Frequency Sweep Rate Research Articles

Fine Structure of Magnetospheric Magnetosonic Waves: 1. Elementary Rising‐Tone Emissions Within Individual Harmonic

AbstractThe present study uncovers the fine structures of magnetosonic waves by investigating the EFW waveforms measured by Van Allen Probes. We show that each harmonic of the magnetosonic wave may consist of a series of elementary rising‐tone emissions, implying a nonlinear mechanism for the wave generation. By investigating an elementary rising‐tone magnetosonic wave that spans a wide frequency range, we show that the frequency sweep rate is likely proportional to the wave frequency. We studied compound rising‐tone magnetosonic waves, and found that they typically consist of multiple harmonics in the source region, and may gradually become continuous in frequency as they propagate away from source. Both elementary and compound rising‐tone magnetosonic waves last for ∼1 min which is close to the bounce period of the ring proton distribution, but their relation is not fully understood.

Line integrated density measurements on the Versatile Experiment Spherical Torus (VEST) using frequency sweep interferometer

A frequency sweep interferometer (FSI) operating in the frequency range of 50–75 GHz is installed in the versatile experiment spherical torus spherical tokamak to measure the line integrated density (LID). FSI measures the time derivative of phase to calculate the group delay, which is proportional to the LID under the condition that the microwave frequency is much higher than the plasma frequency. Since the group delay is calculated from the time derivative of phase and the frequency sweep rate, FSI is very sensitive to the measurement noise. In the view point of signal processing, derivative exaggerates the measurement noise. Therefore, sophisticated techniques for phase measurement and frequency linearization are required to obtain meaningful results with FSI. The detailed techniques and the hardware setup are explained in the paper. The LID measured by FSI is benchmarked with the LID measured by a conventional 94 GHz heterodyne interferometer. The two measurements agree well. A conventional interferometer can no longer provide LID when severe phase errors occur. This is because phase errors propagate to subsequent measurements. However, FSI provides LID during the entire discharge time successfully regardless of frequent measurement failure because the LID is obtained in FSI from the time derivative of phase rather than the phase. In this sense, FSI is suitable as a diagnostics for steady state plasmas. The main cause for the phase errors is identified as the beam path displacement due to the refraction of the plasma.

SNR Improvement of Optical Frequency Domain Polarimetry Against Laser Frequency Sweep Nonlinearity

A high-precision measurement of distributed polarization crosstalk (DPC) is necessary for developing the device with an ultrahigh polarization extinction ratio of even more than 80 dB. Optical frequency domain polarimetry (OFDP) is a novel DPC measurement method with a potential ultra-wide dynamic range. The degradation of dynamic range caused by interference phase error is a common issue in optical frequency domain measurement techniques. In this work, we enhanced the dynamic range by solving the phase error problem induced by the laser frequency sweep nonlinearity to improve the measurement precision of weak polarization crosstalk. The aliasing issue caused by the fluctuation of the frequency sweep rate is the primary reason for the limited dynamic range. We proposed a modified dynamic range limit model of OFDP considering the aliasing issue. The experimental results agree with the inflection points predicted by the modified dynamic range limit model. Under the guidance of the model, we achieved a dynamic range of more than 115 dB with different optical path differences of the interferometer and various sweep rates of the laser. Compared to the DPC measurement method with a dynamic range of 100 dB, the measurement repeatability is improved from 7.0 dB to <1.0 dB for polarization crosstalk less than -95 dB.

Acoustically Evoked Compound Action Potentials Recorded From Cochlear Implant Users With Preserved Acoustic Hearing.

Less traumatic intracochlear electrode design and the introduction of the soft surgery technique allow for the preservation of low-frequency acoustic hearing in many cochlear implant (CI) users. Recently, new electrophysiologic methods have also been developed that allow acoustically evoked peripheral responses to be measured in vivo from an intracochlear electrode. These recordings provide clues to the status of peripheral auditory structures. Unfortunately, responses generated from the auditory nerve (auditory nerve neurophonic [ANN]) are somewhat difficult to record because they are smaller than the hair cell responses (cochlear microphonic). Additionally, it is difficult to completely segregate the ANN from the cochlear microphonic, complicating the interpretation and limiting clinical applications. The compound action potential (CAP) is a synchronous response of multiple auditory nerve fibers and may provide an alternative to ANN where the status of the auditory nerve is of primary interest. This study is a within-subject comparison of CAPs recorded using traditional stimuli (clicks and 500 Hz tone bursts) and a new stimulus (CAP chirp). We hypothesized that the chirp stimulus might result in a more robust CAP than that recorded using traditional stimuli, allowing for a more accurate assessment of the status of the auditory nerve. Nineteen adult Nucleus L24 Hybrid CI users with residual low-frequency hearing participated in this study. CAP responses were recorded from the most apical intracochlear electrode using a 100 μs click, 500 Hz tone bursts, and chirp stimuli presented via the insert phone to the implanted ear. The chirp stimulus used in this study was CAP chirp generated using parameters from human-derived band CAPs ( Chertoff et al. 2010 ). Additionally, nine custom chirps were created by systematically varying the frequency sweep rate of the power function used to construct the standard CAP chirp stimulus. CAPs were recorded using all acoustic stimuli, allowing for within-subject comparisons of the CAP amplitude, threshold, percentage of measurable CAP responses, and waveform morphology. Considerable variation in response morphology was apparent across stimuli and stimulation levels. Clicks and CAP chirp significantly evoked identifiable CAP response more compared to 500 Hz tone bursts. At relatively high stimulation levels, the chirp-evoked CAPs were significantly larger in amplitude and less ambiguous in morphology than the click-evoked CAPs. The status of residual acoustic hearing at high frequencies influenced the likelihood that a CAP could be reliably recorded. Subjects with better preserved hearing at high frequencies had significantly larger CAP amplitudes when CAP chirp was used. Customizing the chirp stimulus by varying the frequency sweep rates significantly affected the CAP amplitudes; however, pairwise comparisons did not show significant differences between chirps. CAPs can be measured more effectively using broadband acoustic stimuli than 500 Hz tone bursts in CI users with residual low-frequency acoustic hearing. The advantage of using CAP chirp stimulus relative to standard clicks is dependent on the extent of preserved acoustic hearing at high frequencies and the stimulus level. The chirp stimulus may present an attractive alternative to standard clicks or tone bursts for this CI population when the goal is to record robust CAP responses.

Statistical Analysis of Electromagnetic Ion Cyclotron Rising‐Tone Emissions Based on Deep Learning

AbstractSeveral studies have shown the importance of electromagnetic ion cyclotron (EMIC) rising‐tone emissions to the rapid precipitation of energetic radiation belt electrons. Based on a large number of Van Allen Probes observations from October 2012 to July 2019, we identify EMIC rising‐tone emissions using a convolutional neural network (CNN), a modern deep learning technique. Results of training indicate that the CNN is capable of identifying EMIC rising‐tone emissions with a recall of 99.3%. The statistical analysis of the wave events identified reveals that the average occurrence rate of the events is about 0.016%, with a high occurrence rate from the forenoon to the dusk sector at L &gt; 5. There are also events observed at L &lt; 5, which are scattered at almost all magnetic local times. The events in the hydrogen and helium bands have comparable wave amplitudes on average, but the larger amplitude events tend to occur around noon and in the afternoon sector in the hydrogen and helium bands, respectively. In addition, the frequency sweep rate tends to increase with the wave frequency. The frequency sweep rates of the hydrogen band EMIC rising‐tone emissions are about 6 times larger than those of the helium band events. There is also a positive correlation between the wave amplitudes and the sweep rates of the hydrogen band emissions.

Off-equatorial effects of the nonlinear interaction of VLF chorus waves with radiation belt electrons

Nonlinear processes are involved in both the growth of VLF chorus waves and the energization of radiation belt electrons trapped in the wave potential. Nonlinear theory has led to analytic formulae describing both these processes. To investigate these processes, observations from the Van Allen Probes twin spacecraft provide simultaneous in situ information on VLF chorus waves, radiation belt and injected electrons, and local plasma parameters. We combine the theoretical treatment summarized by Omura (2021) with these in situ observations to investigate the characteristics and effects of nonlinear radiation belt processes at the off-equatorial location of the spacecraft observations. We show the smooth phase transition between initial subpackets of chorus wave elements, conducive to extended trapping and enhancement of resonant electrons. The structure of the chorus wave element changes as it propagates away from the equator. Frequency dispersion due to the variation of parallel wave group velocity with frequency contributes to the chorus waveform frequency sweep rate observed at an off-equatorial location. Nonlinear damping at the local value of ½ fce progressively erodes wave amplitude at frequencies above ½ fceEQ. We examine the important dependencies of the nonlinear inhomogeneity factor on the time rate of change of the wave frequency and the field-aligned gradient of the magnetic field and discuss their implication for the energization of trapped non-relativistic and MeV electrons. The 0.5–2% energy gain we find for 3–6 MeV seed electrons indicates that prompt local acceleration of highly relativistic and ultra-relativistic radiation belt electrons can take place directly through their nonlinear interaction with an individual VLF chorus wave element.

Simultaneous distance and vibration mapping of FMCW-LiDAR with akinetic external cavity diode laser

In this study, the simultaneous distance and vibration mapping of frequency-modulated continuous-wave light detection and ranging (FMCW-LiDAR) is performed using an electro-optical external cavity diode laser (ECDL). Owing to the akinetic operation regime of the ECDL, a uniform (R2 = 1.0000) interference signal can be generated over a bandwidth of 1 GHz at an optical frequency sweep rate of 10 kHz without any postprocessing or system for linearization. Furthermore, the proposed ECDL exhibits a high optical frequency sweep rate of 200 kHz with a considerable linearity of R2 = 0.99975. Based on a point sensing experiment using the FMCW-LiDAR system, three measurands, namely, distance, vibration frequency, and vibration velocity change, are demonstrated with a highly linear relationship between the beat frequency and amplitude of each individual parameter. Furthermore, temporal variations in multiple targets with rapidly frequency-varying vibrations, such as those occurring in music or voice sounds, can be successfully acquired by tracking the temporal change in the beat frequency of each target. Moreover, three-dimensional (3D) mapping of distance, vibration frequency, and vibration velocity change is simultaneously implemented in the same 3D space. The results show that the proposed FMCW-LiDAR system can be used for the 3D visualized display of various measurands within the same space frame.

Error revising of blade tip-timing parameter identification caused by frequency sweep rate

Blade tip-timing (BTT) is a rotating blade vibration measurement technology. It is a universal and effective method to acquire blade tip displacement data by frequency sweep and identify vibration parameters by single-parameter method. However, when the frequency sweep rate is too large, the vibration parameters obtained by single-parameter method will have large errors because the transient response cannot be immediately attenuated. For this problem, a dimensionless frequency sweep parameter is introduced, and two methods are proposed in this paper. When the engine order is known, an improved single-parameter method is proposed. For the unknown engine order, a revised method of vibration parameters is proposed. The effectiveness of the proposed two methods has been verified by simulation and experiment data. The results showed that when the frequency sweep parameter is between 0.3 and 15, the improved method and the revised method both significantly improve the vibration parameter identification accuracy.

Dynamic Distance Measurement Based on a Fast Frequency-Swept Interferometry.

To improve the precision of dynamic distance measurement based on the frequency-swept interferometry (FSI) system, a Doppler-induced error compensation model based on a scheme increasing the frequency sweeping rate is proposed. A distance demodulation method based on a Fourier transformation is investigated when the defined quasi-stationary coefficient approaches a constant. Simulations and experiments based on dynamic distance with a sinusoidal change demonstrate that the proposed method has a standard deviation of 0.09 μm within a distance range of 4 μm at a sweeping rate of 60 KHz.

Error Revising of Blade Tip-Timing Parameter Identification Caused by Frequency Sweep Rate

Error Revising of Blade Tip-Timing Parameter Identification Caused by Frequency Sweep Rate

Fine Structure of Chorus Wave Packets: Comparison Between Observations and Wave Generation Models

AbstractIntense lower band chorus waves are ubiquitous in the inner magnetosphere. Their properties have been modeled by various codes and investigated using measurements of many spacecraft missions. This study aims to compare simulated and observed properties of chorus waves. We present detailed comparisons between results from four different codes of nonlinear chorus wave generation and statistical observations from satellites, focusing on the fine structure of such chorus waves. We show that simulations performed with these different codes well reproduce the observed wave packet characteristics, although in somewhat complementary parameter domains as concerns wave packets sizes, amplitudes, and frequency sweep rates. In particular, simulations generate both the frequently observed short wave packets with high positive and negative frequency sweep rates, and the more rare long and intense packets with mainly rising tones. Moreover, simulations reproduce quantitatively both the increase of the size of the observed chorus wave packets with their peak amplitude, and the fast decrease of their frequency sweep rate as their size increases. This confirms the reliability of the main existing codes for accurately modeling chorus wave generation, although we find that initial conditions should be carefully selected to reproduce a given parameter range.

Discrete Rising Tone Elements of Whistler‐Mode Waves in the Vicinity of the Moon: ARTEMIS Observations

AbstractWe report on discrete rising‐tone elements of whistler‐mode waves observed by Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) in the vicinity of the Moon. The two‐probe ARTEMIS observations suggest that a free energy source for the wave generation is provided by electron anisotropy resulting from lunar surface absorption and magnetic reflection. High time resolution dynamic spectra reveal that the waves consist of multiple rising tone elements, exhibiting striking similarities to the well‐known whistler‐mode chorus in planetary magnetospheres. The observed frequency sweep rates are generally consistent with those predicted by the nonlinear growth theory of chorus emissions by Omura et al. (2008, https://doi.org/10.1029/2007JA012622). These results imply that whistler‐mode waves can grow nonlinearly into chorus‐like emissions even around airless bodies without magnetospheres and that a well‐defined dipole field is not a prerequisite for the chorus generation.

On the Frequency Sweep Rate Estimation in Airborne FMCW SAR Systems

Use of Frequency Modulated Continuous Wave (FMCW) Synthetic Aperture Radar (SAR) systems requires to accurately know the electronic parameters of the system. In particular, the use of an incorrect value of the Frequency Sweep Rate (FSR) introduces geometric distortions in the focused images. Recently, a method, that we name FSR Estimate Through Corner reflectors (FSRETC), has been proposed to estimate the FSR value actually employed by the radar. The method is based on the use of the SAR image focused with the available erroneous FSR. Moreover, it exploits a number of Corner Reflectors (CRs) deployed over the illuminated area. In this work, we provide an assessment of the capabilities of the FSRETC algorithm. The overall analysis is performed through the use of a real dataset consisting of 10 acquisitions carried out in 2018 (5 acquisitions) and 2019 (5 acquisitions) with an airborne FMCW SAR system. The presented experimental analysis shows that even with a single acquisition, use of two CRs sufficiently far from each other in the range direction, allows achieving an accurate estimate of the searched FSR. Moreover, it is shown that the obtained estimate is very stable over the time. Therefore, the overall procedure can be applied only once, since the estimated values can be safely used for the subsequent missions, at least for the time interval considered in the work, that is, 14 months. In addition, the presented results pose the basis for an enhanced measurement strategy that allows effective application of the FSRETC algorithm through the use of only one CR.

Full Particle Simulation of Whistler‐Mode Triggered Falling‐Tone Emissions in the Magnetosphere

AbstractWe perform a one‐dimensional electromagnetic full particle simulation for triggered falling‐tone emissions in the Earth's magnetosphere. The equatorial region of the magnetosphere is modeled with a parabolic magnetic field approximation. The short whistler‐mode waves with a large amplitude are excited and propagate poleward from an artificial current oscillating with a constant frequency and amplitude. Following the excited waves, clear emissions are triggered with a falling frequency. Without the inhomogeneity of the background magnetic field, no triggered emission appears. The falling tone has several subpackets of amplitude and decreases the frequency in a stepwise manner. The positive resonant current formed by resonant electrons in the direction of the wave magnetic field clearly shows that an electron hill is formed in the phase space and causes the frequency decrease. The entrapping of the resonant electrons at the front of the packets and the decrease of the amplitude at the end of packets are essential for the generation of falling‐tone emissions. Each wavefront of the emission has a strongly negative resonant current −JE, which results in the wave growth. In the formation process of the resonant currents, we investigate the inhomogeneous factor S, which controls the nonlinear motion of the resonant electrons interacting with waves. The factor S consists of two terms, a frequency sweep rate and a gradient of the background magnetic field. The resonant current JE in the wave packet changes its sign from negative to positive as the packet moves away from the equator, terminating the wave growth.

Spatial Extent of Quasiperiodic Emissions Simultaneously Observed by Arase and Van Allen Probes on 29 November 2018

AbstractRecent availability of a considerable amount of satellite and ground‐based data has allowed us to analyze rare conjugated events where extremely low and very low frequency waves from the same source region are observed in different locations. Here, we report a quasiperiodic (QP) emission, showing one‐to‐one correspondence, observed by three satellites in space (Arase and the Van Allen Probes) and a ground station. The main event was on 29 November 2018 from 12:06 to 13:08 UT during geomagnetically quiet times. Using the position of the satellites we estimated the spatial extent of the area where the one‐to‐one correspondence is observed. We found this to be up to 1.21 Earth's radii by 2.26 hr MLT, in radial and longitudinal directions, respectively. Using simple ray tracing calculations, we discuss the probable source location of these waves. At ∼12:20 UT, changes in the frequency sweep rate of the QP elements are observed at all locations associated with magnetic disturbances. We also discuss temporal changes of the spectral shape of QP observed simultaneously in space and on the ground, suggesting the changes are related to properties of the source mechanisms of the waves. This could be linked to two separate sources or a larger source region with different source intensities (i.e., electron flux). At frequencies below the low hybrid resonance, waves can experience attenuation and/or reflection in the magnetosphere. This could explain the sudden end of the observations at the spacecraft, which are moving away from the area where waves can propagate.

Rapid Frequency Variations Within Intense Chorus Wave Packets

AbstractWhistler mode chorus waves are responsible for electron acceleration in Earth's radiation belts. It is unclear, however, whether the observed acceleration is still well described by quasi‐linear theory, or if this acceleration is due to intense waves that require nonlinear treatment. Here, we perform a comprehensive statistical analysis of intense lower‐band chorus wave packets to investigate the relationships between wave frequency variations, packet length, and wave amplitude, and their temporal variability. We find that 15% of the wave power is carried by long packets, with low frequency sweep rates (linear trend in time) that agree with the nonlinear theory of chorus wave growth. Eighty‐five percent of the wave power, however, comes from short packets with large frequency variations around the linear trend. The kappa‐like probability distribution of these variations is consistent with random superposition of different waves that could result in a destruction of nonlinear resonant interaction.

A Model of the Subpacket Structure of Rising Tone Chorus Emissions

AbstractThe nonlinear growth theory of chorus emissions is used to develop a simple model of the subpacket formation. The model assumes that the resonant current, which is released from the source to the upstream region, radiates a new whistler mode wave with a slightly increased frequency, which triggers a new subpacket. Saturation of the growth in amplitude is controlled by the optimum amplitude. Numerical solution of advection equations for each subpacket, with the chorus equations acting as the boundary conditions, produces a chorus element with a subpacket structure. This element features an upstream shift of the source region with time and an irregular growth of frequency, showing small decreases between adjacent subpackets. The influence of input parameters on the number of subpackets, the shift of the source, the frequency sweep rate, and the maximum amplitude is analyzed. The model well captures basic features of instantaneous frequency measurements provided by the Van Allen Probes spacecraft. The modeled wave field can be used in future particle acceleration studies.

Frequency-Sweep-Range-Reconfigurable Complementary Linearly Chirped Microwave Waveform Pair Generation by Using a Fourier Domain Mode Locking Optoelectronic Oscillator Based on Stimulated Brillouin Scattering

A Fourier domain mode locking (FDML) optoelectronic oscillator (OEO) based on stimulated Brillouin scattering (SBS) is proposed to generate complementary linearly chirped microwave waveform (LCMW) pairs with flexibly-reconfigurable frequency sweep range and excellent frequency sweep linearity. The FDML OEO involves an SBS-based dual-passband microwave photonic filter with its two passbands linearly and fast scanning in the opposite direction at an identical frequency sweep rate, which is realized by using a single laser source to obtain a fast frequency sweep probe light and a two-tone pump light through electro-optic modulation. A proof-of-concept experiment is carried out to demonstrate the proposed scheme. In the experiment, frequency-sweep-range-reconfigurable complementary LCMW pairs with period of 20.5 μs are generated in the range of 5 GHz to 18 GHz, where the maximum time-bandwidth product and chirp rate are 82000 and ±0.195 GHz/µs, respectively. Most importantly, the frequency sweep linearity is measured to be 1.76%, which is much better than the results obtained in the existing FDML OEOs.

Numerical and Experimental Investigation of the Design of a Piezoelectric De-Icing System for Small Rotorcraft Part 2/3: Investigation of Transient Vibration during Frequency Sweeps and Optimal Piezoelectric Actuator Excitation

The objective of this research project is divided in four parts: (1) to design a piezoelectric actuator based de-icing system integrated to a flat plate experimental setup, develop a numerical model of the system and validate experimentally; (2) use the experimental setup to investigate actuator activation with frequency sweeps and transient vibration analysis; (3) add an ice layer to the numerical model, predict numerically stresses at ice breaking and validate experimentally; and (4) implement the concept to a blade structure for wind tunnel testing. This paper presents the second objective of this study, in which the experimental setup designed in the first phase of the project is used to study transient vibration occurring during frequency sweeps. Acceleration during different frequency sweeps was measured with an accelerometer on the flat plate setup. The results obtained showed that the vibration pattern was the same for the different sweep rate (in Hz/s) tested for a same sweep range. However, the amplitude of each resonant mode increased with a sweep rate decrease. Investigation of frequency sweeps performed around different resonant modes showed that as the frequency sweep rate tends towards zero, the amplitude of the mode tends toward the steady-state excitation amplitude value. Since no other transient effects were observed, this signifies that steady-state activation is the optimal excitation for a resonant mode. To validate this hypothesis, the flat plate was installed in a cold room where ice layers were accumulated. Frequency sweeps at high voltage were performed and a camera was used to record multiple pictures per second to determine the frequencies where breaking of the ice occur. Consequently, the resonant frequencies were determined from the transfer functions measured with the accelerometer versus the signal of excitation. Additional tests were performed in steady-state activation at those frequencies and the same breaking of the ice layer was obtained, resulting in the first ice breaking obtained in steady-state activation conditions as part of this research project. These results confirmed the conclusions obtained following the transient vibration investigation, but also demonstrated the drawbacks of steady-state activation, namely identifying resonant modes susceptible of creating ice breaking and locating with precision the frequencies of the modes, which change as the ice accumulates on the structure. Results also show that frequency sweeps, if designed properly, can be used as substitute to steady-state activation for the same results.

Capture of high energy orbit of Duffing oscillator with time-varying parameters.

This work investigates the time response of a Duffing oscillator with time-varying parameters (excitation frequency, linear stiffness, and mass) by approximate analytical and numerical methods. When the excitation frequency sweep covers the multisolution range, the characteristics of the response (maximum response, jump-up frequency, and jump-down frequency) mainly depend on the frequency sweep rate. If the frequency sweep is ended in the multisolution range, the sweep rate determines the energy orbit that the final response will capture. The results can be explained by comparing the state spaces of the oscillator with the change of basin of attraction of the high-energy orbit during the sweep. Furthermore, if the excitation is fixed at a specific frequency in the multisolution range, a method of natural frequency temporary modulation is proposed for the capture of the high-energy orbit. For practical realization, this method is completed by two ways, that is, the linear stiffness temporary modulation and mass temporary modulation. The modulation schedules of time-varying linear stiffness and mass are determined quantitatively, and it is proved that they could help capture the high-energy orbit similar to the excitation frequency sweep. The developed methods and results of this work can provide the guidelines to design nonlinear systems to work on preferred energy orbit.