In this paper, we perform one-dimensional particle-in-cell simulations to investigate the properties of perpendicular magnetosonic waves in a plasma system consisting of three components: cool electrons, cool protons, and tenuous ring distribution protons, where the waves are excited by the tenuous proton ring distribution. Consistent with the linear theory, the spectra of excited magnetosonic waves can change from discrete to continuous due to the overlapping of adjacent unstable wave modes. The increase of the proton to electron mass ratio, the ratio of the light speed to the Alfven speed, or the concentration of protons with a ring distribution tends to result in a continuous spectrum of magnetosonic waves, while the increase of the ring velocity of the tenuous proton ring distribution leads to a broader one, but with a discrete structure. Moreover, the energization of both cool electrons and protons and the scattering of ring distribution protons due to the excited magnetosonic waves are also observed in our simulations, which cannot be predicted by the linear theory. Besides, a thermalized proton ring distribution may lead to the further excitation of several lower discrete harmonics with their frequencies about several proton gyrofrequencies.

Ion Bernstein modes, also known as magnetosonic waves in the magnetospheric community, are considered to play an important role in radiation belt electron acceleration. The detailed properties of perpendicular magnetosonic waves excited in the inner magnetosphere by a tenuous proton ring distribution are investigated in a two series paper with a combination of the linear theory and one-dimensional particle-in-cell simulations. Here, in this paper, we study the properties of the excited magnetosonic waves under different plasma conditions with the linear theory. When the proton to electron mass ratio or the ratio of the light speed to the Alfven speed is small, the excited magnetosonic waves are prone to having a discrete spectrum with only several wave modes. With the increase of the proton to electron mass ratio or the ratio of the light speed to the Alfven speed, the lower hybrid frequency also increases, which leads to the increase of both the number and frequency of the excited wave modes. Meanwhile, the growth rate of these wave modes also increases. When the proton to electron mass ratio or the ratio of the light speed to the Alfven speed is sufficiently large, the spectrum of the excited magnetic waves becomes continuous due to the overlapping of the adjacent wave modes. The increase of the density of the protons with the ring distribution can also result in the increase of the growth rate, which may also change the discrete spectrum of the excited waves to a continuous one, while the increase of the ring velocity of the tenuous proton ring distribution leads to a broader spectrum, but with a smaller growth rate.

Plasma emission (PE), i.e., electromagnetic radiation at the plasma frequency and its second harmonic, is a general process occurring in both astrophysical and laboratory plasmas. The prevailing theory presents a multi-stage process attributed to the resonant coupling of beam-excited Langmuir waves with ion-acoustic waves. Here, we examine another possibility of the fundamental PE induced by the resonant coupling of Z-mode and whistler (W) waves. Earlier studies have been controversial in the plausibility and significance of such process in plasmas. In this study, we show that the matching condition of three-wave resonant interaction (Z + W → O) can be satisfied over a wide regime of parameters based on the magnetoionic theory, demonstrate the occurrence of such process, and further evaluate the rate of energy conversion from the pumped Z or W mode to the fundamental O mode with particle-in-cell simulations of wave pumping. The study presents an alternative form of the fundamental PE, which could possibly play a role in various astrophysical and laboratory scenarios with both Z and W modes readily excited through the electron cyclotron maser instability.

Although magnetosonic waves in the Earth's magnetosphere have been well understood by the linear theory, low harmonic magnetosonic waves, which often lack of free energy, can be unusually present. By employing a 1‐D particle‐in‐cell simulation model, we have investigated the generation of those unusual lower harmonic magnetosonic waves in a plasma containing a proton ring distribution. In our simulation, the higher harmonic magnetosonic waves (from~9Ω_h to ~12Ω_h) are firstly excited due to the unstable proton ring, which can be well explained by the linear theory. Several lower harmonic magnetosonic waves (below 5Ω_h), which well separates away from the higher harmonics, soon appear in the system. Those lower harmonics, which do not have any positive linear growth rates, can be generated by a nonlinear mechanism. The bicoherence analysis demonstrates that there is a strong phase coupling among the unusual lower harmonic magnetosonic waves and the magnetosonic waves generated due to the proton ring, supporting the idea that the lower harmonic waves could be driven by the wave‐wave couplings of the generated magnetosonic waves. This wave‐wave coupling generation mechanism is further confirmed by another two simulations, where two or three pump magnetosonic waves are initially injected. The lower‐frequency waves, that is, the fundamental wave and its second harmonic, are also successfully reproduced due to the nonlinear coupling of pump magnetosonic waves. Our simulations not only propose a potential generation mechanism of unusual lower harmonic magnetosonic waves in the Earth's magnetosphere, but also give some new insights on the evolution of magnetosonic spectra.

The excitation of magnetosonic waves in the meridian plane of a rescaled dipole magnetic field is investigated, for the first time, using a general curvilinear particle‐in‐cell simulation. Our simulation demonstrates that the magnetosonic waves are excited near the equatorial plane by tenuous ring distribution protons. The waves propagate nearly perpendicularly to the background magnetic field along both radially inward and outward directions. Different speeds of inward and outward propagation result in the asymmetrical distribution about the source region. The waves are accompanied by energization of both cool protons and electrons near the wave source region. The cool protons are heated perpendicularly, while the cool electrons can be heated in the parallel direction and also experience enhanced perpendicular drift at the presence of intense wave power. The implications of simulation results to the observations of magnetosonic waves and related particle heating in the inner magnetosphere are also discussed.