Cyclotron Waves Research Articles

Two‐Dimensional Hybrid Simulation of the Second‐Harmonic Generation of EMIC Waves in the Inner Magnetosphere

AbstractTwo‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation.

Nonresonant Scattering of Energetic Electrons by Electromagnetic Ion Cyclotron Waves: Spacecraft Observations and Theoretical Framework

AbstractElectromagnetic ion cyclotron (EMIC) waves lead to rapid scattering of relativistic electrons in Earth's radiation belts, due to their large amplitudes relative to other waves that interact with electrons of this energy range. A central feature of electron precipitation driven by EMIC waves is deeply elusive. That is, moderate precipitating fluxes at energies below the minimum resonance energy of EMIC waves occur concurrently with strong precipitating fluxes at resonance energies in low‐altitude spacecraft observations. This paper expands on a previously reported solution to this problem: nonresonant scattering due to wave packets. The quasi‐linear diffusion model is generalized to incorporate nonresonant scattering by a generic wave shape. The diffusion rate decays exponentially away from the resonance, where shorter packets lower decay rates and thus widen the energy range of significant scattering. Using realistic EMIC wave packets from δf particle‐in‐cell simulations, test particle simulations are performed to demonstrate that intense, short packets extend the energy of significant scattering well below the minimum resonance energy, consistent with our theoretical prediction. Finally, the calculated precipitating‐to‐trapped flux ratio of relativistic electrons is compared to ELFIN observations, and the wave power spectra is inferred based on the measured flux ratio. We demonstrate that even with a narrow wave spectrum, short EMIC wave packets can provide moderately intense precipitating fluxes well below the minimum resonance energy.

Linear Theory Analysis and One‐Dimensional Hybrid Simulations of High‐Frequency EMIC Waves in a Dipole Magnetic Field

AbstractNarrowband (Δf ≲ 0.1fcp), high‐frequency (0.9fcp ≲ f < fcp) electromagnetic ion cyclotron (EMIC) waves, or HFEMIC waves for short, are a relatively new type of EMIC waves, where fcp is the proton cyclotron frequency. Here, we investigate the instability threshold conditions and the nonlinear evolution of HFEMIC waves at parallel propagation. First, linear theory analysis is extended to a regime relevant to HFEMIC waves (parallel proton beta β‖p < 0.01). The instability threshold follows a similar anisotropy‐β‖p relation and requires a large value of anisotropy (T⊥p/T‖p ≳ 10) for wave growth. As a result of decreasing group velocity, the convective growth rate at a fixed threshold exhibits a similar inverse relation with β‖p. Heavy ions affect the instability only weakly, primarily through the introduction of stop bands. Second, we carry out one‐dimensional hybrid simulations in a parabolic background magnetic field, with initial parameters constrained by observation. Despite the narrow source region (within about ±3° latitude), HFEMIC waves can grow well above the thermal noise level due in large part to a small group velocity of HFEMIC waves. The saturation level is well within the range of observational amplitudes, and the quasilinear process primarily determines the wave evolution. Finally, we demonstrate that the present results compare favorably to the recent statistical results, thereby supporting anisotropic low‐energy protons as free energy source for HFEMIC waves.

A semi-analytical model of RF condensation that can handle localized power depositions

A nonlinear effect, RF (radio frequency) condensation, can be used to facilitate RF stabilization of magnetic islands. Previously studied semi-analytical models for RF condensation are suited mainly for broad deposition profiles and are unable to handle power depositions that are localized in the interior of a magnetic island. The power deposition profile of electron cyclotron waves, in particular, can be highly localized near a cyclotron resonance. Here, a model is developed that can handle both localized profiles and broad profiles. This allows a comparison of RF condensation for narrow vs broad deposition profiles, and it allows a study of the dependence of RF condensation of localized deposition profiles on key parameters.

Low-frequency whistler waves driven by energetic electrons in plasmas of solely electron cyclotron wave heating

Whistler waves are a type of low-frequency electromagnetic wave common in nature, which is usually associated with energetic electron phenomena. This study presents experimental observations of low-frequency whistler wave instabilities driven by energetic electrons through wave–particle interactions on EXL-50. The energetic electrons are generated by electron cyclotron waves (ECWs) through stochastic heating [Wang et al., J. Plasma Phys. 89, 905890603 (2023)] and do not match the characteristics of the runaway electrons [Shi et al., Nucl. Fusion 62, 086047 (2022)]. In the steady-state plasma of the Energy iNNovation XuanLong-50 (EXL-50), whistler waves within the 30–120 MHz frequency range were observed during electron cyclotron resonance heating. These waves displayed multiple frequency bands, and the frequencies of waves were directly proportional to the Alfvén velocity. Furthermore, it was interesting to find that superposition of lower hybrid wave into ECW resulted in the suppression of these whistler waves. The experimental results may indicate that the whistler waves are driven by energetic electrons (excluding runaway electrons). These discoveries carry significant implications for several areas of research, including the investigation of wave–particle interactions, the development of radio frequency wave current drivers, their potential impact on the electron dynamics in future fusion devices, and even the presence of unusually low-frequency whistler waves in Earth's radiation belts.

Numerical study of minority ion heating scenarios in a spherical tokamak plasma

In this study, D(H) minority ion cyclotron resonance heating (ICRH) scenarios in Nan Chang spherical tokamak (NCST) were simulated using the full-wave code TORIC. NCST is a low-aspect-ratio (R/a = 1.67) spherical tokamak, with its core plasma parameters characterized by a magnetic field intensity of 0.36 T and a density of 1018 m−3. Our simulation results demonstrate that the ion cyclotron wave can penetrate the core plasma of the NCST more effectively with a lower toroidal mode number, indicating that resonant ions can absorb the wave energy efficiently. Furthermore, it is found that as the minority ion H concentration is increased, a noticeable decline in the left-handed electric field adjacent to the ion cyclotron resonance layer is observed. Optimal heating efficiency is attained when maintaining a minority ion H concentration within the range 5%–10%. The minority ion velocity distribution was simulated to estimate the tail temperature of minority-ICRH, which is expected to exceed 10 keV. The difference in the power efficiency with different plasma compositions [Ar(H) and D(H)] was also simulated. When the H-ion cyclotron resonance layer is located at the core plasma, the power-absorption fraction of H in Ar(H) plasma surpasses that of D and H combined in D(H) plasma under identical conditions. These simulations provide a crucial foundation and theoretical reference not only for NCST but also for other spherical tokamaks conducting ICRH experiments.

On the Spatial and Temporal Evolution of EMIC Wave‐Driven Relativistic Electron Precipitation: Magnetically Conjugate Observations From the Van Allen Probes and CALET

AbstractElectromagnetic ion cyclotron (EMIC) waves have been shown to be able to drive strong electron precipitation, particularly at MeV energies. However, the spatio‐temporal evolution of both the waves and the resulting precipitation is still not well understood. Here we investigate the evolution of relativistic electron precipitation driven by EMIC waves through combined observations from the Van Allen Probes and the CALorimetric Electron Telescope experiment onboard the International Space Station. Two case studies are examined where EMIC waves near the magnetic equator and precipitation at low altitude were detected in close magnetic conjunction, both of which were confined to narrow radial regions but persisted multiple hours. These observations, combined with quasilinear calculations, confirm that long‐lived EMIC waves can drive hours‐long MeV electron precipitation loss. However, the magnitude of the precipitation varied significantly during one of the events, as resonance conditions, particularly plasma density, evolved.

Energetic Particle Precipitation in Sub‐Auroral Polarization Streams

AbstractSub‐auroral polarization streams (SAPS) are one of the most intense manifestations of magnetosphere‐ionosphere coupling. Magnetospheric energy transport to the ionosphere within SAPS is associated with Poynting flux and the precipitation of thermal energy (0.03–30 keV) plasma sheet particles. However, much less is known about the precipitation of high‐energy (≥50 keV) ions and electrons and their contribution to the low‐altitude SAPS physics. This study examines precipitation within one SAPS event using a combination of equatorial THEMIS and low‐altitude DMSP and ELFIN observations, which, jointly, cover from a few eV up to a few MeV energy range. Observed SAPS are embedding the ion isotropy boundary, which includes strong 300–1,000 keV ion precipitation. SAPS are associated with intense precipitation of relativistic electrons (≤3 MeV), well equatorward of the electron isotropy boundary. Such relativistic electron precipitation is likely due to electron scattering by electromagnetic ion cyclotron waves at the equator.

Frequency Chirping of Electromagnetic Ion Cyclotron Waves in Earth's Magnetosphere

AbstractElectromagnetic ion cyclotron (EMIC) waves are known to exhibit frequency chirping occasionally, contributing to the rapid acceleration and precipitation of energetic particles in the magnetosphere. However, the chirping mechanism of EMIC waves remains elusive. In this work, a phenomenological model of whistler mode chorus waves named the Trap‐Release‐Amplify (TaRA) model is applied to EMIC waves. Based on the proposed model, we explain how the chirping of EMIC waves occurs, and give predictions on their frequency chirping rates. For the first time, we relate the frequency chirping rate of EMIC waves to both the wave amplitude and the background magnetic field inhomogeneity. Direct observational evidence is provided to validate the model using previously published events of chirping EMIC waves. Our results not only provide a new model for EMIC wave frequency chirping, but more importantly, they indicate the potential wide applicability of the underlying principles of TaRA model.

Conjugate Observations of Magnetospheric and Ionospheric Phenomena During a Substorm Event

AbstractThis study investigates the comprehensive magnetospheric and ionospheric phenomena during a substorm event on 14 December 2013. The methodology involves analyzing data from satellites located within the plasmasphere at dusk‐side of the Earth, as well as data from ionospheric satellites mapped in the subauroral region. Magnetospheric data were analyzed to identify key features during the substorm event. Proton injection into the ring current, presence of proton and helium band electromagnetic ion cyclotron (EMIC) waves with different polarization characteristics, and harmonic structures in these EMIC waves were identified. These harmonic structures coincided with the appearance of magnetosonic waves characterized by rising tone structures and heating of low‐energy protons (<100 eV). Ionospheric satellites (DMSP F17 and POES 15) recorded enhanced proton precipitation contributing to the intensification of subauroral proton arcs. The analysis revealed that these enhanced proton fluxes were associated with variations in field‐aligned currents (FACs) and drove dynamics within the Sub‐Auroral Polarization Streams (SAPS). By combining and analyzing the magnetospheric and ionospheric data sets, this study provides a comprehensive understanding of magnetosphere‐ionosphere coupling during substorms, particularly on the duskside. The complex interdependence and causal relationships among EMIC waves, proton precipitation, subauroral proton arcs, FAC variations, and SAPS dynamics were highlighted.

Properties of an Interplanetary Shock Observed at 0.07 and 0.7 au by Parker Solar Probe and Solar Orbiter

The Parker Solar Probe (PSP) and Solar Orbiter (SolO) missions opened a new observational window in the inner heliosphere, which is finally accessible to direct measurements. On 2022 September 5, a coronal mass ejection (CME)-driven interplanetary (IP) shock was observed as close as 0.07 au by PSP. The CME then reached SolO, which was radially well-aligned at 0.7 au, thus providing us with the opportunity to study the shock properties at different heliocentric distances. We characterize the shock, investigate its typical parameters, and compare its small-scale features at both locations. Using the PSP observations, we investigate how magnetic switchbacks and ion cyclotron waves are processed upon shock crossing. We find that switchbacks preserve their V–B correlation while compressed upon the shock passage, and that the signature of ion cyclotron waves disappears downstream of the shock. By contrast, the SolO observations reveal a very structured shock transition, with a population of shock-accelerated protons of up to about 2 MeV, showing irregularities in the shock downstream, which we correlate with solar wind structures propagating across the shock. At SolO, we also report the presence of low-energy (∼100 eV) electrons scattering due to upstream shocklets. This study elucidates how the local features of IP shocks and their environments can be very different as they propagate through the heliosphere.

Simulation of ion cyclotron wave heating in the EXL-50U spherical tokamak based on dispersion relations

This study investigates the single-pass absorption (SPA) of ion cyclotron range of frequency (ICRF) heating in hydrogen plasma of the EXL-50U spherical tokamak, which is an upgraded EXL-50 device with a central solenoid and a stronger magnetic field. The reliability of the kinetic dispersion equation is confirmed by the one-dimensional full-wave code, and the applicability of Porkolab's simplified theoretical SPA model is discussed based on the kinetic dispersion equation. Simulations are conducted to investigate the heating effects of the fundamental and second harmonic frequencies. The results indicate that with the design parameters of the EXL-50U device, the SPA for second harmonic heating is 63%, while the SPA for fundamental heating is 13%. Additionally, the optimal injection frequencies are 23 MHz at 0.9 T and 31 MHz at 1.2 T. The wave vector of the antenna parallel to the magnetic field, with a value of , falls within the optimal heating region. Simulations reveal that the ICRF heating system can play an important role in the ion heating of the EXL-50U.

Electromagnetic Ion Beam Instability in the Solar Corona

Remote-sensing measurements indicate that heavy ions in the corona undergo an anisotropic and mass-charge dependent energization. A popular explanation to this phenomenon is the damping of the Alfvén/ion cyclotron waves. In this paper, we propose that the ion beam instability can be an important source of the Alfvén/ion cyclotron waves, and we study the excitation of the ion beam instability in the corona at the heliocentric distance ∼3R ⊙ and the corresponding energy transfer process therein based on plasma kinetic theory. The results indicate that the existence of the motionless heavy ions inhibits the ion beam instability. However, the anisotropic beams of heavy ions promote the excitation of the ion beam instability. Besides, the existence of α beams can provide a second energy source for exciting beam instability. However, when both the proton beam and the α beam reach the instability excitation threshold, the proton beam driven instability excites preferentially. Moreover, the excitation threshold of the Alfvén/ion cyclotron instability driven by ion beam is of the local Alfvén speed or even less in the corona.

Effects of counter-current driven by electron cyclotron waves on neoclassical tearing mode suppression

Through theoretical analysis, we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode (NTM). The equation is used with this model to obtain the modified Rutherford equation with co-current and counter-current contributions. Consistent with the reported experimental results, numerical simulations have shown that the localized counter external current can only partially suppress NTM when it is far from the resonant magnetic surface. Under some circumstances, the Ohkawa mechanism dominated current drive (OKCD) by electron cyclotron waves can concurrently create both co-current and counter-current. In this instance, the minimal electron cyclotron wave power that suppresses a particular NTM was calculated by the Rutherford equation. The result is marginally less than when taking co-current alone into consideration. As a result, to suppress NTM using OKCD, one only needs to align the co-current with a greater OKCD peak well with the resonant magnetic surface. The effect of its lower counter-current does not need to be considered because the location of the counter-current deviates greatly from the resonant magnetic surface.

High-quality dense ZnO thin films: work function and photo/electrochemical properties

Compact ZnO (wurtzite) thin films are prepared on four different substrates by (i) spray pyrolysis or (ii) pulsed reactive magnetron sputtering combined with a radio frequency electron cyclotron wave resonance plasma. Films are characterized by AFM, XRD, Kelvin probe, cyclic voltammetry, electrochemical impedance spectroscopy, and UV photoelectrochemistry. Film morphologies, defect concentrations, crystallite size, and orientation provided specific fingerprints for the electronic structure of ZnO close to the conduction band minimum. Fabricated films are referenced, if relevant, to a model system based on a wurtzite single crystal with either Zn-face or O-face termination. Kelvin probe measurements of the ZnO/air interface distinguished effects of annealing and UV excitation, which are attributed to removal of oxygen vacancies close to the surface. In turn, the work function, at the electrochemical interface, specifically addressed the growth protocol of the ZnO electrodes but not the effects of crystallinity and annealing. Finally, high photocurrents of water oxidation are observed exclusively on virgin films. This effect is then discussed in terms of photocorrosion, and work function changes due to UV light.Graphical

Mediation of collisionless turbulent dissipation through cyclotron resonance

The dissipation of turbulence in astrophysical systems is fundamental to energy transfer and heating in environments ranging from the solar wind and corona to accretion disks and the intracluster medium. Although turbulent dissipation is relatively well understood in fluid dynamics, astrophysical plasmas often exhibit exotic behaviour, arising from the lack of interparticle collisions, which complicates turbulent dissipation and heating in these systems. Recent observations by NASA’s Parker Solar Probe mission in the inner heliosphere have shed new light on the role of ion cyclotron resonance as a potential candidate for turbulent dissipation and plasma heating. Here, using in situ observations of turbulence and wave populations, we show that ion cyclotron waves provide a major pathway for dissipation and plasma heating in the solar wind. Our results support recent theoretical predictions of turbulence in the inner heliosphere, known as the helicity barrier, that suggest a role of cyclotron resonance in ion-scale dissipation. Taken together, these results provide important constraints for turbulent dissipation and acceleration efficiency in astrophysical plasmas.

Modeling the Simultaneous Dropout of Energetic Electrons and Protons by Magnetopause Shadowing

AbstractMagnetopause shadowing (MPS) effect could drive a concurrent dropout of radiation belt electrons and ring current protons. However, its relative role in the dropout of both plasma populations has not been well quantified. In this work, we study the simultaneous dropout of MeV electrons and 100s keV protons during an intense geomagnetic storm in May 2017. A radial diffusion model with an event‐specific last closed drift shell is used to simulate the MPS loss of both populations. The model well captures the fast shadowing loss of both populations at L* > 4.6, while the loss at L* < 4.6, possibly due to the electromagnetic ion cyclotron wave scattering, is not captured. The observed butterfly pitch angle distributions of electron fluxes in the initial loss phase are well reproduced by the model. The initial proton losses at low pitch angles are underestimated, potentially also contributed by other mechanisms such as field line curvature scattering.

Impact of microwave beam scattering by density fluctuations on the electron–cyclotron power deposition profile in tokamaks

Electron–cyclotron waves are a tool commonly used in tokamaks, in particular to drive current. Their ability to drive current in a very localized manner renders them an optimal tool for MHD mode mitigation. However, such applications require high accuracy and good control of the power deposition location to efficiently target the magnetic islands. It has been indirectly observed that the suprathermal electron distribution, resulting from the wave absorption, is broader than what is expected from experimentally-constrained forward drift-kinetic modeling. The present paper explores the possibility that beam scattering through the turbulent edge of the plasma may explain this observed discrepancy. In particular, full-wave studies exhibit three beam broadening regimes, from superdiffusive to diffusive, with an intermediate regime characterized by a Lorentzian beam profile with a slightly increased full-width at half maximum with respect to the quiet plasma case. In the tokamak à configuration variable, dedicated plasma scenarios have been developed to test this hypothesis. A realistic worst-case fluctuation scenario falls into this intermediate beam broadening regime. By comparing the experimental hard x-ray emission from suprathermal electron Bremmstrahlung with the emission calculated by coupling a full-wave model to a Fokker–Planck solver, it is shown that, in the tested cases, the beam broadening is not sufficient to explain the aforementioned discrepancy between simulation and experiment and that another mechanism must play the main role in broadening the suprathermal electron distribution.

Proton- and Alpha-driven Instabilities in an Ion Cyclotron Wave Event

Ion-scale wave events or wave storms in the solar wind are characterized by enhancements in magnetic field fluctuations as well as coherent magnetic field polarization signatures at or around the local ion cyclotron frequencies. In this paper, we study in detail one such wave event from Parker Solar Probe's (PSP) fourth encounter, consisting of an initial period of left-handed (LH) polarization abruptly transitioning to a strong period of right-handed (RH) polarization, accompanied by a clear core beam structure in both the alpha and proton velocity distribution functions. A linear stability analysis shows that the LH-polarized waves are anti-sunward propagating Alfvén/ion cyclotron waves primarily driven by a proton cyclotron instability in the proton core population, and the RH polarized waves are anti-sunward propagating fast magnetosonic/whistler waves driven by a firehose-like instability in the secondary alpha beam population. The abrupt transition from LH to RH is caused by a drop in the proton core temperature anisotropy. We find very good agreement between the frequencies and polarizations of the unstable wave modes as predicted by linear theory and those observed in the magnetic field spectra. Given the ubiquity of ion-scale wave signatures observed by PSP, this work gives insight into which exact instabilities may be active and mediating energy transfer in wave–particle interactions in the inner heliosphere, as well as highlighting the role a secondary alpha population may play as a rarely considered source of free energy available for producing wave activity.

On the possibility of mode coupling for low frequency electromagnetic waves in plasmas with anisotropy of temperature

We study the dispersion relation for low frequency electromagnetic waves propagating along the ambient magnetic field and investigate the possibility of occurrence of coupling between waves in the ion cyclotron branch and waves in the whistler branch. The results obtained show that the coupling may occur in the case of conditions leading to the ion cyclotron instability, for sufficiently high value of the ratio between perpendicular and parallel ion temperature, and does not occur in the case of conditions leading to the ion firehose instability. The results also show that the decrease in the value of the plasma beta may lead to the disappearance of the mode coupling conditions. Regarding the effect of the electron population, it is shown that the change in the shape of the electron velocity distribution, from Maxwellian to bi-Kappa form, does not change the results obtained, as long as the electron temperatures are isotropic, but the increase in anisotropy in the electron temperatures may lead to the disappearance of the coupling between the different waves. The consequences of the frequency dependency of the mode coupling conditions are discussed considering wave propagation in an inhomogeneous medium, leading to the conclusion that the energy of a packet of waves of a given mode can be absorbed or mode converted over an extended region of space. These findings can be of relevance for the analysis and understanding of processes related to the conversion between ion cyclotron waves and whistler waves.