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Low‐frequency chorus waves (below 0.1 fce_eq ${f}_{\\text{ce}\\_\\text{eq}}$, where fce_eq ${f}_{\\text{ce}\\_\\text{eq}}$ is equatorial electron gyrofrequency) can induce the depletion of relativistic electrons in Earth's radiation belts by effective pitch angle scattering, demonstrating distinct effects on radiation belt dynamics compared to typical chorus waves (0.1–0.8 fce_eq ${f}_{\\text{ce}\\_\\text{eq}}$). However, their generation mechanism and environmental drivers remain poorly understood. Analysis of Van Allen Probes data reveals that low‐frequency chorus waves predominantly occur in the region of MLT range of 0–7 hr and L ∼ 6. These waves show a strong correlation with intense substorm activity and moderate magnetic storms, with the majority of waves clustering during storm‐time substorms. Their excitation mechanism is driven by the coexistence of isotropic low‐energy electrons (below 30 keV) and anisotropic high‐energy electrons (above 50 keV) during the storm's peak, along with concurrent geomagnetic field weakening due to enhanced ring currents.

Magnetosonic (MS) waves can be generated by hot Maxwellian ring protons locally within the Martian upper ionosphere, characterized by a weak ambient magnetic field and the presence of cold plasma abundant in heavier ions. A comprehensive study on the resonant instabilities of MS waves making use of the derived growth rates show that ring proton population with energies around 100 eV is optimal for wave generation. Highly oblique propagation leads to sharp harmonic structures at frequencies closer to local proton gyrofrequency. An increase in ring energy, ωpe/Ωce${\\omega }_{pe}/{{\\Omega }}_{ce}$ratio, and heavier ion concentration decreases the wave growth rates. When the background ions have very low temperatures, O2+${\\mathrm{O}}_{2}^{+}$ions lower the growth rate more as compared to O+${\\mathrm{O}}^{+}$ions. Additionally, the increase in temperatures of cold electrons and ions have opposite effects, with the former increasing the growth rate and the latter decreasing it. Plain Language Summary Magnetosonic (MS) waves with frequencies near the local proton gyrofrequency are frequently observed in the Martian upper ionosphere. Recent observations confirm the presence of hot ring proton distributions coinciding with these wave detections. While instability of MS waves generated by ring protons have been studied in the context of Earth's magnetosphere, the Martian environment is notably different due to weaker ambient magnetic field and the presence of heavier ions in the background plasma. The current study on MS wave generation in Martian upper ionosphere reveals that an increase in ring energy, ωpe/Ωce${\\omega }_{pe}/{{\\Omega }}_{ce}$ratio, and background ion temperature all contribute to a decrease in wave growth rates, whereas a higher background electron temperature enhances the growth rate. Heavier ions at low temperature in the background plasma also suppress the growth rate, with O2+${\\mathrm{O}}_{2}^{+}$ions having predominant effect. Maxwellian ring protons with energies around 100 eV, likely penetrating from the magnetosheath, can locally generate lower harmonics of highly oblique MS waves in the Martian upper ionosphere. Key Points Hot Maxwellian ring protons of energy around 100 eV are favorable for the generation of Magnetosonic waves in the Martian upper ionosphere O2+${\\mathrm{O}}_{2}^{+}$ions are the primary contributors to the growth rate decrease when the heavier ions are at very low temperatures The growth rate is significantly affected by the ratio of electron plasma to cyclotron frequency and temperature of background species

Magnetosonic (MS) waves are dominant plasma waves causing severe Martian ionospheric erosion. They are generally considered to originate upstream of Martian bow shock with frequencies near the upstream proton gyrofrequency. However, whether MS waves can be locally excited lacks theoretical analysis. Here we present an event of MS waves with frequencies above and closely related to the local proton gyrofrequency in the Martian ionosphere. Concurrently, ring beam hot proton distributions are observed due to the penetration of magnetosheath protons. By employing the observed plasma and magnetic field data, the calculated linear growth rates for MS waves agree well with the observed wave power spectra, demonstrating that they can be locally excited by unstable ring beam hot protons at Mars. Our results could be of great help in understanding the excitation of MS waves in a heavy ion‐rich environment around unmagnetized planets. Plain Language Summary Magnetosonic (MS) wave is one of the most important plasma waves contributing to the Martian atmospheric loss. They are generally considered to originate upstream of the Martian bow shock. Recent observations at Mars have shown that some MS waves with frequencies near the local proton gyrofrequency were accompanied by ring/shell‐like hot proton distributions. However, whether these waves can be locally excited by such protons lacks the support of the theoretical analysis. In this letter, on the basis of linear instability analysis, we show that MS waves with frequencies well above the local proton gyrofrequency can be locally excited by unstable ring beam hot protons in the Martian ionosphere. These results advance our knowledge of the MS wave excitation in a heavy ion‐rich environment around planets without an intrinsic magnetic field. Key Points Magnetosonic waves above the local proton gyrofrequency are observed in the Martian ionosphere Ring beam hot proton distribution associated with magnetosonic waves is formed by the penetration of solar wind protons simultaneously Magnetosonic waves are locally generated by the ring beam hot protons

Magnetosonic (MS) waves with frequencies above the proton gyrofrequency can be locally generated by ring‐beam protons in the Martian heavy ion‐rich ionosphere. In this study, we conduct a parametric analysis to investigate the effects of heavy ion concentrations, energy (Erb), and angle (αrb) of ring‐beam protons, and wave normal angle on the excitation features of Martian ionospheric MS waves. We find the growth rates and frequency range of MS waves decrease by including O+ and O2+ ions but are insensitive to their relative concentrations. With increasing Erb or αrb, the growth rates of MS waves show a general dropping tendency. Meanwhile, their frequency and wavenumber range are almost unaffected by increasing Erb but shrink to a narrower range mainly distributed in high frequencies by increasing αrb. Unstable MS waves expand to a wider wavenumber range but shrink to a narrower frequency range as they become more oblique. Plain Language Summary Magnetosonic (MS) waves are highly compressible electromagnetic emissions in space. Generally, they are locally excited by ring‐like hot protons in plasmas that lack heavy ions. However, a recent study reveals that they can also be locally excited by ring‐beam protons in the Martian heavy ion‐rich ionosphere. Motivated by these differences, we conduct a detailed parametric analysis to investigate how the heavy ion concentrations, the energy and angle of ring‐beam protons, and the wave normal angle affect the dispersion relation and growth rate of Martian MS wave. We find that O+ and O2+ ions lower the growth rates and frequency range of MS waves but the effects of their relative concentrations are insignificant. In addition to the heavy ions, the excitation features of MS waves strongly depend on the wave normal angle and the distribution properties of ring‐beam protons. These results deepen our understanding of the MS wave excitation features in the unmagnetized planet environment with plentiful heavy ions. Key Points O+ and O2+ ions lower the growth rates and frequency range of Magnetosonic (MS) waves but the effects of their relative concentrations are insignificant The growth rates of MS waves show a general dropping tendency with increasing ring‐beam energy or angle Unstable MS waves expand to a wider wavenumber range but shrink to a narrower frequency range as they become more oblique

Previous statistical studies have described the distributions and properties of whistler‐mode waves in Jupiter's magnetosphere, but explaining these wave distributions requires modeling wave propagation from their generation near the magnetic equator. In this letter, we conduct ray tracing of whistler‐mode waves based on realistic Jovian magnetic field and density models. The ray tracing results generally agree with the statistical wave distributions based on Juno measurements. The modeled ray paths show that high‐frequency waves generated near the equator are confined within 20° magnetic latitude due to Landau damping, low‐frequency waves can propagate to higher latitudes and lower M‐shells, with changing wave normal angles, and a portion of low‐frequency waves could propagate to high M shells at high latitudes. Our modeling results provide a theoretical interpretation of whistler‐mode wave distributions and properties, providing essential insights for future radiation belt models at Jupiter. Plain Language Summary Scientists have recently been paying more attention to “whistler‐mode waves” in Jupiter's magnetosphere, as these waves play a key role in the movement of high‐energy electrons within Jupiter's radiation belts. A recent study by Ma, Li, Zhang, Kang, et al. (2024), https://doi.org/10.1029/2024gl111882, using data from NASA's Juno spacecraft, provides detailed insights into these waves, especially at frequencies lower than the “equatorial electron gyrofrequency” in Jupiter's magnetosphere. The study uncovers new information on how these waves propagate through Jupiter's magnetic fields, especially in relation to their origin and angles of inclination relative to the background magnetic field. In the present study, we use computer models to trace how these waves propagate through Jupiter's magnetosphere, based on realistic magnetic field and density conditions. Our models reveal that the waves observed at higher latitudes and farther from Jupiter likely originate near the equator at lower frequencies and evolve as they propagate. This interpretation aligns with the findings from the Juno spacecraft and helps explain how these waves propagate within Jupiter's magnetosphere. Key Points Realistic ray tracing is conducted for Jovian whistler mode waves and results are able to reproduce statistical observations High‐frequency waves originated from equator are confined within 20° latitude and separated from high‐latitude waves originated elsewhere Low‐frequency waves maintain high wave power from the equator to high latitudes and can propagate to low M with varying wave normal angles

Injection flux tubes, characterized by localized equatorial magnetic field enhancements and concomitant hot plasma populations, contribute to Saturn's magnetospheric convection cycle by transporting magnetic flux radially inward. The sharp magnetic gradients at the flux‐tube edges have been demonstrated to enable the trapping of equatorially mirroring particles, leading to their energy‐dispersionless signatures in spacecraft observations. Here, we present a statistical distinction between flux tubes with and without particle‐trapping features in the electron cyclotron harmonic (ECH) wave properties. The particle‐trapping flux tubes carry stronger ECH waves in the high‐harmonic bands, whereas the other category is usually accompanied only by fundamental‐mode waves. This distinction is largely attributed to the higher content of energetic electrons within the particle‐trapping flux tubes. These results improve our understanding of the association between injection flux tubes and the high‐band ECH waves therein, suggesting a unique role of particle‐trapping flux tubes in Saturnian magnetospheric dynamics. Plain Language Summary In Saturn's magnetosphere, the plasma convection involves the inward motion of localized injection flux tubes characterized by enhanced magnetic field strength and energetic particle fluxes. The flux enhancements of particles at different energies are usually asynchronous because of their energy‐dependent drift speeds around Saturn. In certain events, however, this picture could be modified by sharp magnetic gradients at flux‐tube edges, which lead to the trapping of near‐equatorial particles manifested by their simultaneous flux enhancements over a wide energy range. Here, we analyze the Cassini observations of injection flux tubes, categorize them into those with and without particle‐trapping features, and examine their associated electrostatic wave properties. The particle‐trapping flux tubes are statistically associated with waves at discrete frequencies between harmonics of the electron gyrofrequency, known as electron cyclotron harmonic waves. These emissions occur in both the fundamental‐mode and high‐harmonic bands. In contrast, non‐trapping flux tubes are predominantly accompanied by fundamental‐mode waves only. The different wave properties are attributed to the higher content of energetic electrons in particle‐trapping flux tubes. These findings highlight the role of injection flux tubes in Saturn's magnetospheric dynamics. Key Points Particle‐trapping flux tubes with energy‐dispersionless features of equatorially mirroring particles carry intense electron cyclotron harmonic (ECH) waves in high bands Particle‐trapping flux tubes correspond to stronger magnetic field enhancements and higher content of energetic electrons than other events Parametric analysis demonstrates the important role of energetic electrons above 1 keV in the excitation of ECH waves in high harmonic bands

The wave amplitude is vital for quantifying the impact of electromagnetic ion cyclotron (EMIC) waves on inner magnetospheric dynamics. Previous numerical studies mainly focused on the evolution of total wave energy/amplitude, whose maximum is usually modeled as a function of initial conditions. Recent quasilinear theory analysis shows existence of a second saturation of multi‐band EMIC waves which exhibits a dip of the total amplitude, emphasizing the need for more precise band‐specific models. Through one‐dimensional hybrid simulations, we reproduce the second saturation phenomenon and separately model wave characteristics for H+‐ and He+‐bands waves, including the maximum amplitudes and the time to maximum as a function of the initial maximum growth rate. Moreover, new parameters for the anisotropy‐beta inverse correlation of hot protons are obtained at the second saturation stage. We further present an in situ observation that first demonstrates the existence of the second saturation. Plain Language Summary Electromagnetic ion cyclotron (EMIC) waves can be naturally generated by hot protons with frequencies below the proton gyrofrequency. In the inner magnetosphere, the presence of heavy ions, such as helium and oxygen ions, leads to the classification of EMIC waves into distinct bands separated by the heavy ion gyrofrequencies. The wave properties and evolution characteristics can vary significantly across different bands, influencing their role in plasma dynamics. This study employs one‐dimensional hybrid simulations to separately model the wave characteristics across different bands, which has seldom been done yet. The maximum amplitude and the time to maximum are well modeled by simple two‐parameter power law functions of the initial maximum growth rate through the optimal fitting. Furthermore, the simulations capture the phenomenon of “second saturation” where a new saturation stage occurs after the usual first saturation. We also identify an anisotropy‐beta inverse correlation for hot protons at the second saturation stage. Importantly, we provide the first direct observational evidence of the second saturation, demonstrating strong agreement between observational data and simulation results. Key Points A series of one‐dimensional hybrid simulations are conducted to investigate the saturation process of parallel H+‐ and He+‐band EMIC waves Wave characteristics in H+‐ and He+‐ bands are separately parameterized as a function of the initial maximum growth rates An in situ observational case is presented to demonstrate the second saturation of multi‐band EMIC waves

We develop first-principles theory of kinetic plasma turbulence governed by the Vlasov-Maxwell-Landau equations in the limit of vanishing collision rates. Following an exact renormalization-group approach pioneered by Onsager, we demonstrate the existence of a “collisionless range” of scales (lengths and velocities) in one-particle phase space where the ideal Vlasov-Maxwell equations are satisfied in a “coarse-grained sense.” Entropy conservation may nevertheless be violated in that range by a “dissipative anomaly” due to nonlinear entropy cascade. We derive “4/5th-law-type” expressions for the entropy flux, which allow us to characterize the singularities (structure-function scaling exponents) required for its nonvanishing. Conservation laws of mass, momentum, and energy are not afflicted with anomalous transfers in the collisionless limit. In a subsequent limit of small gyroradii, however, anomalous contributions to inertial-range energy balance may appear due to both cascade of bulk energy and turbulent redistribution of internal energy in phase space. In that same limit, the “generalized Ohm’s law” derived from the particle momentum balances reduces to an “ideal Ohm’s law” but only in a coarse-grained sense that does not imply magnetic flux freezing and that permits magnetic reconnection at all inertial-range scales. We compare our results with prior theory based on the gyrokinetic (high-gyrofrequency) limit, with numerical simulations, and with spacecraft measurements of the solar wind and terrestrial magnetosphere.

Whistler‐mode waves are commonly observed within the lunar environment, while their variations during Interplanetary (IP) shocks are not fully understood yet. In this paper, we analyze two IP shock events observed by Acceleration, Reconnection, Turbulence and Electrodynamics of the Moons Interaction with the Sun (ARTEMIS) satellites while the Moon was exposed to the solar wind. In the first event, ARTEMIS detected whistler‐mode wave intensification, accompanied by sharply increased hot electron flux and anisotropy across the shock ramp. The potential reflection or backscattering of electrons by the lunar crustal magnetic field is found to be favorable for whistler‐mode wave intensification. In the second event, a magnetic field line rotation around the shock region was observed and correlated with whistler‐mode wave intensification. The wave growth rates calculated using linear theory agree well with the observed wave spectra. Our study highlights the significance of magnetic field variations and anisotropic hot electron distributions in generating whistler‐mode waves in the lunar plasma environment following IP shock arrivals. Plain Language Summary The surface of the Earth's Moon is frequently exposed to the incoming solar wind flow and IP shocks due to its lack of internal magnetic fields that can deflect the solar wind particles. Within the lunar environment, whistler‐mode waves, characterized by electromagnetic fluctuations with frequencies below the electron gyrofrequency, are commonly present. Interplanetary shocks that are often associated with significant disturbances in electron flux and magnetic field can potentially lead to anisotropic distributions of electrons, which are known to provide free energy source for whistler‐mode wave generation. To assess the whistler wave generation under shock conditions, we conduct an in‐depth analysis of two IP shock events. These events provide clear evidence of shock‐induced enhancements in electron pitch angle anisotropy and flux, as well as a potential rotation of magnetic field around the shock region, resulting in the intensification of whistler‐mode waves downstream of the shock. We calculated a timeseries of linear wave growth rate for the entire duration of shock events, which remarkably accounted for the observed whistler‐mode wave spectra both before and after the shock arrival. Our findings are important for understanding the associated physical process of whistler‐mode wave generation in the lunar plasma environment during IP shock events. Key Points Two Interplanetary shock events in the lunar environment are analyzed to unveil whistler wave generation around shock region Linear wave growth calculations show that whistler‐mode waves are generated locally due to enhanced electron anisotropy and flux Magnetic field line connection to lunar surface is found to be important for enhancing whistler wave intensity

Electromagnetic ion cyclotron (EMIC) instabilities in the inner magnetosphere are investigated with considering the effect of temperature anisotropic electrons. The perpendicular anisotropic electrons (Ae > 1) impose an inhibiting effect on EMIC instabilities, whereas parallel anisotropic electrons (Ae < 1) may generate a promoting or inhibiting effect depending on the direction of wave group velocity. The electron firehose modes can be coupled with EMIC modes. Three unanticipated secondary waves nearby the ion cyclotron frequencies are aroused by the electrons resonating with EMIC waves. The strong wave growth at proton gyrofrequency indicates that the electrons as an important energy provider for EMIC modes have been largely overlooked in previous studies. For the first time, we report a backward EMIC wave with the group velocity in opposite direction of the phase velocity. We suggest the new‐found effects from hot anisotropic electrons may improve our understanding of EMIC instabilities in the inner magnetosphere. Plain Language Summary Electromagnetic ion cyclotron (EMIC) waves are produced by the anisotropic ions. It is generally believed that electrons have nothing to do with the generation of these waves. However, recent studies for the solar wind have demonstrated that temperature anisotropic electrons can affect the EMIC instability. We extend the study into the inner magnetosphere. The wave growth rate and dispersion relation are calculated in a multicomponent plasma consisting of H+, He+, and O+. Our studies suggest that MeV electrons with Ae > 1 have a strong inhibiting effect on the EMIC instability. Whereas, Ae < 1 electrons may generate a promoting or inhibiting effect depending on the direction of wave group velocity. A wave mode coupling occurs between the EFH and EMIC waves. The dispersion curves of EMIC waves in the three bands may turn over from below the ion cyclotron frequencies to above them due to a reversal of the group velocity. The special wave mode modulation greatly changes the dispersion relations, and brings the characteristic frequency of EMIC waves into better agreement with the statistical data, such as the occasional presence of hydrogen waves at ω > ΩH and helium waves at ω < 0.5ΩHe, and the infrequent occurrence of oxygen waves at ω < ΩO. Key Points Ae > 1 electrons inhibit electromagnetic ion cyclotron (EMIC) instabilities, whereas Ae < 1 electrons promote or inhibit EMIC instabilities depending on the Vg direction The resonating electrons can provide energy for EMIC modes and generate secondary waves nearby the ion cyclotron frequencies For the first time, we report a backward EMIC wave with a group velocity in opposite direction of the phase velocity