higher order harmonics suppression in extreme ultraviolet and soft x-ray

The extreme ultraviolet and soft x-ray sources are widely used in various domains. Suppressing higher order harmonics and improving spectral purity are significant. This paper describes a novel method of higher order harmonics suppression with single order diffraction gratings in extreme ultraviolet and soft x-ray. The principle of harmonic suppression with single order diffraction grating is described, and an extreme ultraviolet and soft x-ray non-harmonics grating monochromator is designed based on the single order diffraction grating. The performance is simulated by an optical design software. The emergent beams of a monochromator with different gratings are measured by a transmission grating spectrometer. The results show that the single order diffraction grating can suppress higher order harmonics effectively, and it is expected to be widely used in synchrotron radiation, diagnostics of laser induced plasma, and astrophysics.

ADAPTIVE HARMONIC CANCELLATION APPLIED IN ELECTRO-HYDRAULIC SERVO SYSTEM WITH ANN

The method for harmonic cancellation based on artificial neural network (ANN)is proposed. The task is accomplished by generating reference signal with frequency that should beeliminated from the output. The reference input is weighted by the ANN in such a way that it closelymatches the harmonic. The weighted reference signal is added to the fundamental signal such thatthe output harmonic is cancelled leaving the desired signal alone. The weights of ANN are adjustedby output harmonic, which is isolated by a bandpass filter. The above concept is used as a basis forthe development of adaptive harmonic cancellation (AHC) algorithm. Simulation results performedwith a hydraulic system demonstrate the efficiency and validity of the proposed AHC control scheme.

Location of micro-cracks in plates using time reversed nonlinear Lamb waves

A promising tool to detect micro-cracks in plate-like structures is used for generating higher harmonic Lamb waves.In this paper,a method combining nonlinear S0 mode Lamb waves with time reversal to locate micro-cracks is presented and verified by numerical simulations.Two different models,the contact acoustic nonlinearity(CAN)model and the Preisach-Mayergoyz(PM)model,are used to simulate a localized damage in a thin plate.Pulse inversion method is employed to extract the second and fourth harmonics from the received signal.Time reversal is performed to compensate the dispersion of S0 mode Lamb waves.Consequently,the higher harmonics generated from the damaged area can be refocused on their source.By investigating the spatial distribution of harmonic wave packets,the location of micro-cracks will be revealed.The numerical simulations indicate that this method gives accurate locations of the damaged area in a plate.Furthermore,the PM model is proved to be a suitable model to simulate the micro-cracks in plates for generation of higher harmonics.

Higher Order Harmonics and its Application for Flux Mapping

This paper proposes a flux mapping method directly using the higher order harmonics (HOH) of the neutronics equation of the nominal core. The bi-orthogonality and completeness of the HOH set are studied. and they are the theoretical basis for the flux mapping method. Using the bi-orthogonality of HOH and the strict formula for eigenvalue estimation. the process and formulas for HOH calculation called as the source iteration method with source correction are derived. The analysis can predict any order of harmonics for 2-or 3-dimensional geometries.Preliminary verification of the capability for flux mapping is also given. and other applications of HOH for reactor operation analysis and failure diagnosis are underway.

Completeness of the Higher Order Harmonics

Applications using higher orderharmonics (HOH) require knowledge ofthe completeness ofthe HOHfor the diffusion difference equation.This papershowsthatthe set of HOHforthefission sourceis complete ,butthat the setfortheflux usingthe multi group modelis notcomplete .This paperusesthe assumption thatthe set offlux vectors of HOHfor every group is complete. This assumption can be proven only forthose groups into which noscattering neutrons enter.However,itisalso shownto betrueforseveralpracticalreactor models.Analysisshows thatthe number of HOHwith non zero eigenvaluesis equaltothe numberofdifference meshes withfissile material, and thatthe eigenvalues have positive realvalues.This assumptionis valuablefor HOHapplications,butrequires furthertheoreticalstudyto verify whetheritisuniversally applicable.

Quantitative research on higher order harmonics in metrology beamline

The synchrotron radiation spectra of the spherical grating monochromator(SGM)working in the soft X-ray and VUV region are often contaminated by significant amounts of higher order harmonics.They cannot be suppressed completely by suitable filters.Higher order contributions in the spectral radiation standard and metrology beamline were researched using transmission grating(made in-house)and IRD AXUV100G(USA)photodiode detector.The exit beam was dispersed with the transmission grating behind the exit slit of the monochromator,and the contributions of the different orders were analyzed.The higher order distributions were quantitatively determined for three gratings with line densities of 1800,600 and 200 l/mm.Experiment results show that in wavelengths between 5 nm and 15 nm the contributions of the higher orders to the detector signal are restricted to less than 7%even without the use of filters.In wavelength regions between 5 nm and 34 nm,the contributions of the higher orders to the detector signal are less than 14%with proper Al,Si_(3)N_(4) and Zr filters,and after being modified by quantum efficiency of the detector,the higher order contributions are restricted to less than 6.5%.The study also shows that higher orders are almost totally suppressed by MgF_(2) filter when the wavelength ranges between 115–140 nm.

Investigation on the fabrication of the 3rd harmonic superconducting cavity for the SSRF storage ring

A third harmonic superconducting niobium cavity has been proposed for installation in the Shanghai Synchrotron Radiation Facility （SSRF） storage ring to improve the Touschek lifetime. In order to investigate the feasibility of the superconducting cavity fabrication indigenously and the possibility to master the fabrica tion techniques, cavities were fabricated from copper and niobium sheets by deep drawing and electron-beam welding, and a series of measurements, such as resonant frequency, shape dimensions and wall thickness, were carried out during this process. After analysis of various problems existing in the fabrication process, technique improvements were proposed, and finally the precise shape as designed and resonant frequency within 1.2 MHz were achieved for the new completed cavities. In addition, full annealing was finally proved to be a good cure for niobium sheets＇ tearing up during deep drawing. By fabricating niobium cavities successfully, some problems to the next step were cleared. This paper introduces the process of cavity fabrication and its technique improvements towards forming, and the initial vertical test result of niobium cavity is also presented.

Active control for performance enhancement of electrically controlled rotor

Electrically controlled rotor （ECR） system has the potential to enhance the rotor perfor- mance by applying higher harmonic flap inputs. In order to explore the feasibility and effectiveness for ECR performance enhancement using closed-loop control method, firstly, an ECR rotor performance analysis model based on helicopter flight dynamic model is established, which can reflect the performance characteristics of ECR helicopter at high advance ratio. Based on the simulation platform, an active control method named adaptive T-matrix algorithm is adopted to explore the feasibility and effectiveness for ECR performance enhancement. The simulation results verify the effectiveness of this closed-loop control method. For the sample ECR helicopter, about 3% rotor power reduction is obtained with the optimum 2/rev flap inputs at the advance ratio of 0.34. And through analyzing the distributions of attack of angle and drag in rotor disk, the underlying physical essence of ECR power reduction is cleared. Furthermore, the influence of the key control parameters, including convergence factor and weighting matrix, on the effectiveness of closed-loop control for ECR performance enhancement is explored. Some useful results are summarized, which can be used to direct the future active control law design of ECR performance enhancement.