Figure 2. Spatial distributions of the third harmonic Langmuir wave energy and the density fluctuations (left panel) and their anti-correlation (ideal panel) when it comes to pitch angle being ( theta= 80 ^ ).

, suggesting that the 2nd harmonic electro-magnetic emission most likely corresponds to the coupling of forward and backward Langmuir waves. The analysis of the bi-spectral analysis at different pitch angles reveal that the basic and harmonic waves are primary, and the other harmonics are all produced by their coalescence. It is for that reason clear that the electron beam-driven Langmuir waves act as a kind of “pump” to generate electro-magnetic waves through the mode conversion and the nonlinear wave coupling.

Summary

Our mathematical results suggest the following possible radiation processes of the radio emission: (1) The essential electromagnetic emission arises from the scattering of Langmuir wave and thermal ions, namely, ( L+ i rightarrow F), due to the reality that hot plasma was adopted in the simulations. Another possible explanation is the decay of Langmuir waves, specifically, ( L rightarrow S+F), where S represents the ion acoustic waves. (2) The second harmonic electro-magnetic emission is created first by means of the decay of Langmuir waves, specifically, ( L rightarrow L+ F), and after that by means of the coupling of forward and backwards Langmuir waves, particularly, ( L+L rightarrow 2H). (3) The higher harmonic electromagnetic emission probably results from the coupling of Langmuir waves and harmonic electro-magnetic waves, specifically, (L+( n-1) Hrightarrow nH) (Cairns 1999). It is argued that large pitch angles of the electron beam assists in the density variations, which even more enhance the wave coupling, allowing the higher-order harmonic radio emissions.

Based upon the recent paper: T. M. Li, C. Li, P. F. Chen and W. J. Ding. Particle-in-cell simulation of plasma emission in solar radio bursts, A&A 653, A169 (2021 ). DOI: https://doi.org/10.1051/0004-6361/202140973

Referrals:

Cairns, I. H. 1988, J. Geophys. Res., 93, 858

Ginzburg, V. L., & & Zhelezniakov, V. V. 1958, Sov. Astron., 2, 653

Yoon, P. H. 1997, Phys. Plasmas, 4, 3863

Solar radio radiation is one of the most sensitive emissions during solar eruptions, where type III radio bursts can supply hints for electron velocity and proliferation. Type III radio bursts are commonly accepted to arise from the plasma emission, which is observationally supported by the presence of Langmuir waves, and excited electromagnetic waves at harmonic and essential frequencies from the nonlinear wave coupling (Ginzburg & & Zhelezniakov 1958). Such a mechanism has been further established based upon numerical and analytical research studies (Yoon 1997). However, it was often argued that this mechanism might not work effectively when the plasma is more allured. Besides, the third or perhaps greater harmonic emissions were observed in some events, and it is unsure whether the plasma emission system can discuss these features or not.

Particle-in-cell (PIC) simulations provide an effective technique to study solar radio bursts from the very first principle. We carried out 2.5 D PIC simulations to investigate type III radio bursts when electron beams with different pitch angles are injected into a highly magnetized plasma (plasma beta is much smaller than 1).

Simulation outcomes

The black lines represent the electron beam mode. The blue curves indicate the dispersion relation of the essential Langmuir waves. The black rushed curves suggest the dispersion relation of the harmonic Langmuir waves.

The black rushed curves show the dispersion relation of the harmonic Langmuir waves., showing that the second harmonic electromagnetic emission probably corresponds to the coupling of forward and backwards Langmuir waves. The analysis of the bi-spectral analysis at different pitch angles show that the essential and harmonic waves are primary, and the other harmonics are all produced by their coalescence. It is therefore clear that the electron beam-driven Langmuir waves act as a kind of “pump” to produce electromagnetic waves via the mode conversion and the nonlinear wave coupling. It is argued that large pitch angles of the electron beam facilitates the density changes, which even more enhance the wave coupling, allowing the higher-order harmonic radio emissions.

Figure 1. Dispersion diagrams of the electrostatic field Ex (left panels) and the electromagnetic field Ez (right panels) in the cases of the following pitch angles (from leading to bottom): ( theta= 0 ^ ), (theta= 30 ^ circ ), and ( theta= 80 ^ circ ). To understand how these wave modes are produced, we compare in Figure 2 the energy distributions of the third harmonic Langmuir modes to the density fluctuations along the x-direction, in the case of pitch angle of( theta= 80 ^ circ ). We find both density bumps and cavities, and the density cavities typically represent the maxima of wave energy (left panel) and the anti-correlation coefficient is derived to be ~ 0.52 (best panel). This suggests that the spreading and reflecting of the Langmuir wave packets by the density variations most likely plays a crucial role in creating harmonic Langmuir modes and exciting electromagnetic modes.