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Electromagnetic emissions at fundamental and harmonic plasma frequencies by an electron beam in a randomly inhomogeneous solar wind plasma
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During type III solar bursts, electron beams accelerated to high energies propagate in the solar corona and wind, generating electromagnetic emissions at the plasma frequency ωp and its harmonic 2ωp, both observed in the vicinity of the Earth and in the solar wind, as recently by the Parker Solar Probe and Solar Orbiter missions. They result from a series of linear and non-linear phenomena where Langmuir wave turbulence generated by electron beams as well as wave-wave, wave-particle and wave-plasma interactions play an essential role. However, the physical mechanisms involved are far from being elucidated to date, partly because of the random density fluctuations that characterize actual solar wind plasmas and crucially modify the predictions of existing theoretical models, developed for homogeneous plasmas.
Two-dimensional (2D) Particle-In-Cell (PIC)numerical simulations have investigated the electromagnetic radiation emitted at the fundamental plasma frequency ωp by an electron beam propagating in a solar wind plasma characterized by random density fluctuations, under physical conditions typical of type III solar bursts (Krafft and Savoini, APJL, 917:L23, 2021, Krafft and Savoini, APJL, 924:L24, 2022) Wave, beam, and plasma dynamics are computed over several thousand plasma periods ωp-1, for the cases of a homogeneous plasma and an inhomogeneous plasma with density fluctuations of the order of 5%. These 2D-PIC simulations, performed under strong physical and numerical constraints (high spatial and temporal resolutions and realistic physical conditions), are a real challenge considering the results obtained so far in the literature. For the first time, the essential impact of the random fluctuations of density of a few percent inherent to solar wind plasmas on the physical mechanisms governing the electromagnetic radiation at frequency ωp is demonstrated and characterized. The obtained results show that not only the nonlinear wave interactions but also the processes of wave transformations forming Langmuir turbulence on the fluctuations of density (reflection, refraction, scattering, tunneling, conversion, localization, self-organization), contribute consistently to the generation of the emissions at frequency ωp.
During beam relaxation, the amount of electromagnetic energy radiated at frequency ωp in a randomly inhomogeneous plasma (Krafft and Savoini, APJL, 924:L24, 2022) strongly exceeds that observed when the plasma is homogeneous. Moreover, the fraction of Langmuir wave energy involved in the generation of electromagnetic emission at ωp saturates around 10-4, i.e., an order of magnitude above that achieved when the plasma is homogeneous. While the emission at 2ωp always exceeds the fundamental emission at ωp in a homogeneous plasma, the latter is largely dominant when the plasma contains random fluctuations of density, at least for several thousand ωp-1 plasma periods before being dominated by the emission at 2ωp when the total electromagnetic energy saturates. For the first time the crucial role played by solar wind density fluctuations in the wave-wave and wave-matter interaction mechanisms behind the transformations of Langmuir wave turbulence generated by a particle beam into electromagnetic radiation during type III radio solar bursts has been demonstrated.

Electromagnetic waves emitted at the frequency 2ωp (Krafft and Savoini, APJL, 917:L23, 2021), are produced by nonlinear processes of coalescence between two Langmuir waves, despite the interactions of these waves with density fluctuations that strongly affect their spectral distributions; asymptotically, they exhibit isotropic spectra whereas quadrupolar radiation is observed in homogeneous plasma. The fraction of the initial beam energy transferred to them is an order of magnitude smaller than in the case of a homogeneous plasma, while the ratio of their energy to the energy carried by the Langmuir wave turbulence is notably higher during the entire nonlinear phase.

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