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Efficient radiation at second and/or higher harmonics of Wce has been suggested to circumvent the escaping difficulty of the electron cyclotron maser emission mechanism when it is applied to solar radio bursts, such as spikes. In our earlier study, we developed a three-step numerical scheme to connect the dynamics of energetic electrons within a large-scale coronal loop structure with the microscale kinetic instability energized by the obtained nonthermal velocity distribution and found that direct and efficient harmonic X-mode (X2 for short) emission can be achieved due to the strip-like features of the distribution. That study only considered the radiation from the loop top at a specific time. Here we present the emission properties along the loop at different locations and timings. We found that, in accordance with our earlier results, few to several strip-like features can appear in all cases, and the first two strips play the major role in exciting X2 and Z (i.e., the slow extraordinary mode) that propagate quasi-perpendicularly. For the four sections along the loop, significant excitation of X2 is observed from the upper two sections, and the strongest emission is from the top section. In addition, significant excitation of Z is observed for all loop sections, while there is no significant emission of the fundamental X mode. The study provides new insight into coherent maser emission along the coronal loop structure during solar flares.

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

Content. Electron-cyclotron maser emission (ECME) is the favored mechanism for solar radio spikes and has been investigated extensively since the 1980s. Most studies relevant to solar spikes employ a loss-cone-type distribution of energetic electrons, generating waves mainly in the fundamental X/O mode (X1/O1), with a ratio of plasma oscillation frequency to electron gyrofrequency (${\omega}_ {pe}/{\Omega}_{ce}$) lower than 1. Despite the great progress made in this theory, one major problem is how the fundamental emissions pass through the second-harmonic absorption layer in the corona and escape. This is generally known as the escaping difficulty of the theory. Aims. We study the harmonic emissions generated by ECME driven by energetic electrons with the horseshoe distribution to solve the escaping difficulty of ECME for solar spikes. Methods. We performed a fully kinetic electromagnetic PIC simulation with ${\omega}_ {pe}/{\Omega}_{ce}$ = 0.1, corresponding to the strongly magnetized plasma conditions in the flare region, with energetic electrons characterized by the horseshoe distribution. We also varied the density ratio of energetic electrons to total electrons ($n_e/n_0$) in the simulation. Results. We obtain efficient amplification of waves in Z and X2 modes, with a relatively weak growth of O1 and X3. With a higher-density ratio, the X2 emission becomes more intense, and the rate of energy conversion from energetic electrons into X2 modes can reach $\sim$0.06% and 0.17%, with $n_e/n_0$= 5% and 10%, respectively. Conclusions. We find that the horseshoe-driven ECME can lead to an efficient excitation of X2 and X3 with a low value of ${\omega}_ {pe}/{\Omega}_{ce}$, providing novel means for resolving the escaping difficulty of ECME when applied to solar radio spikes. The simultaneous growth of X2 and X3 can be used to explain some harmonic structures observed in solar spikes., Comment: 10 pages, 9 figures