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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. 

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.