Ultralow Frequency Waves Research Articles

Direct observations of cross-scale wave-particle energy transfer in space plasmas.

The collisionless plasmas in space and astrophysical environments are intrinsically multiscale in nature, behaving as conducting fluids at macroscales and kinetically at microscales comparable to ion and/or electron gyroradii. A fundamental question in understanding the plasma dynamics is how energy is transported and dissipated across scales. Here, we present spacecraft measurements in the terrestrial foreshock, a region upstream of the bow shock where the solar wind population coexists with the reflected ions. In this region, the fluid-scale, ultralow-frequency waves resonate with the reflected ions to modify the velocity distributions, which in turn cause the growth of the ion-scale, magnetosonic-whistler waves. The latter waves then resonate with the electrons, and the accelerated electrons contribute to the excitation of electron-scale, high-frequency whistler waves. These observations demonstrate that the chain of wave-particle resonances is an efficient mechanism for cross-scale energy transfer, which could redistribute the kinetic energy and accelerate the particles upstream of the shocks.

Foreshock Ultralow Frequency Waves at Mars: Consequence on the Particle Acceleration Mechanisms at the Martian Bow Shock

Foreshock Ultralow Frequency Waves at Mars: Consequence on the Particle Acceleration Mechanisms at the Martian Bow Shock

Ultralow frequency waves in the South Atlantic anomaly: Application of FY-3E observations

Ultralow frequency waves in the South Atlantic anomaly: Application of FY-3E observations

Magnetospheric Control of Ionospheric TEC Perturbations via Whistler-Mode and ULF Waves.

The weakly ionized plasma in the Earth's ionosphere is controlled by a complex interplay between solar and magnetospheric inputs from above, atmospheric processes from below, and plasma electrodynamics from within. This interaction results in ionosphere structuring and variability that pose major challenges for accurate ionosphere prediction for global navigation satellite system (GNSS) related applications and space weather research. The ionospheric structuring and variability are often probed using the total electron content (TEC) and its relative perturbations (dTEC). Among dTEC variations observed at high latitudes, a unique modulation pattern has been linked to magnetospheric ultra-low-frequency (ULF) waves, yet its underlying mechanisms remain unclear. Here using magnetically conjugate observations from the THEMIS spacecraft and a ground-based GPS receiver at Fairbanks, Alaska, we provide direct evidence that these dTEC modulations are driven by magnetospheric electron precipitation induced by ULF-modulated whistler-mode waves. We observed peak-to-peak dTEC amplitudes reaching 0.5 TECU (1 TECU is equal to electrons/ ) with modulations spanning scales of 5-100km. The cross-correlation between our modeled and observed dTEC reached 0.8 during the conjugacy period but decreased outside of it. The spectra of whistler-mode waves and dTEC also matched closely at ULF frequencies during the conjugacy period but diverged outside of it. Our findings elucidate the high-latitude dTEC generation from magnetospheric wave-induced precipitation, addressing a significant gap in current physics-based dTEC modeling. Theses results thus improve ionospheric dTEC prediction and enhance our understanding of magnetosphere-ionosphere coupling via ULF waves.

Ultra-relativistic electron flux enhancement under persistent high speed solar wind stream

The physical mechanisms usually applied to explain the relativistic electron enhancement have been delved into to elucidate non-adiabatic electron acceleration resulting in the ultra-relativistic electron population observed in the outer radiation belt. We considered multisatellite observations of the solar wind parameters, magnetospheric waves, and particle flux to report an unusual local acceleration of ultra-relativistic electrons under a prolonged high-speed solar wind stream (HSS). A corotating interaction region reaches the Earth’s bowshock on August 3, 2016, causing a minor geomagnetic storm. Following this, the magnetosphere was driven for 72 h by a long-term HSS propagating at 600 km/s. During this period, the magnetosphere sustained both ultra-low frequency (ULF) and very-low frequency (VLF) waves in the outer radiation belt region. Besides the waves, the relativistic and ultra-relativistic electron fluxes were enhanced with different time lags regarding the magnetic storm main phase. The efficiency of wave-particle interaction in enhancing ultrarelativistic electrons is evaluated by the diffusion coefficient rates, considering both ULF and VLF waves together with phase space density analyses. Results show that local acceleration by whistler mode chorus waves can occur in a time scale of 2–4 h, whereas ULF waves take around 10’s of hours and magnetosonic waves take a time scale of days. This result is confirmed by the phase space density analysis. Accordingly, it shows that peaks of local acceleration of 1 MeV electrons are consistent with the observation of the highest chorus wave amplitude at the same L-shell and MLT. Thus, we argue that whistler mode chorus waves interacting with relativistic electrons are the main physical mechanisms leading to ultra-relativistic electron enhancement, while ULF and fast magnetosonic waves are found as secondary physical processes. Lastly, our analysis contributes to understanding how whistler and ULF waves can contribute to ultra-relativistic electrons showing up in the inner magnetosphere under the HSS driver.

Global magnetic field properties in the solar wind interaction of Mercury from MESSENGER measurements

The space environment of Mercury is shaped by its proximity to the Sun and by the relatively weak planetary magnetic field, presenting a unique regime of plasmas and shock conditions. We present the global magnetic properties in Mercury's space environment based on more than 4 years of MESSENGER Magnetometer data. We used 20 Hz magnetic field data to examine the magnetic strength, the field configurations, and the fluctuations. We considered both compressional and transverse modes, with frequencies from 5 mHz to 10 Hz, which cover typical ultra-low frequency waves at Mercury. We identified regions of the solar wind, the magnetosheath, and the magnetosphere during over 4\,000 MESSENGER orbits. The solar wind and magnetosheath data were analysed in the solar wind interplanetary magnetic field (IMF) coordinate system, and the magnetosphere data were analysed in the aberrated Mercury solar magnetospheric coordinate system. Each data point was relocated into normalised space using averaged magnetopause and bow-shock models. The magnetic environments for a quasi-parallel and quasi-perpendicular IMF were compared. Under the typical Parker-spiral IMF, the magnetic environment of Mercury features strong fluctuations that are dominated by the transverse mode and stem from interactions at the bow shock and the magnetopause. When they are subjected to a quasi-perpendicular IMF, the magnetic fluctuations diminish, and the magnetic field strength becomes highly compressed throughout the bow shock, magnetosheath, and magnetosphere. Unlike Earth, Mercury exhibits weaker dawn-dusk asymmetries in magnetic field strength and lacks substantial magnetosheath-generated sources of magnetic fluctuations. The magnetic field draping pattern associated with the IMF cone angle at Mercury also differs from that at Earth. Our comparative analysis highlights the critical role of the solar wind Mach number, the radial IMF component, and the system scale size in shaping planetary space environments.

Ultra-low frequency and broadband flexural wave attenuation using an inertant nonlinear metamaterial beam

Attenuation of elastic waves in the extremely low frequency range is a considerable challenge. While linear acoustic metamaterials can manipulate elastic waves, their effectiveness is often limited to a narrow frequency range. The present paper proposes a novel inertant nonlinear metamaterial beam to address the challenging problem of the ultra-low frequency broadband flexural wave attenuation. The amplitude-frequency response and dispersion relations of the flexural waves are obtained using the first-order harmonic balance method, where four different resonant units are investigated and the resulting band gaps are compared. Finite element (FE) simulations are also conducted to evaluate the transmission spectra of the flexural vibration through a finite metamaterial beam. The good consistency between the band gaps predicted by the analytical model and the FE simulation verifies the correctness and effectiveness of the developed analytical approach. The results of this study demonstrate that introducing the inertance and softening nonlinearity into the resonant units can significantly widen the flexural wave band gaps within the low-frequency range. This finding provides a viable solution for engineering applications that require low-frequency vibration suppression and isolation.

Ultralow-frequency Waves in Jupiter’s Magnetopause Boundary Layer

Ultralow-frequency (ULF) waves (∼tens of minutes period) are widely identified in the Jovian system and are believed to be associated with energy dissipation in the magnetosphere and ionosphere. Due to the magnetodisk oscillation related to planetary rotation, it is challenging to identify the periodicities inside the magnetosphere, although remote sensing observations of the polar emissions provide clear evidence of the tens of minutes pulsations. In this study, we take advantage of Juno’s in situ measurements in the magnetopause boundary layer for a long duration, i.e., >4 hr, to directly assess the tens of minutes periodicities of the boundary dynamics caused by the interactions between the internal plasma and external solar wind. Through periodogram analysis on the magnetic field and particle data, we find ULF waves with periodicities of ∼18 minutes, ∼40 minutes, and ∼70–80 minutes, which is generally consistent with pulsations in multiple remote sensing observations. A multiple-harmonic ULF phenomenon was also identified in the observations. The periodicities from in situ measurements provide crucial clues in understanding the origin of pulsating wave/auroral emissions in the Jovian system. The results could also further our understanding of energy transfer and release between the internal plasma of Jupiter and external solar wind.

Generation of 30 s Waves Observed Upstream of the Martian Bow Shock: A Case Study

The foreshock region filled with turbulences is a natural lab for studying interactions between plasma and waves. The underlying processes are vital for dissipating the energy carried by the solar wind into the Martian environment. In this study, we analyze an ultralow-frequency wave observed on 2015 August 14 by Mars Atmosphere and Volatile Evolution upstream of the Martian bow shock. The wave properties match with those of 30 s waves; the dispersion calculation shows that the upstream plasma was capable of generating the observed waves. The analysis of the ion behaviors implies the wave generated without a field-aligned beam, while the growth rate of waves seems to be modulated by the interplanetary magnetic field conditions. These results indicate the unique role of the Martian foreshock in the interaction between the solar wind and the planet.

Ultra-Low Frequency Waves of Foreshock Origin Upstream and Inside of the Magnetospheres of Earth, Mercury, and Saturn Related to Solar Wind–Magnetosphere Coupling

This review examines ultra-low frequency (ULF) waves across different planetary environments, focusing on Earth, Mercury, and Saturn. Data from spacecraft missions (CHAMP, Swarm, and Oersted for Earth; MESSENGER for Mercury; and Cassini for Saturn) provide insights into ULF wave dynamics. At Earth, compressional ULF waves, particularly Pc3 waves, show significant power near the equator and peak around Magnetic Local Time (MLT) = 11. These waves interact complexly with Alfvén waves, impacting ionospheric responses and geomagnetic field line resonances. At Mercury, ULF waves transition from circular to linear polarization, indicating resonant interactions influenced by compressional components. MESSENGER data reveal a lower occurrence rate of ULF waves in Mercury’s foreshock compared to Earth’s, attributed to reduced backstreaming protons and lower solar wind Alfvénic Mach numbers, as ULF wave activity increases with heliocentric distance. Short Large-Amplitude Magnetic Structures (SLAMS) observed at Mercury and Saturn show distinct characteristics compared to those of Earth, including the presence of whistler precursos waves. However, due to the large differences in heliospheric distances, SLAMS (their temporal scale size correlate with the ULF wave frequency) at Mercury are significantly shorter in duration than at Earth or Saturn, since the ULF wave frequency primarily depends on the strength of the interplanetary magnetic field. This review highlights the variability of ULF waves and SLAMS across planetary environments, emphasizing Earth’s well-understood ionospheric interactions and the unique behaviours observed for Mercury and Saturn. These findings enhance our understanding of space plasma dynamics and underline the need for further research regarding planetary magnetospheres.

Design, modeling and experiments of bistable wave energy harvester with directional self-adaptive characteristics

Wave energy is a abundant renewable resource, but the direction variability and ultra-low frequency limit its widespread application. Therefore, a novel bistable wave energy harvester with directional self-adaptive characteristics is proposed in this paper, which utilizes the collision between the driving ball and the generator beam to transform the multi-directional ultra-low frequency wave vibration into localized high-frequency vibration. Moreover, the theoretical analytical model of harvester when subjected to wave motions was established, including the dynamic analysis of driving ball before the collision, the collision response analysis during the collision, and the bistable properties of generator beam after the collision. Finally, the key parameters affecting the output performance, such as the mass of the driving ball, the maximum inclination angle of the wave and the external load resistance, were analyzed using experiments. The maximum open-circuit voltage RMS value is 1815.28 mV, and the maximum power is 2.06 μW. The proposed harvester can effectively harvest ultra-low frequency energy vibration energy in multi-directions.

Innovative Designs in Vibration Energy Harvesting: Performance Evaluation and Comparative Analysis

This paper explores the realm of vibration energy harvesting (VEH) and its potential applications in powering electronic devices. With the increasing demand for constant power supply in various sectors, including medical, transportation, and communication, the drawbacks of traditional battery solutions prompt the exploration of alternative energy sources. Vibration, omnipresent in our environment, presents itself as a promising source of mechanical energy that can be converted into electrical power. This study delves into three distinct VEH designs: a flute-inspired broadband piezoelectric device with mechanical intelligence, an electromagnetic harvester utilizing a magnet-array-based vibration-to-rotation conversion mechanism, and a piezoelectric harvester for ultra-low frequency waves with magnetic coupling driven by rotating balls. Through extensive analysis and experimentation, each design's performance, features, and potential applications are evaluated and compared. While each design offers unique advantages and limitations, understanding their characteristics facilitates identifying suitable scenarios for deployment, thereby advancing the development of self-powered devices.

Climatology of the open–closed boundary using ULF wave observations from South Pole, McMurdo, and distributed Antarctic AGOs

It has been shown that a proxy determination of the magnetospheric open–closed magnetic field line boundary (OCB) location can be made by examining the ultra-low-frequency (ULF) wave power in magnetometer data, with particular interest in the Pc5 ULF waves with periods of 3–10 min. In this study, we present a climatology of such Pc5 ULF waves using ground-based magnetometer data from the South Pole Station (SPA), McMurdo (MCM) station, and the Automatic Geophysical Observatories (AGOs) located across the Antarctic continent, to infer OCB behavior and variability during geomagnetically quiet times (i.e., Ap < 30 nT). For each season [i.e., austral fall (20 February 2017–20 April 2017), austral winter (20 May 2017–20 July 2017), austral spring (20 August 2017–20 October 2017), and austral summer (20 November 2017–20 January 2018)], north–south (i.e., H-component) magnetic field line residual power–spectral density (PSD) measurements taken during geomagnetically quiet periods within a 60-day window centered at the austral solstice/equinox are averaged in 10-min temporal bins to form the climatology at each station. These residual PSDs thus enable the analysis of Pc5 activity (and lower period “long-band” oscillations) and, thus, OCB location/variability as a function of season and magnetic latitude. The dawn and dusk transitions across the OCB are analyzed, with a discussion of dawn and dusk variability during nominally quiet geomagnetic periods. In addition, latitudinal dependencies of the OCB and peak Pc5 periods at each station are discussed, along with the empirical Tsyganenko model comparisons to our site measurements.

A self-powered and self-monitoring ultra-low frequency wave energy harvester for smart ocean ranches

The ocean ranch environment contains ultra-low-frequency wave energy that can be utilized for powering low-power equipment. Therefore, this article proposes a smart ocean ranch self-powered and self-monitoring system (SOR-SSS) which consists of several key components: a mass pendulum ball (MPB), a commutation wheel system (CWS), an electromagnetic energy harvesting unit (EEHU), and four piezoelectric energy harvesting units (PEHU). Through six-degree-of-freedom vibration test bench experiments, the SOR-SSS achieved a maximum output power of 17.56 mW under a working condition of 0.4Hz, which was sufficient to power 152 LED lights. Additionally, by training the experimental base data using the LSTM algorithm, two different tasks were trained with a maximum accuracy of 99.72% and 99.80%, respectively. These results indicate that the SOR-SSS holds significant potential for collecting and predicting ultra-low-frequency blue energy. It can provide an effective energy supply and monitoring solution for smart ocean ranch.

Nonlinear Drift‐Bounce Resonance Between Charged Particles and Ultralow Frequency Waves

AbstractUltra‐low frequency (ULF) waves contribute significantly to the dynamic evolution of Earth's magnetosphere by accelerating and transporting charged particles within a wide energy range. A substantial excitation mechanism of these waves is their drift‐bounce resonant interactions with magnetospheric particles. Here, we extend the conventional drift‐bounce resonance theory to formulate the nonlinear particle trapping in the ULF wave‐carried potential well, which can be approximately described by a pendulum equation. We also predict the observable signatures of the nonlinear drift‐bounce resonance, and compare them with spacecraft observations. We further discuss potential drivers of the pendulum including the convection electric field and the magnetospheric dayside compression, which lead to additional particle acceleration or deceleration depending on magnetic longitude. These drivers indicate preferred regions for nonlinear ULF wave growth, which are consistent with previous statistical studies.

A multi-satellite survey scheme for addressing open questions on the Earth’s outer radiation belt dynamics

The Earth’s outer radiation belt is highly dynamic, containing relativistic electron fluxes that can increase by several orders of magnitude during magnetospheric disturbances. This greatly increases the likelihood of spacecraft malfunction or failure and significantly influences the solar-terrestrial system’s energy and mass coupling, highlighting the importance of fully understanding the mechanisms governing these dynamics from both theoretical and practical perspectives. Although many theories have been proposed, further research is essential to quantify the specific contributions of different dynamic mechanisms for improving space weather forecasting. To address this, observations of the outer radiation belt with high spatial–temporal resolution to distinguish the spatial and temporal variations are essential. We introduce a 10-CubeSat constellation survey scheme in the geosynchronous transfer orbit (GTO) to achieve this required observation. Three baseline instruments are proposed to be employed: the high energy electron detector (HEED), the search coil wave detector (SCWD), and the magnetometer (MAG). Two groups of physical processes will be investigated: wave-particle interactions involving charged particles interacting with whistler-mode waves, electromagnetic ion cyclotron (EMIC) waves, and ultra-low frequency (ULF) waves; and radial transport encompassing shock-induced injections, substorm injections, storm convection and magnetopause shadowing. The performance parameters of instruments and platform of the constellation are presented. Additionally, aligned with the concept of constellation survey, we outline the COSPAR-coordinated space program, COnstellation of Radiation BElt Survey (CORBES), which will provide a crucial scientific contribution in the absence of the Van Allen Probes. The program’s excellent observational capability enables a comprehensive understanding of the underlying physical mechanisms governing the outer radiation belt dynamics and improved space weather forecasting.

Artificial excitation and propagation of ultra-low frequency signals in the polar ionosphere

This paper has established a relatively comprehensive model for ultra-low frequency (ULF) current induced by thermal pressure gradients and its propagation. In the ULF current excitation model, we decomposed the current into a constant term unaffected by altitude and a product with a function significantly influenced by altitude. Combining this with the EISCAT background, we determined that for modulation frequencies below 5 Hz, the optimal height for ULF current excitation corresponds to the critical frequency height. We calculated the ionospheric currents at heating altitudes of 332 km for modulation frequencies of 5 Hz; the corresponding maximum currents were 1.03 × 10−10 A·m−2. By incorporating the current into the ULF waves propagation model based on magnetoionic theory, we found that the electromagnetic field energy is mainly concentrated in the horizontal direction, indicating that the energy primarily propagates outward through magnetosonic waves. The dominant components are the electric field component Ey and the magnetic field component Bz, whose maximum values reached 1.1 μV·m−1 and 1.5 pT. Unfortunately, magnetosonic waves cannot propagate downward due to the sharp variation in the real part of the refractive index between 200 and 300 km. However, the shear Alfvén waves component By can propagate downward, and there is still an intensity of approximately 0.1 pT at the bottom of the ionosphere, which is because the refractive index of shear Alfvén waves is most uniform in the parallel magnetic field direction, allowing By to propagate parallel to the magnetic field effectively.

The Distribution of Pc5 Ultralow-frequency Waves at Geostationary Orbit

Using GOES magnetometer data spanning over 30 yr, we study the distribution of Pc5 ultralow-frequency waves at geosynchronous orbit. The CLEAN algorithm was applied to detect narrowband Pc5 waves. This method was first used in astronomical radio interferometry, but has since been applied to many other areas. The algorithm allows for identification of multiple individual peaks within the same power spectral density. We found close to 30,000 events in each magnetic field component in field-aligned coordinates. With some exceptions, results were in agreement with previous studies. Wave occurrence along magnetic local time (MLT) was higher in the 18–23 MLT sector. However, the largest accumulated wave amplitudes were observed on the dayside, peaking close to local noon. As expected, wave amplitudes were larger during more active solar wind conditions. For the radial and parallel components, amplitudes were maximum at the interplanetary magnetic field clock angle of −30° to −45°. The resultant database of Pc5 ultralow-frequency wave events can be used to constrain radiation belt models, while the CLEAN method provides a unique technique to automatically detect narrowband plasma waves in the magnetosphere and beyond.

Comparing Influences of Solar Wind, ULF Waves, and Substorms on 20 eV–2 MeV Electron Flux (RBSP) Using ARMAX Models

AbstractElectron fluxes (20 eV–2 MeV, RBSP‐A satellite) show reasonable simple correlation with a variety of parameters (solar wind, IMF, substorms, ultralow frequency (ULF) waves, geomagnetic indices) over L‐shells 2–6. Removing correlation‐inflating common cycles and trends (using autoregressive and moving average terms in an ARMAX analysis) results in a 10 times reduction in apparent association between drivers and electron flux, although many are still statistically significant (p < 0.05). Corrected influences are highest in the 20 eV–1 keV and 1–2 MeV electrons, more modest in the midrange (2–40 keV). Solar wind velocity and pressure (but not number density), IMF magnitude (with lower influence of Bz), SME (a substorm measure), a ULF wave index, and geomagnetic indices Kp and SymH all show statistically significant associations with electron flux in the corrected individual ARMAX analyses. We postulate that only pressure, ULF waves, and substorms are direct drivers of electron flux and compare their influences in a combined analysis. SME is the strongest influence of these three, mainly in the eV and MeV electrons. ULF is most influential on the MeV electrons. Pressure shows a smaller positive influence and some indication of either magnetopause shadowing or simply compression on the eV electrons. While strictly predictive models may improve forecasting ability by including indirect driver and proxy parameters, and while these models may be made more parsimonious by choosing not to explicitly model time series behavior, our present analyses include time series variables in order to draw valid conclusions about the physical influences of exogenous parameters.

ULF Wave Transport of Relativistic Electrons in the Van Allen Belts: Criteria for Transition to Radial Diffusion

AbstractRelativistic electrons in the radiation belts can be transported as a result of wave‐particle interactions (WPI) with ultra‐low frequency (ULF) waves. Such WPI are often assumed to be diffusive, parametric models for the radial diffusion coefficient often being used to assess the rates of radial transport. However, these WPI transition from initially coherent interactions to the diffusive regime over a finite time, this time depending on the ULF wave power spectral density, and local resonance conditions. Further, in the real system on the timescales of a single storm, interactions with finite discrete modes may be more realistic. Here, we use a particle‐tracing model to simulate the dynamics of outer radiation belt electrons in the presence of a finite number of discrete frequency modes. We characterize the point of the onset of diffusion as a transition from separate discrete interactions in terms of wave parameters by using the “two‐thirds” overlap criterion (Lichtenberg & Lieberman, 1992, https://doi.org/10.1007/978‐1‐4757‐2184‐3), a comparison between the distance between, and the widths of, the electron's primary resonant islands in phase space. Further, we find the particle decorrelation time in our model system with typical parameters to be on the timescale of hours, which only afterward can the system be modeled by one‐dimensional radial diffusion. Direct comparison of particle transport rates in our model with previous analytic diffusion coefficient formulations show good agreement at times beyond the decorrelation time. These results are critical for determining the time periods and conditions under which ULF wave radial diffusion theory can be applied.