Sixth Harmonics Research Articles

Spectra of standing kink waves in loops and the effects of the lower solar atmosphere

Understanding the effects of the lower solar atmosphere on the spectrum of standing kink oscillations of coronal loops, in both the decaying and decayless regime, is essential for developing more advanced tools for coronal seismology. We aim to reveal the effects of the chromosphere on the spatial profiles and frequencies of the standing kink modes, create synthetic emission maps to compare with observations, and study the results using spatial and temporal coronal seismology techniques. We excited transverse oscillations in a 3D straight flux tube using (a) a broadband footpoint driver, (b) a sinusoidal velocity pulse, and (c) an off-centre Gaussian velocity pulse, using the PLUTO code. The flux tube is gravitationally stratified, with footpoints embedded in chromospheric plasma. Using the FoMo code, we created synthetic observations of our data in the Fe IX 17.1 nm line and calculated the spectra with the Automatic Northumbria University Wave Tracking code. We also numerically solved the generalised eigenvalue system for the 1D wave equation to determine the effects of the stratification on the kink modes of our system. The synthetic observations of the loops perturbed by the velocity pulses show a single dominant mode that our 1D analysis reveals to be the third harmonic of the system. For the broadband driver, the synthetic emission shows multiple frequency bands, associated with both the loop and the driver. Finally, using seismological techniques, we highlight the possibility of misidentifying the observed third, sixth, and ninth harmonics with the first, second, and third harmonics of the coronal part of the loop. Unless more advanced techniques of spatial seismology are used with many data points from observations along the entire loop length, this misidentification can result in overestimating the mean magnetic field by a factor equal to the period ratio of the fundamental over the third harmonic. For longer coronal loops it is easy to misidentify the detected standing kink modes for lower-order modes of the system, which can have important seismological implications. To prevent these errors and properly constrain the value of the estimated mean magnetic field, additional observations of the loops footpoints using transition region and chromospheric lines are necessary.

Influence of Stator/Rotor Torque Ratio on Torque Performance in External-Rotor Dual-Armature Flux-Switching PM Machines

External-rotor dual-armature flux-switching PM (ER-DA-FSPM) machines have high torque density and decent fault tolerance, making them promising candidates for in-wheel machine applications in electric vehicles. The torque output and optimal design parameters of ER-DA-FSPM machines are affected by the stator/rotor torque ratio, which is the focus of this paper. Firstly, this paper analyzes airgap flux density harmonics of ER-DA-FSPM to provide a clear insight into the torque-generation mechanism. Then, this paper investigates the influence of torque ratio on average torque under the same copper loss. It is found that the average torque decreases with torque ratio increasing due to the reduction of the positive torque component generated by the sixth airgap field harmonics and the rise in the negative torque component from the eighth harmonics. Moreover, this paper also provides the optimal parameter recommendation to guide the machine design. The split ratio should increase, and the arc of PMs should decrease for a larger torque ratio, whilst the other parameters are hardly influenced. Next, this paper makes a comparison among the ER-DA-FSPM machine, external rotor flux-switching PM (ER-FSPM) machine, and surface-mounted PM (ER-SPM) machines. It shows that the ER-DA-FSPM machine, with the torque ratio being 2, can lead to a much larger total torque. In addition, in the event of rotor winding failure, which is more possible due to the existence of slip rings than stator winding failure, the stator can still provide an average torque larger than that of ER-SPM machine and 92.0% that of the ER-FSPM machine, respectively. Finally, the theoretical analysis is verified by the experiments.

Dead‐time compensation for PMSM with phase shift of impedance considered based on adaptive linear neuron method

AbstractA new adaptive‐linear‐neuron‐ (ADALINE‐) based dead‐time compensation method is presented for permanent magnet synchronous motor (PMSM) drives. It is proposed to suppress the sixth current harmonics adaptively in the synchronous reference frame due to dead‐time effects. In order to extract the sixth current harmonics, two ADALINE‐based extractors are used without taking into account the electrical lead angle. An improved ADALINE algorithm is used to calculate compensation voltages, taking into account the phase shift of impedance. The proposed method is capable of operating not only at low speed but also at medium and rated speeds in contrast to the traditional compensation method of ADALINE only at low speed. The new method is effective in steady, load dynamic and speed dynamic states with no needs for any extra hardware to detect phase current polarity. The effectiveness of the proposed compensation method is verified on a 780 W PMSM drive through experiments.

Design of Miniaturized 90-Degree Hybrid Coupler with Wide Rejection Band Using Neural Network.

In this paper, a 3 dB 90-degree hybrid coupler with size reduction and harmonics rejection was designed. In the proposed coupler structure, four simple low-pass filters (LPFs) were applied. An artificial neural network (ANN) was used to determine the dimensions of the applied LPFs based on EM simulation data. The applied ANN model could also provide the desired LPF parameters, including the cut-off frequency (fc), bandwidth (BW), and insertion loss (IL). Designing an applied LPF involves complex mathematical calculations and simulations to optimize parameters. However, by utilizing neural networks, the design process can be significantly streamlined and automated. Neural networks have the ability to learn complex patterns and relationships within data, making them well suited for optimizing the performance of applied components. The proposed 90-degree hybrid coupler works correctly at 1800 MHz and has a small size of 16.6 mm × 15.15 mm, which provides a 73% size reduction compared to a normal 1800 MHz coupler. The designed coupler not only decreases the circuit size but also provides a wide rejection band from 4.8 GHz to 11.2 GHz, which suppresses the second to sixth harmonics. The insertion loss parameter of this 90-degree hybrid coupler is less than 0.1 dB at the working frequency, which shows the superior performance of the proposed coupler.

EMIC Wave Energy Dissipation as a Source of O+ Conics and Warm Plasma Cloak in the Earth's Inner Magnetosphere

AbstractThis study focuses on a specific source of the O+ conics and warm plasma cloak in the Earth's inner magnetosphere due to electromagnetic ion cyclotron (EMIC) wave energy dissipation. We analyze the EMIC wave event observed by Van Allen Probe‐A in the early afternoon off equatorial magnetosphere on 18 November 2015, where the two dominant EMIC wave bands, He+‐band and H+‐band, were observed for ∼4 min. All the wave and plasma parameters, the DC magnetic field, and ion distributions needed for our analysis are taken from the Van Allen Probe‐A observations during the event. The major results of our analysis are as follows. (a) The H+ and He+ heating by EMIC waves is negligible. (b) A strong heating of O+ by the wave energy dissipation around the third, fifth, and sixth harmonics of the O+ gyrofrequency is revealed, where the majority of energy dissipated goes into heating of O+ with the energies ≲100 eV and pitch angles ∼20°–90°. The estimated energy deposition rate is ∼0.1–3.4 eV/s per O+, totaling to the deposition of ∼20–800 eV per O+ during the event. (c) EMIC waves substantially contribute to the formation of O+ conics and warm plasma cloak by heating the upgoing low‐energy ionospheric O+ because waves heat ions with the energies and pitch angles that are characteristic of conics and warm plasma cloak, and the energy deposition per O+ is comparable to those characteristic energies.

АНАЛІЗ РЕЗУЛЬТАТІВ ЕКСПЕРИМЕНТАЛЬНИХ ДОСЛІДЖЕНЬ НЕОДНОРІДНОСТІ МЕРЕЖІ ПОСТІЙНОГО СТРУМУ

The modes of breakage of one line of network sections with parallel lines in electrical distribution networks of power supply to consumers of direct current electric transport have been studied. An analysis of the experimental data was carried out, the results of which indicate the presence of a dependence of the value of the variable component in the rectified current on the distance to the damaged area. Mathematical modeling of the breakage mode of one of the line sections in the network with a serial connection of three sections, each of which has parallel lines, has been carried out. The obtained results of mathematical modeling of the modes of operation of a direct current network with heterogeneity of different sections also indicate the possibility of using the sixth harmonic of the current to determine the occurrence of heterogeneity and the section with this heterogeneity. To reduce the influence of load changes when determining an inhomogeneous section, it is proposed to control the input impedance of the network at a frequency of 300 Hz. It has been established that in these regimes the resistance angle changes the most. A method for determining the occurrence of local damage to a direct current line and the distance to this damage location is proposed, which is based on moni-toring the value of the line current and the input resistance of the line at a frequency of 300 Hz. References 7, Figures 4, Tables 2.

Design a Wilkinson power divider with improved passband and rejection band

ABSTRACT In this paper, a Wilkinson power divider based on a new harmonic suppressor structure is proposed with suppressed harmonics and improved operating band parameters. The proposed suppressor structure consists of three resonators. The first resonator is an elliptic rectangular shaped resonator with a short base line and two slots. These slots decrease the resonant frequency location, without changing the dimensions of the resonator. This mode has been fully analysed by investigating the effect of surface current density. The second resonator is an elliptic resonator with a long base length to suppress the second harmonic. The third resonator is a rectangular suppressor to suppress higher order harmonics. The proposed power divider is fabricated and measured. The operating frequency of this power divider is 1.26 GHz, the return loss is 31.5 dB and the insertion loss is 3.1 dB. The operating bandwidth is from 0.99 to 1.4 GHz with a return loss better than 15 dB which shows the fractional bandwidth of FBW = 34%. The second to sixth harmonics have suppression level better than 50 dB, and for higher harmonics up to the 14th harmonic, they have suppression level better than 25 dB.

A Compact Filtering Coupler with Unwanted Harmonic Rejection Using LC Composite Lines for Communication Systems Applications

In this paper, new LC lumped components and composite lines are used to create a filtering branch line coupler (FBLC) with a small size and wide suppression band. New composite lines are proposed using applied LC lumped components, which are used as the coupler main branches. The proposed FBLC suppresses second to sixth harmonics with high attention level and provides a wide stopband from 1.6 GHz to 5 GHz with more than 20 dB of attention. The presented coupler is analyzed, designed, simulated, and implemented. The measured results show that the proposed FBLC correctly operates at 800 MHz with less than 0.25 dB of insertion loss. In addition, more than 29 dB of return loss and isolation is measured at operating frequency, which shows the correct performance of the proposed design. The size of the proposed FBLC is equal to 23.7 mm × 25.5 mm (0.086λ × 0.093λ), which shows an 87% size reduction. The proposed FBLC with the designed frequency can be used in the communication systems for narrow-band Internet of things (NB-IoT) and traffic control radar applications.

Electromagnetic Ion Cyclotron Harmonic Waves Generated via Nonlinear Wave‐Wave Couplings

AbstractIn this letter, we report an electromagnetic ion cyclotron (EMIC) harmonic event observed by the Van Allen Probe B, whose generation is demonstrated to result from nonlinear wave‐wave resonances through the bicoherence analysis. Hybrid simulation shows that the second to sixth harmonics could be excited in sequence after a pump EMIC wave is initially injected, which is in consistent with the observations of EMIC harmonic. It indicates the important role of the second harmonic in the generation of higher harmonics. Finally, the statistical distribution for the amplitude of EMIC second harmonic waves indicates that the energy transfer rate from the fundamental wave to the second harmonic is mainly less than 2%, which might be too low to result in third and other higher harmonics above the observational level. Our results will give some new insights into the excitation of EMIC harmonic waves in the inner magnetosphere.

Excitation of high cyclotron harmonics in a high-current relativistic gyrotron in the frequency multiplication regime

Using the averaged equations supplemented with 3D particle-in-cells simulation methods, we have studied the frequency multiplication regime in a high-current relativistic gyrotron. The paper shows that the ratio between the output power of the higher (fifth or sixth) harmonics and that of the fundamental cyclotron resonance may be of about 0.1-0.3%. Accordingly, the nonlinear transformation coefficient is several orders of magnitude higher than the values achievable in gyrotrons with weakly-relativistic electron beams. Keywords: gyrotron, harmonic excitation, high-current relativistic electron beams.

Возбуждение высоких циклотронных гармоник в сильноточном релятивистском гиротроне в режиме умножения частоты

Using the averaged equations supplemented with 3D particle-in-cells simulation methods, we study the frequency multiplication regime in high-current relativistic gyrotron. We show that the ratio between the output power of the higher (fifth or sixth) harmonics and that on the fundamenta cyclotron resonance may be of about 0.1-0.3%. Accordingly, the nonlinear transformation coefficient as several orders higher than the values achievable in gyrotrons with weakly relativistic electron beams.

First observation of laser-beam interaction in a dipole magnet

As a new-generation light source, free-electron lasers (FELs) provide high-brightness X-ray pulses at the angstrom-femtosecond space and time scales. The fundamental physics behind the FEL is the interaction between an electromagnetic wave and a relativistic electron beam in an undulator, which consists of hundreds or thousands of dipole magnets with an alternating magnetic field. Here, we report the first observation of the laser-beam interaction in a pure dipole magnet, in which the electron beam energy modulation with 40-keV amplitude and 266-nm period is measured. We demonstrate that such an energy modulation can be used to launch a seeded FEL, that is, lasing at the sixth harmonic of the seed laser in a high-gain harmonic generation scheme. The results reveal the most basic process of the FEL lasing and open up a new direction for the study and exploitation of laser-beam interactions.

Reactive power characteristics and vibration properties under SISC in synchronous condensers

A stator interturn short-circuit (SISC) fault in synchronous condensers can bring about serious damage if the fault is not detected in time. At present, researches on SISC fault characteristics and diagnosis methods are still scarce because only in recent years are synchronous condensers adopted in power grids. Different from previous studies, this paper considers the practical operation condition of synchronous condensers that need to change exciting current frequently and work in either under-excitation or over-excitation according to the actual demand of power grids. Detailed reactive power and unbalanced magnetic pull (UMP) expressions under SISC are deduced firstly based on the analysis of the magnetic flux density variation. It can be seen that the reactive power increases under under-excitation running and decreases under over-excitation running after SISC. The second, fourth and sixth harmonics of stator UMP/vibration are enlarged under the SISC. Specifically, the sixth harmonic augments with the increase of exciting current in the over-excitation running, while the variation of the sixth harmonic with exciting current depends on parameters and fault degree of synchronous condensers under the under-excitation operation. Moreover, the two-dimensional finite-element analysis (FEA) and experimental tests are performed on a customized synchronous machine. In addition, the FEA of a TTS-300-2 synchronous condenser is accomplished in order to validate the proposed theoretical analysis further. The research conclusions of fault characteristics in this paper provide potential solutions for the monitoring and diagnosis of SISC in synchronous condensers.

Parasitic Effects of PWM-VSI Control Leading to Torque Harmonics in AC Drives

Precise torque control without pulsations is one of the major quality issues in pulse-width modulated voltage-source inverter (PWM-VSI) drives. Theoretically, it could be postulated that at frequencies of some kHz, the machine’s inertia absorbs switching frequency torque harmonics, and the resulting torque becomes smooth; though, in reality, parasitic effects in voltage source inverters may cause additional torque harmonics of low order. In particular, first, second and sixth torque harmonics are observed. Such torque harmonics are especially dangerous for normal drive operation, since they may be amplified by drive train resonances at corresponding rotational velocities. New parasitic effects in PWM-VSI control, leading to torque harmonic of low order, are described in the paper, and recommendations for their compensation are given.

Flux-Weakening Control of Dual Three-Phase PMSM Based on Vector Space Decomposition Control

This article proposes a flux-weakening (FW) control for dual three-phase permanent magnet synchronous machine (DTPMSM) based on vector space decomposition (VSD) control, where the output voltage in αβ subplane is employed for voltage feedback in the FW control loop. As the fundamental components are mapped to αβ subplane while the fifth and seventh harmonics are projected to harmonic z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> subplane, the FW current from this new control in αβ subplane is sixth harmonic-free regardless of the fifth and sixth harmonics being resulted from the nonsinusoidal back electromotive force (EMF) or inverter nonlinearity. The proposed control is compared with the conventional FW feedback control extended for DT-PMSM, where the FW control is applied to the two sets of three-phase windings separately. The experimental results show that the proposed FW control based on VSD is superior to the conventional FW control in terms of reduction in current unbalance and harmonic currents.

Ultrawideband Harmonic Suppression in Microstrip Patch Antenna Using Novel Defected Ground Structures

Suppressing higher-order modes up to sixth harmonics of the fundamental working frequency in a single-layer microstrip line-fed patch antenna has been successfully demonstrated. Higher-order modes of the antenna are suppressed by simultaneously employing a circular head open stub connected to the feed line and a novel defected ground structure (DGS) beneath the feed line. The filtering property of the antenna has been improved by the novel DGS significantly. The role played by the novel DGS is carefully analyzed, and the effect of some key parameters of DGS is further discussed. A microstrip patch antenna with the working frequency 3.13 GHz (fc) is designed and manufactured. The designed antenna possesses an ultrawideband harmonic suppression capability ranging from 2fc to 6fc. More importantly, the area occupied by the novel DGS is decreased by 41% compared to the earlier design.

Small non-sphericity of a convergent shock wave arising in a cavitation bubble in acetone during its collapse

A numerical study of the features of the growth of small deformations of a radially-convergent shock wave in a collapsing cavitation bubble in acetone has been performed. The liquid temperature and pressure are 273.15 K and 15 bar, respectively. At the beginning of collapse, the bubble radius is 500 μm, the bubble is filled with the saturated vapor of acetone. The initial bubble non-sphericity in the form of the second, fourth and sixth spherical harmonics are considered. The dynamics of the vapor in the bubble and the surrounding liquid are governed by the axisymmetric gas dynamics equations closed by wide-range equations of state. The bubble surface is explicitly traced. It is shown that the small non-sphericity of the shock wave during its convergence, similarly to that of the surface of a bubble during its collapse, increases with decreasing its radius in the form of oscillations with growing amplitude. Moreover, the dependence of the increase in the amplitude of those oscillations on the radius of the shock wave in the interval from its formation to its reaching the “hot” bubble nucleus with a radius r < 0.25 μm, can be described by a power law with an index of -1.18.

High‐Order Solar Migrating Tides Quench at SSW Onsets

AbstractSudden stratospheric warming events (SSWs) are the most spectacular atmospheric vertical coupling processes, well‐known for being associated with diverse wave activities in the upper atmosphere and ionosphere. The first four solar tidal harmonics have been reported as being engaged. Here, combining mesospheric winds detected by three midlatitude radars, we demonstrate at least the first six harmonics that occurred during SSW 2018. Wave number diagnosis demonstrates that all six harmonics are dominated by migrating components. Wavelet analyses reveal that the fourth, fifth, and sixth harmonics quench after the SSW onset. The six harmonics and the quenching appear also in a statistical analysis based on near‐12‐year observations from one of the radars. We attribute the quenching to reversal of the background eastward wind.

The 27-day periodicity and its sub harmonics

Significant short-term variations of ≈1.7, ≈2.4, ≈2.8, ≈3.3, ≈3.8 days periods are found when high resolution data (five minutes average) of interplanetary electric field (Ey), south ward component of magnetic field (Bz) and geomagnetic index (AE) is subjected to wavelet analysis. The fourth, fifth, sixth sub harmonics of ≈27-day period, and few other short-term periods are significantly reported by Singh and Badruddin (Astrophys. Space Sci. 359:60, 2015a; Solar Phys. 290:3071, 2015b and Solar Phys. 294:27, 2019) in cosmic ray intensity, geomagnetic activity index and various solar wind plasma and field parameters. The reported and observed periods ≈6.8 day, ≈5.5 day, ≈4.4 day, ≈3.9 day, ≈3.4 day, ≈3.0 day, ≈2.8 day, ≈2.4 day, ≈2.2 day, ≈2.0 day, ≈1.9 day, ≈1.8 day; and ≈1.7 day are close to integral multiples of 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15 and 1/16 of one solar rotation period (≈27.0 day), hence these periods could be sub harmonics of fundamental period (≈27 day). If so, then these results lead to infer some sort of continuous simultaneous oscillations of active regions having integral multiple frequencies and varying amplitudes occurring on the solar disc.

Aerodynamic Analyses on the Steady and Unsteady Loading-Noise Sources of Drone Propellers

This study investigated the small drone propeller noise, particularly the discrete blade passing frequency (BPF) tone and its harmonics at low frequencies less than 1000 Hz. The unsteady Reynolds-averaged Navier–Stokes equations were solved to investigate the steady and unsteady loading noise sources around the blades with a radius of 17 cm rotating at 5000 rpm (a blade tip Mach number is 0.264). The uRANS computations showed eccentric ellipsoidal isobaric surfaces on the upper and lower blade surfaces identified as a steady loading noise source of the drone propeller. A simple mathematical model of an ellipsoidal steady loading noise with the lattice Boltzmann method predicted the BPF tone and even-number harmonics comparable to NASA’s SPL measurement of two different APC 1147 SF and DJI 9443 CF drone propellers. The decaying rate of $$- 6$$ in the SPL spectrum was quite closely matched for the first two discrete tones. The transient pressure fluctuation characteristics on the upper surface of the rotating blades revealed that the unsteady loading noise by blade–vortex interactions is found most closely related to the third and sixth harmonics of the round per second noise. An unexpected fifth component also arose in some other rotational speeds because of the random nature of the phase difference of pressure fluctuations, even at the same positions of the two propeller blades.