Fully Kinetic Simulations of Radio Emission from a Propagating Electron Beam

Type III radio bursts are associated with energetic electrons accelerated by solar flares from the lower corona. The standard theory links these emissions to a conversion of plasma oscillations excited by the bump-on-tail instability into electromagnetic waves. Since electron beams can propagate to large heliospheric distances and continue to emit radio waves, the instability must be finely balanced, not to disrupt their propagation (so-called Sturrock’s dilemma). To explain this, many models invoking contrasting processes have been proposed (e.g. quasilinear vs strong turbulence description of interactions between various plasma modes). In this study, we perform 2D PIC simulations of beam injection, propagation, and emissions in a large system without periodic boundary conditions. Results demonstrate that the beam decouples from the excited electrostatic oscillations near the injection site and propagates through the background plasma with relatively small energy loss. Downstream, the instability continues to operate only at the beam front. The main body of the beam between downstream and upstream reaches a quasi-steady state. It may become unstable again where the background plasma is colder or less dense. Background temperature variations affect the beam instability more than background density fluctuations. Radio emissions at plasma frequency and its second harmonic are primarily generated upstream in the region of intense fluctuations, where both classical signatures of three-wave conversion processes and those associated with modulational instability are detected. Our results are consistent with satellite data showing that electron beams often continue to generate type III radio bursts even beyond 1 AU. They illustrate in a first-principle model how a beam state consistent with subsequent quasilinear relaxation emerges shortly after beam injection.

contrasting processes have been proposed (e.g. quasilinear vs strong turbulence description of interactions between various plasma modes). In this study, we perform 2D PIC simulations of beam injection, propagation, and emissions in a large system without periodic boundary conditions. Results demonstrate that the beam decouples from the excited electrostatic oscillations near the injection site and propagates through the background plasma with relatively small energy loss. Downstream, the instability continues to operate only at the beam front. The main body of the beam between downstream and upstream reaches a quasi-steady state. It may become unstable again where the background plasma is colder or less dense. Background temperature variations affect the beam instability more than background density fluctuations. Radio emissions at plasma frequency and its second harmonic are primarily generated upstream in the region of intense fluctuations, where both classical signatures of three-wave conversion processes and those associated with modulational instability are detected. Our results are consistent with satellite data showing that electron beams often continue to generate type III radio bursts even beyond 1 AU. They illustrate in a first-principle model how a beam state consistent with subsequent quasilinear relaxation emerges shortly after beam injection.

Fully Kinetic Simulations of Radio Emission from a Propagating Electron Beam (SM35D-1996)
Tien Vo 1,3 (Tien.Vo@colorado.edu), Vadim Roytershteyn 2 , and Cynthia Cattell 1 1 University of Minnesota -Twin Cities 2 Space Science Institute 3 University of Colorado -Boulder Fully kinetic PIC simulations are used to investigate how flare accelerated electron beams propagate over long distances while continually generating electromagnetic waves. The simulations describe the relevant linear and nonlinear kinetic processes from first principles and are performed in a large domain with open boundary conditions. The beam is injected from one side of the domain and experiences a rapid relaxation due to the action of instabilities over distances of tens of electron inertial lengths. However, only about 15% of the beam energy density is lost during this process. This enables the beam to propagate in a marginally stable state over long distances. Both fundamental and second harmonic emissions, signatures of nonlinear conversion processes, are observed. At large distances from the source, instabilities exist only in the front of the beam, unless the background plasma changes downstream.

Abstract
V. Discussions

I. Introduction
References

II. Simulation parameters
Type III radio bursts are produced as electrons accelerated by solar flares propagate out through the corona and into the solar wind. The standard theory for radio emission involves the conversion of Langmuir waves excited by electron beams via the bump-on-tail instability (see Fig. 1) [1].
However, an issue with this picture is the so-called Sturrock's dilemma [3]. The beam propagation is in theory completely disrupted after a few kms by means of radio emission. Since signatures of type III emissions are observed at 1 AU, the instability needs to be finely balanced with the beam propagation so that electrons could travel far from the Sun.
To explain this, many models invoking contrasting processes have been proposed, for example, quasilinear vs strong turbulence description of interactions between various plasma modes [4,5]. The former proposes that the reabsorption of wave energy back into the stream may allow it to persist to large distances. The latter involves weak/strong turbulent processes that could shift the stream created waves out of resonance with the electrons fast enough to stabilize it.
In this study, we perform 2D PIC simulations of beam injection, propagation, and wave emissions and study the signatures relating to each model and their evolution in the simulation box.

Overview:
The beam in Panel A excites Langmuir waves in Panel C, whose wavevector is consistent with the bump-on-tail instability, as shown in the spectrogram in Panel D.

Beam evolution:
In Panel A, the beam plateaus shortly after being injected ( / ≥ 50) and reaches a quasi-steady state where no further energy is lost to the instability in Panel B (see also Fig. 3). It only loses 15% of the initial energy.

Wave evolution:
• In Panel C, wave pileup occurs near the injection site, while the instability continues to operate only at the beam front downstream. • Some reabsorption occurs in between, resulting in a quiescent region separating these two regions of different intensity in wave activities. • In Panel E, only the strongly piled-up waves near the injection site ( / ≤ 50) exceed the threshold for turbulent processes, while the waves downstream evolve quasi-linearly.    • Waves participating in classic 3-wave interaction processes are observed (see Fig. 4 & 5). • Signature of the modulational instability connected to strong turbulence is observed in Fig. 4D (spectrogram taken near the injection site). The signature diminishes downstream, consistent with the wave energy density in Fig. 1E.
• Most previous PIC studies of this type [6,7] used periodic boundary conditions, which imposes a uniformly strong coupling between the beam and the excited waves. However, as seen in our simulation, the beam quickly decouples from the waves and stabilizes, leaving the instability only active at the front of the beam, while the rest of it plateaus. Thus, the escaping beam loses only a fraction of its initial energy and propagates in a marginally stable state, but it can become unstable again due to background temperature and/or density variations at larger heliospheric distances (see Fig. 6). The energy loss of the beam after the initial relaxation is consistent with that of quasi-linear evolution [8].
• In the context of type III bursts, weak/strong plasma turbulence theories have been investigated with simulations [9,10,11]. Although our model favors the quasi-linear evolution of the downstream beam, signatures of turbulences are also observed due to the strong wave activities near the injection site.