# Ning et al. * PIC simulation of harmonic maser radiation by *-European community of solar radio astronomy

Electron cyclotron maser radiation (ECME) represents a major class of coherent radiation mechanisms in solar radiation bursts. ECME usually has a frequency ratio of $ omega_ {pe} / Omega_ {ce} <1 $の強く磁化されたプラズマで発生し、$ partial f / partial v> It is induced by high energy electrons of 0 $. Where $ f $ is the velocity distribution function. In the active region of the Sun, this mechanism is applied to millisecond spikes characterized by high brightness temperatures, short durations, narrow bandwidths, and strong polarization.

A long-standing problem with ECME that explains spikes is the difficulty of escaping. Fundamental wave radiation ($ omega sim Omega_ {ce} $) cannot escape because the magnetic field strength is the source (Melrose & Dulk 1982). Emissions at harmonics of second order and above ($ omega sim n Omega_ {ce} $, n = 2, 3, …) are more likely to escape. Previous studies using the Rothcorn distribution concluded that only basic emissions (ie, $ n = 1 $) can be increased via ECME (eg, Aschwanden 1990).

To investigate the possibility of harmonic ECME emission ($ n ge 2 $), a fully dynamic electromagnetic 2D3V particle incell (PIC) simulation with a large domain containing a large amount of macroparticles to reduce the noise level. I ran it. As a driver of electron cyclotron maser instability (ECMI), we used horseshoe-shaped (Ning et al. 2021a) and Rothcorn (Ning et al. 2021b) distributions to study wave excitation and subsequent non-linear processes.

**Figure 1.** A snapshot of the velocity distribution at the start of the simulation using the horseshoe (a) and loss cone (b) distributions. The density ratio of high energy electrons to all electrons is set to 10%.

**Distribution of horseshoes**

According to in-situ measurements, Aurora Kilometer Radiation (AKR) is emitted by the horseshoe-shaped ECME. As an analogy to AKR, solar spikes are also associated with electrons moving toward the lower atmosphere and high-energy electrons with a horseshoe-like distribution that can be formed by flare loops (Melrose & Wheatland2016).

The horseshoe distribution used to drive the simulation consists of a shell and a double-sided loss cone distribution (Fig. 1 (a)). Set $ omega_ {pe} / Omega_ {ce} = 0.1 $ to set the density ratio of high energy electrons to all electrons ($ n_e / n_0 $) from 1% to 50 to simulate the ECME process. Changed to%.

**Figure 2.** $ E_ {y} $ $ omega $ -k variance diagram in the vertical direction of a simulation of a horseshoe-shaped distribution with $ n_ {e} / n_ {0} $ varied. “Z”, “X2”, “X3”, and “R” represent Z mode, second harmonic X mode, third harmonic X mode, and relativistic mode branching.

According to the simulation (Figure 2), the horseshoe distribution can efficiently amplify waves in Z mode and X2 mode (frequency 0.96 and 1.92 $ Omega_ {ce} $) along the vertical direction. X3 mode also grows further with lower energy. Note that amplification in X2 and X3 modes will be more efficient if you increase $ n_ {e} / n_ {0} $. If the range of $ n_ {e} / n_ {0} $ is 5% to 50%, the brightness temperature of the obtained X2 is estimated to be $ 10 ^ {11} $ K to $ 10 ^ {15} $ K. , Consistent with the observation results. Of spikes.

Efficient amplification of harmonic radiation provides a solution to the difficulty of avoiding ECME theory. The simultaneous growth of X2 and X3 can explain the polyharmonic structure observed in the solar spikes.

**Rothcorn distribution**

Rothcorn ECME has been extensively investigated by previous studies including linear and quasi-linear analysis. However, nonlinear wave interactions have not been fully studied. We performed a PIC simulation long enough to study the wave excitation mediated by the Rothcorn cyclotron resonance instability and the subsequent wave interaction process.

A double-sided loss cone distribution was adopted (Fig. 1 (b)). In the simulation, the value of $ omega_ {pe} / Omega_ {ce} = 0.25 $ and $ n_ {e} / n_ {0} $ were set to 10%. The simulation continues for 8000 $ omega_ {pe} ^ {-1} $. This represents the longest period of simulation ever performed in a study on the same topic.

**Figure 3.** Wave distribution diagram of electric fields over 7500-8000 $ omega_ {pe} ^ {-1} $ along different directions. Panels (a), (b), and (c) display amplified waves in X1, Z, and X2 modes. $ theta $ represents the angle between the direction of the wave vector and the background magnetic field.

**Figure 4.** Maximum wave energy in space $ vec {k} $ over 7000-8000 $ omega_ {pe} ^ {-1} $; Blue and brown represent the results of the $ E_x $ and $ E_y $ components. Possible conditions for wave vectors that match the coalescing condition are overwritten as arrows of the same color. The black arrow represents the generated target mode wave vector. The $ theta $ value for each wave vector is marked next to it.

Figure 3 shows the dispersion of the waves amplified by the simulation. Rothcorn distribution is via X1 (panel (a); $ omega $ ~ 1.06-1.1 $ Omega_ {ce} $) and Z (panel (b) $ omega $ ~ 1.025 $ Omega_ {ce} $) ECMI Mode. The main result is a separate strong emission at X2 along the diagonal and vertical directions at frequencies of 2.05, 2.09, and 2.14 $ Omega_ {ce} $ (panel (c)).

It is recommended that the X2 emission be generated by a non-linear coalescing process of Z + X1 and / or Z + Z. It is supported by the following arugments / observations: (1) The matching conditions are fully satisfied (Fig. 4). (2) X2 radiation is amplified at different frequencies and discrete angles. (3) X2 begins to grow slower than Z and X1. The energy ratio between X2 mode and Z mode is about 30%, indicating that the coalescing process is efficient for energy conversion.

For the first time, we obtain efficient excitation of X2 induced by Rothcon electron through an efficient wave and wave coalescence process. Such a process represents a new mechanism of X2 emission in plasmas with low $ omega_ {pe} / Omega_ {ce} $.

**Conclusion**

We simulated wave excitation by high-energy electrons using either a horseshoe-shaped or Roscorn distribution. It was found that the horseshoe distribution can generate X2 and X3 simultaneously via the ECME mechanism directly, and the Rothcon distribution can generate X2 via the indirect nonlinear wave coalescence process. The Rothcorn ECMI first amplifies X1 and Z modes, then X1 and Z modes. Combine to produce X2 emissions.

Two studies (Ning et al., 2021a, 2021b) shed new light on the mechanism of harmonic radiation and the solution of ECME’s long-standing escape problem. Our simulations obtain efficient excitation of X2s with narrow bandwidths and propagation angles, explain high luminance temperatures and strong polarization of spikes, and explain why only a few percent of hard X-ray bursts correlate with spikes. I will explain.

**Based on recent papers:**** **

Ning, H., Chen, Y., Ni, SL, Li, CY, Zhang, ZL, Kong, XL, and Yousefzadeh, M. , Harmonic electron cyclotron maser radiated radio spikes driven by horseshoe-shaped distribution high-energy electrons with application to the sun, A & A, 2021a, 651, A118, DOI: https://doi.org/10.1051/0004-6361/202140427

Ning, H., Chen, Y., Ni, SL, Li, CY, Zhang, ZL, Kong, XL, and Yousefzadeh, M. , Harmonic maser emission from electrons with loss cone distribution in the solar active region, ApJL, 2021b, 920, L40, DOI: https://doi.org/10.3847/2041-8213/ac2cc6

**References**

Ashwanden, MJ 1990, A & AS, 85, 1141

Melrose, DB, and Dulk, GA 1982, ApJ, 259, 844

Melrose, DB, and Wheatland, MS 2016, Sol. Physics, 291, 3637

*** Complete list of authors:** Hao Ning, Yao Chen, Sulan Ni, Chuanyang Li, Zilong Zhang, Xiangliang Kong, Mehdi Yousefzadeh

Ning et al. * PIC simulation of harmonic maser radiation by *-European community of solar radio astronomy

https://www.astro.gla.ac.uk/users/eduard/cesra/?p=3108 Ning et al. * PIC simulation of harmonic maser radiation by *-European community of solar radio astronomy