Background Parameter Effects on Linear–Nonlinear Chorus Wave Growth in the Planetary Magnetosphere

We calculated the linear and nonlinear growth rates of whistler‐mode chorus waves with relativistic treatment across different wave frequencies and investigated their dependence on the associated parameters, including background magnetic field strength, cold electron density, and energetic electron temperature. The linear and nonlinear growth rates, with respect to any of the three parameters in the range investigated, are confirmed to often exhibit a peak, at least, in the lower band (i.e., <0.5 fce, electron cyclotron frequency). For a given energetic electron temperature between 0.5 and 500 keV, both linear and nonlinear growth rates at low frequencies can be positive in a specific range of background magnetic field strength and cold electron density, with an optimum growth rate occurring when either parameter is fixed. However, as the electron temperature increases within this range, linear damping becomes more pronounced, resulting in a suppression of linear growth at high frequencies. On the other hand, as the strength of the magnetic field increases, a higher energetic electron temperature is required to sustain wave growth. Notably, nonlinear growth can still occur even when the linear growth rate is negative as previous studies have demonstrated. Parameters leading to such conditions are also demonstrated. Comparisons with previous chorus wave observations confirm the dependence on the parameters and explain the existence of an optimum wave growth condition and overlapping parameter ranges for both linear and nonlinear wave growth.

Chorus emissions are triggered from the linear cyclotron instability driven by the temperature anisotropy of energetic electrons (10-100 keV) in the magnetosphere. Chorus emissions grow as an absolute nonlinear instability near the magnetic equator due to the presence of an electromagnetic electron hole in velocity space. The transition process from the linear wave growth at a constant frequency to the nonlinear wave growth with a rising tone frequency is due to formation of a resonant current - J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> anti-parallel to the wave magnetic field. The rising-tone frequency introduces a phase shift to the electron hole at the equator, and results in a resonant current component anti-parallel to the wave electric field - J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</sub> , which causes the nonlinear wave growth. To confirm this triggering mechanism, we perform Vlasov Hybrid Simulations with J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> and without J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> . The run without J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> does not reproduce chorus emissions, while the run with J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> does successfully reproduce chorus emissions. The nonlinear frequency shift ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> due to J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> plays a critical role in the triggering process. The nonlinear transition time T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> for the frequency shift is found to be of the same order as the nonlinear trapping period, which is confirmed by simulations and observation. The established frequency sweep rate is ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> /T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> , which gives an optimum wave amplitude of chorus emissions.

Whistler mode chorus waves play a key role in controlling electron dynamics in Earth's inner magnetosphere. A criterion has been previously suggested whereby if the maximum value of the linear growth rate of whistler mode waves exceeds a certain critical bound, then fully nonlinear wave growth occurs and chorus waves are generated. This criterion corresponds to a boundary curve in (Nh/N0,AT) space where Nh is the hot electron number density, N0 is the cold electron number density, and AT is the thermal anisotropy. Chorus waves are generated in the region above the boundary curve, while no chorus waves are generated below the boundary curve. In the present study, we make use of a recently published set of 36 particle simulations of chorus, and we thereby are able to confirm the validity of the criterion. It is expected that this simple concept of the theoretical boundary curve based on linear theory will be useful in guiding the choice of parameters in future simulations of chorus and also of practical use in interpreting experimental chorus wave data.

We perform parametric analyses of electromagnetic ion cyclotron (EMIC) triggered emissions with a gradient of the non-uniform ambient magnetic field using a hybrid simulation. According to nonlinear wave growth theory, as the gradient of the ambient magnetic field becomes larger, the theoretical threshold of the wave amplitude becomes larger although the optimum wave amplitude for nonlinear wave growth does not change. With a larger magnetic field gradient, we obtain coherent rising tone spectra because the triggering process of the EMIC triggered emission takes place only under a limited condition on the wave amplitude. On the other hand, with a smaller magnetic field gradient, triggering of the emissions can be caused with various wave amplitudes, and then the sub-packets are generated at various locations at the same time. The concurrent triggering of emissions results in incoherent waves, observed as “broadband” EMIC bursts. Broadband emissions induce rapid precipitation of energetic protons into the loss cone since the scattering by the concurrent triggering takes place faster than that of the coherent emissions. The coherent triggered emission causes efficient proton acceleration around the equator because of the stable particle trapping by the coherent rising tone emission.

A statistical study on the cross‐scale property on the temporal variations of pulsating aurora intensity was conducted on 53 events observed at the Poker Flat Research Range during the period from 1 December 2011 to 1 March 2012. The observed modulation frequency ranged from 1.5 to 3.3 Hz, and strong modulations were not seen in the frequency range higher than about 3 Hz. This suggests that the time of flight of electrons has a time‐smoothing effect on the more rapid variations above 3 Hz. Furthermore, the frequency of modulation showed relatively strong correlation to auroral intensity (correlation coefficient of 0.58), and it can be explained with nonlinear wave growth theory, in which the modulation frequency increases with the wave amplitude of the whistler mode chorus. In contrast, the on‐off pulsations showed no significant correlations with auroral intensity. This result probably implies that several different plasma processes with different time scales from nonlinear wave growth should be taken into account when determining the on‐off periods. In particular, we suggest that long‐term variations in the cold plasma density play a dominant role in controlling the conditions of wave‐particle interactions that have temporal scale of the on‐off pulsation periods.

An Improved Parameterization for Energy Exchange from Wind to Stokes Waves

Nonlinear gyroresonant acceleration is an essential mechanism for the formation of relativistic electrons in Earth's radiation belts, yet we still have only limited knowledge of how electron motion interacts nonlinearly with plasma waves. Here we demonstrate the compelling suppression of whistler‐mode chorus emissions as a resonant wave with energetic electrons by tuning an external transmitter signal in space plasmas. Through forcible modification of electron motions via phase trapping by the external waves, the nonlinear gyroresonant current is suppressed along with the electron hole deformation. Moreover, this can decrease the population of relativistic electrons due to the lack of coherent resonant waves seen by the phase‐organized electrons. Understanding such nonlinear wave suppression effects is crucial for a potential active control of Earth's plasma environment.

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The interaction of a beam propagating in a inhomogeneous solar wind plasma is considered. The properties of the plasma waves are described by the one dimensional Zakharov's equation, the beam is modelled by means of particles moving in the electric fields of the Langmuir waves. We take into account the presence of high level density fluctuations that are known to be present in the solar wind. It is shown that when the level of density fluctuations is low, δn/n0≪3k2λd2, the regime of beam relaxation is very similar to that occurring in a homogeneous plasma and can be described by the quasilinear (QL) equations. In this case, the relaxation length is very short and corresponds to that obtained using the QL approximation. On the contrary, when the level of density fluctuations overcomes some limit, i.e. δn/n0≥3k2λd2, where δn/n0≪1, the plasma inhomogeneities crucially influence the process of relaxation. First, the linear wave growth becomes localized and clearly identifiable wave packets/clumps dominate the wave spectrum; this is associated with the kinematic properties of the waves' propagation and the wave-particle resonant interactions. Most of the wave packets grow in the regions of density gradients. The second important feature revealed by the beam relaxation consists in the generation of a tail of accelerated electrons with velocities V > Vb exceeding the beam drift. The beam widens in both directions, toward lower velocities as well as higher velocities; the density of the accelerated electrons can reach more than 10 ÷ 20 % of the beam density and the energy flux carried by this population can become as large as 40% of the initial energy flux of the beam.

Whistler-mode waves are a wave mode in plasma occurring near and below the electron cyclotron frequency. They are commonly observed in planetary magnetospheres and play a crucial role in accelerating and precipitating magnetospheric electrons. Using Juno’s observations, we investigate these waves in Jupiter’s magnetosphere, focusing on the region between 20 and 80 Jupiter radii on the post-midnight-to-dawn side. Observations from the Waves instrument show that these waves primarily occur in the lobes, where the magnetic field is strong and plasma density is low, rather than in the central magnetodisk, where the field is weaker and plasma is denser. Simultaneous electron measurements from JADE-E, combined with dispersion relation analysis, indicate that these waves are likely driven by a mono-directional electron population between ∼0.1 and 10 keV propagating anti-Jupiter-ward. Further controlled studies show that a local flux minimum at ∼0.3 keV in the electron energy spectrum, commonly observed during whistler-mode waves, is critical for wave growth. Based on their direction of motion, we suggest that these mono-directional electrons and the whistler-mode waves they generate are related to magnetosphere-ionosphere coupling. Our findings offer new insights into the interplay between whistler-mode waves and electrons in Jupiter’s magnetosphere.

Whistler-mode and ULF waves upstream of planetary bow shock play important role in energy transfer and dissipation processes in the planetary environment. A series of whistler-mode waves with their frequencies centered at ~0.4 Hz, accompanied by another series of ~0.04 Hz ULF waves, were observed upstream of the Martian bow shock by MAVEN on 2015 August 14. During the occurrence of waves, a significant flux enhancement of high-energy protons up to &amp;#8764;10 keV, as well as the response of electrons to the ULF waves, were also observed. The pitch angle distributions of electrons were modulated differently according to electrons&amp;#8217; energies. Preliminary dispersion analysis suggests that the solar wind condition was capable of generating ULF waves by ion-ion instabilities, while the observed whistler-mode waves have the potential of resonating with protons of &amp;#8764;1 keV with large pitch angles up to nearly perpendicular to the background magnetic field. Our results indicate the possible connection between co-existence of waves and the origin of energized protons through wave-particle interactions in the Martian environment.

This presentation highlights some advancements in understanding plasma wave generation and wave-particle interactions in space plasmas. Utilizing data from the Van Allen Probes, we conducted a comprehensive analysis of whistler-mode chorus waves, revealing key properties such as source regions, element durations, and the role of magnetic field inhomogeneity. Further comparative studies of plasma waves across different planets provided crucial evidence supporting the universality of the TaRA model. Additionally, we discovered two distinct forms of energy coupling between plasma waves: between whistler-mode waves through wave beating, and between high-frequency electromagnetic ion cyclotron (EMIC) waves and magnetosonic (MS) waves, driven by anisotropic low-energy protons. These findings significantly enhance our understanding of space plasma dynamics and have broad implications for theoretical models and future research in the field. &amp;#160; &amp;#160;&amp;#160;

In the equatorial region of the Earth's inner magnetosphere, the electromagnetic ion cyclotron (EMIC) triggered emissions are generated through interaction with energetic protons. We investigate the generation process of the EMIC triggered emissions in the He+branch and associated precipitation of the energetic protons using a one‐dimensional hybrid simulation with a cylindrical parabolic magnetic geometry. The simulation results show a good agreement with the nonlinear wave growth theory. As the electron density becomes higher as in the plasmasphere or the plasmaplume, the wave amplitude thresholds for both H+ and He+ band triggered emissions become lower and their nonlinear growth rates become higher. The higher hot proton density also makes the thresholds lower. While the H+ branch triggered emissions interact with a few keV protons, the He+ branch triggered emissions interact with more energetic protons of a few hundred keV with a larger nonlinear growth rate.

&amp;lt;p&amp;gt;Based on data from the ZH-1 satellites, companied with Van Allen Probes and NOAA observations, we analyze the high energy particle evolutions in radiation belts, slot region and SAA during August 2018 major geomagnetic storm (minimum Dst &amp;amp;#8776; &amp;amp;#8722;190 nT).&amp;amp;#160;&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;&amp;amp;#160;&amp;amp;#160;1) Relativistic electron enhancements in extremely low L-shell regions (reaching L &amp;amp;#8764; 3) were observed during storm. Contrary to what occurs in the outer belt, such an intense and deep electron penetration event is rare and more interesting. Strong whistler-mode (chorus and hiss) waves, with amplitudes 81&amp;amp;#8211;126 pT, were also observed in the extremely low L-shell simultaneously (reaching L &amp;amp;#8764; 2.5) where the plasmapause was suppressed. The bounce-averaged diffusion coefficient calculations support that the chorus waves can play a significantly important role in diffusing and accelerating the 1&amp;amp;#8211;3 MeV electrons even in such low L-shells during storms.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;2) A robust evidence is clearly demonstrated that the energetic electron flux with energy 30&amp;amp;#8764;600 keV are increased by 2&amp;amp;#8764;3 times in the inner radiation belt near equator and SAA region on dayside during the major geomagnetic storm. This is the first time that the 100s keV electron flux enhancement is reported to be potentially induced by the interaction with magnetosonic waves in extremely low L-shells (L&amp;lt;2) observed by Van Allen Probes. Proton loss in outer boundary of inner radiation belt takes place in energy of 2~220 MeV extensively during the occurrence of this storm but the loss mechanism is energy dependence which is consistent with some previous studies. It is confirmed that the magnetic field line curvature scattering plays a significant role in the proton loss phenomenon in energy 30-100 MeV during this storm. This work provides a beneficial help to comprehensively understand the charged particles trapping and loss in SAA region and inner radiation belt dynamic physics.&amp;lt;/p&amp;gt;

The resonance regions for resonant interactions of radiation belt electrons with obliquely propagating whistler-mode chorus waves are investigated in detail in the Dungey magnetic fields that are parameterized by the intensity of uniform southward interplanetary magnetic field (IMF) Bz or, equivalently, by the values of D=(M/Bz,0)1/3 (where M is the magnetic moment of the dipole and Bz,0 is the uniform southward IMF normal to the dipole’s equatorial plane). Adoption of background magnetic field model can considerably modify the determination of resonance regions. Compared to the results for the case of D = 50 (very close to the dipole field), the latitudinal coverage of resonance regions for 200 keV electrons interacting with chorus waves tends to become narrower for smaller D-values, regardless of equatorial pitch angle, resonance harmonics, and wave normal angle. In contrast, resonance regions for 1 MeV electrons tend to have very similar spatial lengths along the field line for various Dungey magnetic field models but cover different magnetic field intervals, indicative of a strong dependence on electron energy. For any given magnetic field line, the resonance regions where chorus-electron resonant interactions can take place rely closely on equatorial pitch angle, resonance harmonics, and kinetic energy. The resonance regions tend to cover broader latitudinal ranges for smaller equatorial pitch angles, higher resonance harmonics, and lower electron energies, consistent with the results in Ni and Summers [Phys. Plasmas 17, 042902, 042903 (2010)]. Calculations of quasi-linear bounce-averaged diffusion coefficients for radiation belt electrons due to nightside chorus waves indicate that the resultant scattering rates differ from using different Dungey magnetic field models, demonstrating a strong dependence of wave-induced electron scattering effect on the adoption of magnetic field model. Our results suggest that resonant wave-particle interaction processes should be implemented into a sophisticated, accurate global magnetic field model to pursue comprehensive and complete models of radiation belt electron dynamics.