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Electromagnetic radiation at higher harmonics of the plasma frequency ($\omega \sim n\omega_{pe}, n > 2$) has been occasionally observed in type II and type III solar radio bursts, yet the underlying mechanism remains undetermined. Here we present two-dimensional fully kinetic electromagnetic particle-in-cell simulations with high spectral resolution to investigate the beam-driven plasma emission process in weakly magnetized plasmas of typical coronal conditions. We focused on the generation mechanisms of high-harmonic emission. We found that a larger beam velocity ($u_d$) favors the generation of the higher-harmonic emission. The emissions grow later for higher harmonics and decrease in intensity by $\sim$2 orders of magnitude for each jump of the harmonic number. The second and third harmonic ($\rm H_2$ and $\rm H_3$) emissions get closer in intensity with larger $u_d$. We also show that (1) the $\rm H_3$ emission is mainly generated via the coalescence of the $\rm H_2$ emission with the Langmuir waves, i.e., $\rm H_2 + L \rightarrow H_3$, wherein the coalescence with the forward-propagating beam-Langmuir wave leads to the forward-propagating $\rm H_3$, and coalescence with the backward-propagating Langmuir wave leads to the backward-propagating $\rm H_3$; and (2) the $\rm H_4$ emission mainly arises from the coalescence of the $\rm H_3$ emission with the forward- (backward-) propagating Langmuir wave, in terms of $\rm H_3 + L \rightarrow H_4$.

We propose a novel smearing scheme which gives a Gaussian-like profile and is more efficient than the traditional Gaussian smearing in terms of computer time consumption. We also carry out a detailed analysis of the profiles, smearing sizes, and the behaviors of hadron effective masses of different smearing schemes, and point out that having a sufficient number of gauge paths in a smearing scheme is essential to produce strong smearing effects. For a moderate smearing size $\bar{r}\sim 10a$, the time cost for the novel smearing is less than $1/8$ of that for the traditional Gaussian smearing. In practical lattice calculations with larger smearing sizes or finer lattice spacings the improvement will be more substantial.

The electron cyclotron maser instability (ECMI) of extraordinary mode waves was investigated with the parameters observed in Saturn's kilometric radiation (SKR) sources. Previous studies employed simplified dispersion relations, and did not consider the excitation of the relativistic (R) mode. This mode is introduced by considering the relativistic effect in plasmas consisting of both cold and hot electrons. Using particle-in-cell simulations, we investigated the excitation of R and X modes based on the measured data. Using the reported value of the density ratio of energetic to total electrons $n_e/n_0=24\%$, the most unstable mode is the R mode. The escaping X-mode emissions are amplified only if the energetic electrons are dominant with $n_e/n_0 \ge 90\%$. For these cases, only the X mode is excited and the R mode disappears due to its strong coupling. The results are well in line with the linear kinetic theory of ECMI. The properties of both the R and X modes are consistent with the observed SKR emissions. This raises questions about the nature of the measured electric field fluctuations within ``presumed'' SKR sources. The study provides new insights into the ECMI process relevant to SKR emission mechanisms.

According to the standard scenario of plasma emission, escaping radiations are generated by the nonlinear development of the kinetic bump-on-tail instability driven by a single beam of energetic electrons interacting with plasmas. Here we conduct fully-kinetic electromagnetic particle-in-cell simulations to investigate plasma emission induced by the ring-distributed energetic electrons interacting with overdense plasmas. Efficient excitations of the fundamental (F) and harmonic (H) emissions are revealed with radiation mechanism(s) different from the standard scenario: (1) The primary modes accounting for the radiations are generated through the electron cyclotron maser instability (for the upper-hybrid (UH) and Z modes) and the thermal anisotropic instability (for the whistler (W) mode); the F emission is generated by the nonlinear coupling of the Z and W modes and the H emission by the nonlinear coupling of the UH modes. This presents an alternative mechanism of coherent radiation in overdense plasmas.

The standard theory of plasma emission is based on kinetic couplings between a single beam of energetic electrons and unmagnetized thermal plasmas, involving multi-step nonlinear wave-particle and wave-wave interactions. The theory has not yet been completely verified with fully-kinetic electromagnetic particle-in-cell (PIC) simulations. Earlier studies, greatly limited by available computational resources, are controversial regarding whether the fundamental emission can be generated according to the standard theory. To resolve the controversy, we conducted PIC simulations with a large domain of simulation and a large number of macroparticles, among the largest ones of similar studies. We found significant fundamental emission if the relative beam density is small enough (say, $\le$ 0.01), in line with earlier study with a much-smaller domain; the relative intensity (normalized by the total initial beam energy) of all modes, except the mode associated with the beam-electromagnetic Weibel instability, decreases with increasing relative density of the beam. We also found significant transverse magnetic component associated with the superluminal Langmuir turbulence, which has been mistakenly regarded as evidence of the F emission in earlier study. Further investigations are required to reveal their origin.

Previous studies on the beam-driven plasma emission process were done mainly for unmagnetized plasmas. Here we present fully-kinetic electromagnetic particle-in-cell simulations to investigate such process in weakly-magnetized plasmas of the solar corona conditions. The primary mode excited is the beam-Langmuir (BL) mode via the classical bump-on-tail instability. Other modes include the whistler (W) mode excited by the electron cyclotron resonance instability, the generalized Langmuir (GL) waves that include a superluminal Z-mode component with smaller wave number $k$ and a thermal Langmuir component with larger $k$, and the fundamental (F) and harmonic (H) branches of plasma emission. Further simulations of different mass and temperature ratios of electrons and protons indicate that the GL mode and the two escaping modes (F and H) correlate positively with the BL mode in intensity, supporting that they are excited through nonlinear wave-wave coupling processes involving the BL mode. We suggest that the dominant process is the decay of the primary BL mode. This is consistent with the standard theory of plasma emission. Yet, the other possibility of the Z+W$\rightarrow$O--F coalescing process for the F emission cannot be ruled out completely.

Electron cyclotron maser emission (ECME) is regarded as a plausible source for the coherent radio radiations from solar active regions (e.g., solar radio spikes). In this Letter, we present a 2D3V fully kinetic electromagnetic particle-in-cell (PIC) simulation to investigate the wave excitations and subsequent nonlinear processes induced by the energetic electrons in the loss-cone distribution. The ratio of the plasma frequency to the electron gyrofrequency ${\omega}_{pe}/{\Omega}_{ce}$ is set to 0.25, adequate for solar active region conditions. As a main result, we obtain strong emissions at the second-harmonic X mode (X2). While the fundamental X mode (X1) and the Z mode are amplified directly via the electron cyclotron maser instability, the X2 emissions can be produced by the nonlinear coalescence between two Z modes and between Z and X1 modes. This represents a novel generation mechanism for the harmonic emissions in plasmas with a low value of ${\omega}_{pe}/{\Omega}_{ce}$, which may resolve the escaping difficulty of explaining solar radio emissions with the ECME mechanism., Comment: 17 pages, 4 figures