Frequency Drift Research Articles

Harmonic phase-sensitive detection for quartz-enhanced photoacoustic-thermoelastic spectroscopy

Quartz tuning fork (QTF)-based techniques of photoacoustic spectroscopy and thermoelastic spectroscopy play a significant role in trace gas sensing due to unique high sensitivity and compactness. However, the stability of both techniques remains plagued by the inevitable and unpredictable laser power variation and demodulation phase variation. Herein, we investigate the phase change of a QTF when integrating both techniques for enhanced gas sensing. By demonstrating harmonic phase-sensitive methane detection as an example, we achieve stable gas measurement at varying laser power (2.4–9.4 mW) and varying demodulation phase (−90–90°). Besides, this method shows more tolerance to resonant frequency drift, contributing to a small signal fluctuation of ≤ 6.4 % over a wide modulation range (>10 times of the QTF bandwidth). The realization of harmonic-phase detection allows strengthening the stability of QTF-based sensors in a simple manner, especially when stable parameters, such as laser power, demodulation phase, even resonant frequency, cannot always be maintained.

Low temperature coefficient of frequency AlN Lamb wave resonator using groove structure between interdigital transducers

The lithographically tunable and small size features of Lamb wave resonators (LWRs) take a bright future for their use in high frequency narrow band filters. Resonant frequency drift due to temperature variation has a large impact on the narrower passband and a temperature coefficient of frequency (TCF) closer to 0 can broaden the stable temperature range of the resonator. This paper proposes a method of etching grooves in the area of the piezoelectric layer not covered by the Interdigital transducer (IDT) electrodes to improve the temperature stability of the Lamb resonator. Through the finite element method and theoretical analysis, the phase velocity, group velocity, and TCF dispersion curve of different modes of the resonator with groove structure were determined. The reason for the change of TCF under different normalized thicknesses of AlN was explained through the conversion of the LWR from a contour mode resonator (CMR) to a Cross-Sectional Lamé Mode Resonator. Simulation and test have shown that etching grooves have the effect of reducing TCF by adjusting the electromechanical coupling coefficient. The test shows that 205 nm-depth grooves can lower the TCF of the S0 mode IDT-Open LWR from −13.3 to −5.1 ppm/°C and S1 mode from −36.8 to −9.0 ppm/°C, respectively. The TCF of S0 and S1 mode LWRs decreased by 61.7% and 75.5%, respectively, after 205 nm groove etching. The groove etching method greatly raises the temperature stability of the LWR, enabling Lamb wave filters to operate stably over a wider temperature range.

Enhanced Pressure Response of Edge-Deposited Graphene Nanomechanical Resonators.

Nanomechanical resonators made of suspended graphene exhibit high sensitivity to pressure changes. Nevertheless, the graphene resonator pressure performance is affected owing to the gas permeation problem between the graphene film and the substrate. Therefore, we prepared edge-deposited graphene resonators by focused ion beam (FIB) deposition of SiO2, and their gas leakage velocities and pressure-sensing ability were demonstrated. In this paper, we characterize the pressure-sensing response and gas leakage velocities of graphene membranes using an all-optical actuation system. The gas leakage velocities of graphene resonators with diameters of 10, 20, and 40 μm are reduced by 5.0 × 106, 2.0 × 107, and 8.1 × 107 atoms/s, respectively, which demonstrates that the edge deposition structure can reduce the gas leakage of the resonator. Furthermore, the pressure-sensing performance of three graphene resonators with different diameters was evaluated, and their average pressure sensitivities were calculated to be 3.4, 2.4, and 1.9 kHz/kPa, with the largest full-range hysteresis errors of 0.6, 0.7, and 1.0%, respectively. The temperature stabilities of the three sizes of resonators in the temperature range of 300-400 K are 0.016, 0.015, and 0.016%/K, and the maximum resonance frequency drift over 1 h is 0.0058, 0.0048, and 0.0112%, respectively. This work has great significance for the improvement of gas leakage velocity characterization of graphene membrane and graphene resonant pressure sensor performance optimization.

ASOD: an adaptive stream outlier detection method using online strategy

In the current era of information technology, blockchain is widely used in various fields, and the monitoring of the security and status of the blockchain system is of great concern. Online anomaly detection for the real-time stream data plays vital role in monitoring strategy to find abnormal events and status of blockchain system. However, as the high requirements of real-time and online scenario, online anomaly detection faces many problems such as limited training data, distribution drift, and limited update frequency. In this paper, we propose an adaptive stream outlier detection method (ASOD) to overcome the limitations. It first designs a K-nearest neighbor Gaussian mixture model (KNN-GMM) and utilizes online learning strategy. So, it is suitable for online scenarios and does not rely on large training data. The K-nearest neighbor optimization limits the influence of new data locally rather than globally, thus improving the stability. Then, ASOD applies the mechanism of dynamic maintenance of Gaussian components and the strategy of dynamic context control to achieve self-adaptation to the distribution drift. And finally, ASOD adopts a dimensionless distance metric based on Mahalanobis distance and proposes an automatic threshold method to accomplish anomaly detection. In addition, the KNN-GMM provides the life cycle and the anomaly index for continuous tracking and analysis, which facilities the cause analysis and further interpretation and traceability. From the experimental results, it can be seen that ASOD achieves near-optimal F1 and recall on the NAB dataset with an improvement of 6% and 20.3% over the average, compared to baselines with sufficient training data. ASOD has the lowest F1 variance among the five best methods, indicating that it is effective and stable for online anomaly detection on stream data.

The collisional study of EIC waves in a magnetized dusty plasma with the inclusion of a DC electric field

This study investigates Electrostatic Ion Cyclotron (EIC) waves and their behaviour in weakly collisional plasmas, utilizing a proposed kinetic analytical model. The findings include alterations in EIC wave dispersion characteristics due to collisions, with parameters such as dust density, collision frequency, gyro-radius, magnetic field, density ratio, and electric field influencing wave growth rate and frequency. Temperature analysis reveals that higher electron-to-ion temperature ratios lead to increased frequency and critical drift velocity, while decreasing the growth rate. In addition, the critical drift velocity is studied for the unstable mode and it is observed that the relative density ratio increases with a reduction in critical drift velocity. Electron collisions destabilize EIC waves, while ion collisions stabilize them. Furthermore, the presence of dust particles decreases the growth rate of EIC waves as dust grain density increases. These results align with observations reported in previous literature.

On the importance of parallel magnetic-field fluctuations for electromagnetic instabilities in STEP

This paper discusses the importance of parallel perturbations of the magnetic-field in gyrokinetic simulations of electromagnetic instabilities and turbulence at mid-radius in the burning plasma phase of the conceptual high-β, reactor-scale, tight-aspect-ratio tokamak STEP. Previous studies have revealed the presence of unstable hybrid kinetic ballooning modes (hKBMs) and subdominant microtearing modes at binormal scales approaching the ion Larmor radius. In this STEP plasma it was found that the hKBM requires the inclusion of parallel magnetic-field perturbations to be linearly unstable. Here, the extent to which the inclusion of fluctuations in the parallel magnetic-field can be relaxed is explored through gyrokinetic simulations. In particular, the frequently used MHD approximation (dropping δB∥ and setting the ∇B drift frequency equal to the curvature drift frequency) is discussed and simulations explore whether this approximation is useful for modelling STEP plasmas. It is shown that the MHD approximation can reproduce some of the linear properties of the full STEP gyrokinetic system, but is too stable at low ky and nonlinear simulations using the MHD approximation result in very different transport states. It is demonstrated that the MHD approximation is challenged by the high β′ values in STEP, and that the approximation improves considerably at lower β′ . Furthermore, it is shown that the sensitivity of STEP to δB∥ fluctuations is primarily because the plasma sits close to marginality and it is shown that in slightly more strongly driven conditions the hKBM is unstable without δB∥. Crucially, it is demonstrated that the state of large transport typically predicted by local electromagnetic gyrokinetic simulations of STEP plasmas is not solely due to δB∥ physics.

Effects of Axial and Radial Components of Magnetic Field on the Electromagnetic Resistive Instabilities in Hall Thruster Plasma

Abstract A theoretical model is developed to investigate the effect of the axial component of the magnetic field on the electromagnetic resistive instabilities in the Hall thruster. The axial component of the magnetic field plays a vital role in controlling the plasma flow and generating thrust in Hall thruster. It also affects the magnetic topology and magnetic field lines in the Hall thruster. In the present paper, a dispersion relation for the electromagnetic resistive instabilities under the influence of the axial component of the magnetic field is derived. The obtained dispersion equation is solved numerically to study the propagating and growing waves in the magnetized plasmas. It is observed that the growth rate decreases with an axial component of the magnetic field, but it increases with a radial component of the magnetic field. When the axial component of the magnetic field is considered, the amplitude of the growth rate of the resistive instability dropped with azimuthal wavenumber, collision frequency and electron drift velocity by almost 21 %, 35 %, and 33 %, respectively. When, the value of drift velocity exceeds to 4×10^6 m/s, the influence of the axial component of the magnetic field appeared, and the growth rate reduced drastically.

Characteristic times for radiation belt drift phase mixing

Impulsive radial transport events occurring in the radiation belts leave lasting marks in the form of drift echoes, that is, energy-dependent drift phase structures in the radiation belts that evolve at the drift frequency. Drift echoes are known to be transient structures that dissipate due to phase mixing. The objective of this paper is to discuss how much time it takes for drift echoes to dissipate, and what drives this phase-mixing process. While any uncertainty or perturbation in the variables controlling trapped particles’ drift frequency contributes to phase mixing, we highlight two main drivers: the observational uncertainty associated with the finite size of the instrument energy channels, and the natural field fluctuations driving perturbations in trapped particles’ drift frequency. It is the combination of both instrumental and natural sources of phase mixing that determines the observed dissipation and lifetime of drift echoes. This means that the observed magnitude and lifetime of a drift echo are always underestimations of the natural magnitude and lifetime of the structure. This calls into question the applicability of the standard, drift-averaged formulation of radial diffusion. The three key points of the study are the following: First, the time it takes for particles initially localized in local time to phase-mix is measured in hours in the Earth’s radiation belts. Second, phase mixing at the drift scale is primarily due to uncertainties in measured kinetic energy and field perturbations. Third, our analysis can be utilized to set an energy resolution requirement for future particle instruments.

Repeatability of image quality in very low-field MRI.

Very low-field MR has emerged as a promising complementary device to high-field MRI scanners, offering several advantages. One of the key benefits is that very low-field scanners are generally more portable and affordable to purchase and maintain, making them an attractive option for medical facilities looking to reduce costs. Very low-field MRI systems also have lower RF power deposition, making them safer and less likely to cause tissue heating or other safety concerns. They are also simpler to maintain, as they do not require cooling agents such as liquid helium. However, these portable MR scanners are impacted by temperature, lower magnetic field strength, and inhomogeneity, resulting in images with lower signal-to-noise ratio (SNR) and higher geometric distortions. It is essential to investigate and tabulate the variations in these parameters to establish bounds so that subsequent in vivo studies and deployment of these portable systems can be well informed. The aim of this work is to investigate the repeatability of image quality metrics such as SNR and geometrical distortion at 0.05 T over 10 days and three sessions per day. We acquired repeatability data over 10 days with three sessions per day. The measurements included temperature, humidity, transmit frequency, off-resonance maps, and 3D turbo spin echo (TSE) images of an in vitro phantom. This resulted in a protocol with 11 sequences. We also acquired a 3 T data set for reference. The image quality metrics included computing SNR and eccentricity (to assess geometrical distortion) to investigate the repeatability of 0.05 T image quality. The image reconstruction included drift correction, k-space filtering, and off-resonance correction. We computed the experimental parameters' coefficient of variation (CV) and the resulting image quality metrics to assess repeatability. We have explored the impact of electromagnetic interference (EMI) on image quality in very low-field MRI. The investigation involved varying both the distance and amplitude of the EMI-producing coil from the signal generator to analyze their effects on image quality. The range of temperature measured during the study was within 1.5 °C. The off-resonance maps acquired before and after the 3D TSE showed similar hotspots and were changed mainly by a global constant. The SNR measurements were highly repeatable across sessions and over the 10 days, quantified by a CV of 6.7%. The magnetic field inhomogeneity effects quantified by eccentricity showed a CV of 13.7%, but less than 5.1% in two of the three sessions over 10 days. The use of conjugate phase reconstruction mitigated geometrical distortion artifacts. Temperature and humidity did not significantly affect SNR or mean frequency drift within the ranges of these environmental factors investigated. The EMI experiment showed that as the amplitude increased the SNR decreased, and concurrently the root mean square of the background increased with a rise in EMI amplitude or a reduction in distance. We found that humidity and temperature in the range investigated did not impact SNR or frequency. Based on the CV values computed session-wise and for the overall study, our findings indicate high repeatability for SNR and magnetic field homogeneity.

Diagnostic efficacy of complexity metrics from cardiac MRI myocardial segmental motion curves in detecting late gadolinium enhancement in myocardial infarction patients

BackgroundMyocardial segmental motion is associated with cardiovascular pathology, often assessed through myocardial strain features. The stability of the motion can be influenced by myocardial fibrosis. This research aimed to explore the complexity metrics (CM) of myocardial segmental motion curves, observe their correlation with late gadolinium enhancement (LGE) transmural extension (TE), and assess diagnostic efficacy combined with segmental strains in different TE segments. MethodsWe included 42 myocardial infarction patients, dividing images into 672 myocardial segments (208 remote, 384 viable, and 80 unviable segments based on TE). Radial and circumferential segmental strain, along with CM for motion curves, were extracted. Correlation between CM and LGE, as well as the potential distinguishing role of CM, was evaluated using Pearson correlation, univariate linear regression (F-test), multivariate regression analysis (T-test), area under curve (AUC), machine learning models, and DeLong test. ResultsAll CMs showed significant linear correlation with TE (P < 0.001). Six CMs were correlated with TE (r > 0.3), with radial frequency drift (FD) displayed the strongest correlation (r = 0.496, P < 0.001). Radial and circumferential FD significantly differed in higher TE myocardium than in remote segments (P < 0.05). Radial FD had practical diagnostic efficacy (remote vs. unviable AUC = 0.89, viable vs. unviable AUC = 0.77, remote vs. viable AUC = 0.65). Combining CM with segmental strain features boosted diagnostic efficacy than models using only segmental strain features (DeLong test, P < 0.05). ConclusionsThe CM of myocardial motion curves has been associated with LGE infarction, and combining CM with strain features improves the diagnosis of different myocardial LGE infarction degrees.

Vibration controlling effect of tuned liquid column damper (TLCD) on support structural platform (SSP)

A bidirectional fluid-structure coupling model between tuned liquid column damper (TLCD) and support structural platform (SSP) was developed to study effects of TLCD-SSP mass ratio and tuning ratio on reducing SSP vibration. Laboratory experiments of TLCD interaction with SSP were conducted to validate TLCD-SSP coupling model. Good agreements between numerical results and experimental data are obtained. TLCD/SSP mass ratio increases from 1% to 3%, the maximum amplitude of SSP upper displacement decreases from 43.77% to 78.32%, and the upper acceleration damping rate increases from 43.26% to 77.88%. There is a phase differences between dynamic water pressure offered by sloshing inside TLCD and upper displacement curves, and the damping energy dissipation effect is maximized when the hysteresis phase difference reaches π/2. The larger mass ratio is more effective in suppressing the structural vibration. But it also brings about a fundamental frequency drift. It is advised that the mass ratio of water in TLCD to SSP should be 1.5%, the total mass of water and shell of TLCD should be about 2.5% of the mass of SSP, and the intrinsic frequencies of TLCD and SSP should be tuned the same so that the vibration controlling performance of TLCD can be improved maximally.

Asymmetrical Lamb wave mode resonant infrared detector based on lithium niobate thin film

This work explores the infrared (IR) detection capabilities of 750 nm thick Z-cut lithium niobate (LN) thin film resonator at asymmetric modes of various orders: the first, third, fifth, and seventh order asymmetric (A1, A3, A5, and A7), with resonant frequencies of 2.35, 6.68, 11.09, and 15.49 GHz. Under the infrared radiation of 0.575 mW, the responses about admittance minima and frequency drift corresponding to these modes have been experimentally validated. Notably, the A1 mode exhibits the most significant admittance dip response with 2.62 dB, while the A7 mode demonstrates a maximum frequency drift response of 670 kHz. The optimal parameter for noise equivalent power reaches 15.41 pW/Hz1/2, and the optimal detectivity achieves 7.40 × 106 m Hz1/2/W. These findings indicate the immense potential of LN thin-film resonators for infrared sensing applications.

Single-beam velocimetry with dual frequency comb absorption spectroscopy

Laser absorption Doppler velocimeters use a crossed-beam configuration to cancel errors due to laser frequency drift and absorption model uncertainty. This configuration complicates the spatial interpretation of the measurement since the two beams sample different volumes of gas. Here, we achieve single-beam velocimetry with a portable dual comb spectrometer (DCS) with high frequency accuracy and stability enabled by GPS-referencing, and a new high-temperature water vapor absorption database. We measure the inlet flow in a supersonic ramjet engine and demonstrate single-beam measurements that are on average within 19 m/s of concurrent crossed-beam measurements. We estimate that the DCS and the new database contribute 1.6 and 13 m/s to this difference respectively.

Orbital analysis of stars in the nuclear stellar disc of the Milky Way

Context. While orbital analysis studies were so far mainly focused on the Galactic halo, it is possible now to do these studies in the heavily obscured region close to the Galactic Centre. Aims. We aim to do a detailed orbital analysis of stars located in the nuclear stellar disc (NSD) of the Milky Way allowing us to trace the dynamical history of this structure. Methods. We integrated orbits of the observed stars in a non-axisymmetric potential. We used a Fourier transform to estimate the orbital frequencies. We compared two orbital classifications, one made by eye and the other with an algorithm, in order to identify the main orbital families. We also compared the Lyapunov and the frequency drift techniques to estimate the chaoticity of the orbits. Results. We identified several orbital families as chaotic, z-tube, x-tube, banana, fish, saucer, pretzel, 5:4, and 5:6 orbits. As expected for stars located in a NSD, the large majority of orbits are identified as z-tubes (or as a sub-family of z-tubes). Since the latter are parented by x2 orbits, this result supports the contribution of the bar (in which x2 orbits are dominant in the inner region) in the formation of the NSD. Moreover, most of the chaotic orbits are found to be contaminants from the bar or bulge which would confirm the predicted contamination from the most recent NSD models. Conclusions. Based on a detailed orbital analysis, we were able to classify orbits into various families, most of which are parented by x2-type orbits, which are dominant in the inner part of the bar.

Near-Field Probing of Microwave Oscillators with Josephson Microscopy.

Voltage-controlled oscillators, serving as fundamental components in semiconductor chips, find extensive applications in diverse modules such as phase-locked loops, clock generators, and frequency synthesizers within high-frequency integrated circuits. This study marks the first implementation of superconducting Josephson probe microscopy for near-field microwave detection on multiple voltage-controlled oscillators. Focusing on spectrum tracking, various phenomena, such as stray spectra and frequency drifts, were found under nonsteady operating states. Parasitic electromagnetic fields, originating from power supply lines and frequency divider circuits, were identified as sources of interference between units. The investigation further determined optimal working states by analyzing features of the microwave distributions. Our research not only provides insights into the optimization of circuit design and performance enhancement in oscillators but also emphasizes the significance of nondestructive near-field microwave microscopy as a pivotal tool in characterizing integrated millimeter-wave chips.

Frequency drift characterization of a laser stabilized to an optical fiber delay line

Lasers stabilized to optical fiber delay lines have been shown to deliver a comparable short-term (&lt;1 s) frequency noise performance to that achieved by lasers stabilized to ultra-low expansion (ULE) cavities, once the linear frequency drift has been removed. However, for continuous stable laser operations, the drift can be removed only when it can be predicted, e.g., when it is linear over very long timescales. To date, such long-term behaviour of the frequency drift in fiber delay lines has not been, to the best of our knowledge, characterised. In this work we experimentally characterise the frequency drift of a laser stabilised to a 500 m-long optical fiber delay line over the course of several days. We show that the drift still follows the temperature variations even when the spool temperature is maintained constant with fluctuations below tens of mK. Consequently, the drift is not linear over long timescales, preventing a simple feed-forward compensation. However, here we show that the drift can be reduced by exploiting the high level of correlation between laser frequency and the fiber temperature. In our demonstration, by applying a frequency correction proportional to temperature readings, a calculated frequency drift of less than 16 Hz/s over the several days of our test was obtained, corresponding to a 23-fold improvement from uncorrected values.

Long term frequency stabilization and frequency drift suppression of the 313 nm laser

A 313 nm ultraviolet (UV) laser is stabilized through the Pound–Drever–Hall method, and its frequency drift is suppressed by a remote frequency drift correction system. The 313 nm laser is generated through an external cavity diode laser at 1252 nm and two cascaded second harmonic generation (SHG) stages. By locking the 626 nm from the first SHG stage to an ULE cavity and evaluating the beat signal between the 626 nm laser and an optical frequency comb, the 313 nm laser frequency instabilities of 1.80 ×10−12 at 1 s and 4.70 ×10−14 at 64 s averaging time are obtained. With the remote frequency drift correction system, the frequency drift of 313 nm laser is reduced to 0.02 (6) kHz/h. Individual ions in a beryllium Coulomb crystal cooled by the stable 313 nm laser are identified within the 240 s.

High-sensitive double incidence multi-pass cell for trace gas detection based on TDLAS

A high-precision gas detection system with a dual-incidence multi-pass cell (D-MPC) based on TDLAS was developed, which can simultaneously measure quadruple component gases. Two Distributed Feedback (DBF) Laser Diodes with central wavelength of 1654 nm and 2004 nm were utilized to measure methane (CH4) and carbon dioxide (CO2) for evaluating the performance of the system. High sensitivity and low frequency drift were accomplished by utilizing the second harmonic signals (WMS-2f) detection and peak-locking technology. A LabVIEW-based control and acquisition program, which could be used for direct absorption and wavelength modulation, was developed. Kalman adaptive filtering, Least Mean Squares (LMS) adaptive filtering and S-G filtering were employed for denoising in direct absorption spectroscopy (DAS), respectively, and optimal denoising technology of S-G filtering was selected. According to Allan deviation analysis, the optimal detection precision for CH4 and CO2 was 12 ppb at an integration time of 36 s and 270 ppb at an integration time of 43 s, respectively. A two-day continuous monitoring of atmospheric CO2 and CH4 was implemented to verify the system stability and can be applied to other trace gases monitoring.

Self-Oscillating Converter Based on Phase Tracking Closed Loop for a Dynamic IPT System

The coupling of converters with resonant networks poses significant challenges for frequency tracking and power control in inductive power transfer (IPT) systems. This paper presents an implementation method that addresses these issues by dividing the system’s operation into two distinct states: self-oscillating and power-injecting. Based on these states, a phase-closed loop is constructed. Within this closed loop, the phase tracking unit detects and tracks frequency drift, while the power regulating unit incorporates an integrator and adopts a control variable to adjust the output power by modifying the duration of the power injecting state. Meanwhile, the oscillating unit operates in the self-oscillating state. Operating in this manner, the system achieves self-oscillation and demonstrates the capability to effectively track and compensate for system variations within a single cycle. A verification prototype has been constructed, and it demonstrates that the converter within it completely decoupled from the resonant network. Experimental results validate that altering the control variable solely affects the duration of the power-injecting state, allowing for independent control of the output power. When the control variable changes from 2.0 V to 3.5 V, the output power changes from 178 W to 519 W while the self-oscillating state remains unchanged. Furthermore, the system accurately tracks frequency changes, even under significant variations in the coupling coefficient or load, without compromising the power injection state. When the air gap changes from 3 cm to 12 cm, the duration of the self-oscillating state changes from 22.1 μs to 26.3 μs, while the power injecting state remains unchanged. This approach exhibits a robust performance, particularly suitable for dynamic IPT systems sensitive to parameter variations.

Imaging spectroscopy of a spectral bump in a type II radio burst

Context. Observations of solar, type II radio bursts provide a unique opportunity to analyze the nonthermal electrons accelerated by coronal shocks and diagnose the plasma density distribution in the corona. However, there are very few high-frequency resolution interferometric observations of type II radio bursts that are capable of tracking these electrons. Aims. Recently, more spatially resolved high-resolution observations of type II radio bursts have been recorded with the Low-Frequency Array (LOFAR). Using these observations, we aim to track the location of a type II radio burst that experienced a sudden spectral bump. Methods. We present the first radio imaging observations of a type II burst with a spectral bump. We measured the variation in source location and frequency drift of the burst and deducted the density distribution along its propagation direction. Results. We have identified a type II burst that experiences a sudden spectral bump in its frequency-time profile. The overall frequency drift rate is 0.06 MHz s−1, and this corresponds to an estimated speed of 295 km s−1. The projected velocity of the radio source obtained from imaging is 380 km s−1 toward the east. At the spectral bump, a deviation in the source locations of the type II split bands is observed. The band separation increases significantly in the north–south direction. Conclusions. The spectral bump shows an 8 MHz deviation at 60 MHz, which corresponds to a 25% decrease in the plasma density. The estimated crossing distance during the spectrum bump was 29 mm, suggesting that this density variation occurs in a confined area. This indicates that the shock most likely encountered the upper extent of a coronal hole.