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Abstract The magnetospheres of the Earth and other magnetized planets are replete with high‐frequency fluctuations, which are sometimes accompanied by multiple‐harmonic electron cyclotron waves, and lower frequency waves of the whistler‐mode type. Such waves are presumed to be excited by energetic electrons trapped in the dipolar magnetic field, the so‐called loss‐cone electrons, the electron ring distribution being a highly idealized example. The present paper investigates the stability of electron ring distribution with respect to the excitation of quasi‐electrostatic upper‐hybrid wave instability as well as the quasi‐electromagnetic whistler mode instability that operates near electron cyclotron frequency. By employing a two‐dimensional particle‐in‐cell numerical simulation, it is demonstrated that the relatively early dynamics is dominated by the upper‐hybrid wave instability, but over a longer time period it is the whistler mode instability that ultimately determines the final relaxed state. The simulation results are interpreted with the quasilinear theoretical framework. 

Abstract Intense upward electron beams were measured by the Juno JADE instrument in the northern hemisphere, low‐latitude auroral zone source region. In this study we report on how these electron beams interact with plasma near and within the Jovian hectometric (HOM) emission (1 MHz 5 MHz) source region. Within the source region large upward loss cones are observed in the northern polar region at radial distances of 2Rj, magnetic latitude of . Intense, narrow electron beams ( 3 keV) are then observed, but within one second wave‐particle scattering is observed, filling the loss cone to energies 50 keV. These energies persist for several seconds before fading, leaving an empty loss cone again. The loss cone provides a free‐energy source for HOM emission resulting from the cyclotron maser instability. We use quasilinear analysis to examine the generation of HOM and the dynamics of wave‐particle interaction of the electron beams with HOM, and the generation via Landau interaction of whistler mode emission. The dynamic spectrum of the HOM emission generated by the loss‐cone electrons as well as that of the low‐frequency whistler‐mode waves generated by the up‐going electron beam can be constructed by quasilinear theory, which compare well with observation. The saturated state of the energetic electron velocity distribution function constructed via quasilinear theory also compare reasonably with observation. 

Abstract The proton-cyclotron (PC) instability operates in various space plasma environments. In the literature, the so-called velocity moment-based quasi-linear theory is employed to investigate the physical process of PC instability that takes place after the onset of early linear exponential growth. In this method, the proton velocity distribution function (VDF) is assumed to maintain a bi-Maxwellian form for all time, which substantially simplifies the analysis, but its validity has not been rigorously examined by comparing against the actual solution of the kinetic equation. The present paper relaxes the assumption of the velocity moment-based quasi-linear theory by actually solving for the velocity space diffusion equation under the assumption of separable perpendicular and parallel VDFs, and upon comparison with the simplified velocity moment theory, it demonstrates that the simplified method is largely valid, despite the fact that the method slightly overemphasizes the relaxation of temperature anisotropy when the system is close to the marginally stable state. The overall validation is further confirmed with the results of particle-in-cell and hybrid-code simulations. The present paper thus provides a justification for making use of the velocity moment-based quasi-linear theory as an efficient first-cut theoretical tool for the PC instability. 

Abstract Typical solar wind electrons are modeled as being composed of a dense but less energetic thermal “core” population plus a tenuous but energetic “halo” population with varying degrees of temperature anisotropies for both species. In this paper, we seek a fundamental explanation of how these solar wind core and halo electron temperature anisotropies are regulated by combined effects of collisions and instability excitations. The observed solar wind core/halo electron data in (β_∥,T_⊥/T_∥) phase space show that their respective occurrence distributions are confined within an area enclosed by outer boundaries. Here,T_⊥/T_∥is the ratio of perpendicular and parallel temperatures andβ_∥is the ratio of parallel thermal energy to background magnetic field energy. While it is known that the boundary on the high-β_∥side is constrained by the temperature anisotropy-driven plasma instability threshold conditions, the low-β_∥boundary remains largely unexplained. The present paper provides a baseline explanation for the low-β_∥boundary based upon the collisional relaxation process. By combining the instability and collisional dynamics it is shown that the observed distribution of the solar wind electrons in the (β_∥,T_⊥/T_∥) phase space is adequately explained, both for the “core” and “halo” components. 

Abstract The present study provides an evidence for the generation of harmonics of magnetosonic waves in the Martian magnetosheath region. The wave signatures are manifested in the magnetic field measurements recorded by the fluxgate magnetometer instrument onboard the Mars Atmosphere and Volatile Evolution missioN (MAVEN) spacecraft in the dawn sector around 5–10 LT at an altitude of 4,000–6,000 kms. The wave that is observed continuously from 19.1 to 20.7 UT below the proton cyclotron frequency (f_ci ≈ 46 mHz) is identified as fundamental mode of the magnetosonic wave. Whereas harmonics of the magnetosonic wave are observed during 19.7–20.3 UT at frequencies that are multiple off_ci. The ambient solar wind proton density and plasma flow velocity are found to vary with a fundamental mode frequency of 46 mHz. It is noticed that the fundamental mode is mainly associated with the left‐hand (LH), and higher frequency harmonics are associated with the right‐hand (RH) circular polarizations. A clear difference in the polarization and ellipticity is noticed during the time of occurrence of harmonics. The magnetosonic wave harmonics are found to propagate in the quasi‐perpendicular directions to the ambient magnetic field. The results of linear theory and Particle‐In‐Cell simulation performed here are in agreement with the observations. The present study provides a conclusive evidence for the occurrence of harmonics of magnetosonic wave in the close vicinity of the magnetosheath region of the unmagnetized planet Mars. 

Abstract The expanding-box model of the solar wind has been adopted in the literature within the context of magnetohydrodynamics, hybrid, and full particle-in-cell simulations to investigate the dynamic evolution of the solar wind. The present paper extends such a method to the framework of self-consistent quasilinear kinetic theory. It is shown that the expanding-box quasilinear methodology is largely equivalent to the inhomogeneous steady-state quasilinear model discussed earlier in the literature, but a distinction regarding the description of wave dynamics between the two approaches is also found. The expanding-box quasilinear formalism is further extended to include the effects of a spiraling solar-wind magnetic field as well as collisional age effects. The present finding shows that the expanding-box quasilinear approach and the steady-state global-kinetic models may be employed interchangeably in order to address other more complex problems associated with the solar-wind dynamics. 

Abstract The charged particles in the solar wind are often observed to possess a nonthermal tail in the velocity distribution function, a feature that can be fitted with the Kappa model. The anisotropic, or bi-Kappa, model of protons, electrons, and other charged particles is thus adopted in the literature for interpreting the data as well as in the context of the analysis of wave–particle interactions. The present paper develops an approximate but efficient theory of the mirror and cyclotron instabilities excited by the bi-Kappa protons in the solar wind. A velocity moment-based quasi-linear theory of these instabilities is also formulated in order to investigate the saturation behavior. Applications of the formalism are made for instabilities close to the marginally unstable state, which is typical of the solar wind near 1 au. 

Abstract The quasi-steady states of collisionless plasmas in space (e.g., in the solar wind and planetary environments) are governed by the interactions of charged particles with wave fluctuations. These interactions are responsible not only for the dissipation of plasma waves but also for their excitation. The present analysis focuses on two instabilities, mirror and electromagnetic ion cyclotron instabilities, associated with the same proton temperature anisotropyT_⊥>T_∥(where ⊥, ∥ are directions defined with respect to the local magnetic field vector). Theories relying on standard Maxwellian models fail to link these two instabilities (i.e., predicted thresholds) to the proton quasi-stable anisotropies measured in situ in a completely satisfactory manner. Here we revisit these instabilities by modeling protons with the generalized bi-Kappa (bi-κpower-law) distribution, and by a comparative analysis of a 2D hybrid simulation with the velocity-moment-based quasi-linear (QL) theory. It is shown that the two methods feature qualitative and, even to some extent, quantitative agreement. The reduced QL analysis based upon the assumption of a time-dependent bi-Kappa model thus becomes a valuable theoretical approach that can be incorporated into the present studies of solar wind dynamics. 

Context.In recent decades, serious efforts have been made in the analytical and numerical modeling of solar radio bursts generated by the electron beam interacting with the background plasma, including the dynamic spectra with decreasing frequency over time/space. These are type II and type III radio bursts, with the fundamental components at the local plasma frequency (ω_p = 2πf_p) and the harmonics (nω_p = 2πnf_p). Synthetic spectra built for a number of radio events were able to reproduce the decreasing frequency profiles reasonably well, despite the limitations of the approximate analytical theory. Aims.We propose new modeling of dynamic radio emission spectra using weak-turbulence (WT) theory. This novel approach also aims at a self-consistent and quantitative evaluation of radio emissions, based on first-principles modeling of electron beam plasma instabilities and nonlinear wave interaction. Methods.We performed the WT simulation, which has the ability to quantitatively describe the standard plasma emission involving the nonlinear interaction of Langmuir (L), ion-sound (S), and transverse electromagnetic (T) waves. The composite dynamic spectra are constructed for type II- and type III-like events, against the background electron density model that behaves as an inverse square of the distance from the solar source. Results.The new dynamic spectra are obtained distinctly, with a rapid frequency shift for type III emissions (generated by fast electron beams from coronal sources), as well as a less steep frequency drop for type II spectra (whose sources move away from the Sun along with interplanetary shocks). Upon making a qualitative comparison with typical solar radio emission events, we find that our first-principle-based synthetic dynamic spectra are in good agreement. Conclusions.The findings of the present study demonstrate that the theoretical approach taken in this paper can be further applied to obtain (i) quantitatively relevant predictions and replications of the observed dynamic spectra of radio bursts, and (ii) more realistic large-scale models of the solar radio source, for example the type II and type III source models computed from the large-scale magnetohydrodynamics (MHD) simulations or even from direct spacecraft observations. 

Context.In situ observations by the Parker Solar Probe (PSP) have revealed new properties of the proton velocity distributions (VDs), including hammerhead features that suggest a non-isotropic broadening of the beams. Aims.The present work proposes a very plausible explanation for the formation of hammerhead proton populations through the action of a proton firehose-like instability triggered by the proton beam. Methods.We investigated a self-generated firehose-like instability driven by the relative drift of ion populations using a simplified moment-based quasi-linear (QL) theory. While simpler and faster than advanced numerical simulations, this toy model provided rapid insights and concisely highlighted the role of plasma micro-instabilities in relaxing the observed anisotropies of particle VDs in the solar wind and space plasmas. Results.The QL theory proposed here shows that the resulting transverse waves are right-hand polarized and have two consequences on the protons: (i) They reduce the relative drift between the beam and the core, but above all, (ii) they induce a strong perpendicular temperature anisotropy specific to the observed hammerhead ion beam. Moreover, the long-run QL results suggest that these hammerhead distributions are rather transitory states that are still subject to relaxation mechanisms, in which instabilities such as the one discussed here are very likely involved. This foundational work motivates future detailed studies using advanced methods.