Computer Simulations Of Magnetosonic Waves In The Inner Magnetosphere

Magnetosonic waves are very important electromagnetic emissions between a few hertz and several hundreds of hertz in the Earth's radiation belt. These fluctuations are often observed in the vicinity of the equatorial plane by satellite, so magnetosonic waves are often referred to equatorial noise. Magnetosonic waves play a potential role in both scattering and accelerating relativistic electrons in the Van Allen radiation belt. In this paper, we mainly focus on the excitation and evolution of magnetosonic waves in the radiation belt. Using the linear theory and 1D particle-in-cell (PIC) simulation model, we study both spectral properties and plasma energization during the generation of magnetosonic waves by ring distribution protons, and we also investigate the wave wave interaction of magnetosonic waves.Moreover, with a 2D general curvilinear particle-in-cell simulation model, we investigate the generation and propagation of magnetosonic waves in the meridian plane of the dipole magnetic field. The principal results are shown as follows.1. Generation of magnetosonic waves over a continuous spectrumWith the linear theory, we study the spectral properties of the perpendicular magnetosonic waves excited by ring distribution proton. We find that ring distribution proton can cause an instability generating discrete wave bands and another generating continuous wave bands. Generation of a continuous frequency spectrum of magnetosonic waves can be explained as emergence of neighboring discrete peaks. A condition for a discrete instability and a continuous instability is formulated. The former occurs when growth rate is small y < 0.5?h while the latter occurs when growth rate is comparable to or above 0.5?h. PIC simulation results confirm the linear theory on generation of continuous frequency spectrum and discrete frequency spectrum.2. A parametric study for the generation of magnetosonic wavesUsing the linear theory and 1D PIC simulation models, we investigate the properties of the excited perpendicular magnetosonic waves under different plasma conditions. 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, both the frequency and growth rate increase, and the spectrum of the excited waves becomes broader. Moreover, a continuous spectrum may be formed due to the merging of growth rate peaks when the proton to electron mass ratio and the ratio of the light speed to the Alfven speed are sufficiently large. The increase of the density of the ring distribution protons can enhance the growth rate of the excited waves while the frequencies nearly keep unchanged, and then a continuous spectrum is easier to be formed. The increase of the proton ring velocity tends to increase the number of unstable wave modes. Although the spectrum of magnetosonic waves becomes broader, the growth rate of the excited wave modes becomes smaller.3. Magnetosonic waves interact with background plasmaUsing 1D PIC simulation model, we investigate both spectral properties and plasma energization during the generation of magnetosonic waves by ring distribution protons. As the wave normal angle decreases, the spectral range of excited magnetosonic waves becomes broader and the upper frequency limit may even extend beyond the lower hybrid resonant frequency. For the exactly perpendicular magnetosonic waves, there is no energization in the parallel direction for both background cold protons and electrons. For the perpendicular direction,background electrons and protons are subject to bulk motions due to wave electric field; electrons follow drift motion due to instantaneous wave electric field while protons follow unmagnetized motion. For magnetosonic wave with a finite parallel wave number, there exists a nonnegligible fluctuating parallel electric field, which results in a rapid and significant energization in the parallel direction for background electrons. At the same time, background electrons can also be efficiently energized in the perpendicular direction due to the coupling with the magnetosonic wave fields.However, background protons can only be heated in the perpendicular direction.4. The wave-wave interaction of magnetosonic wavesUsing 1D PIC simulation model, we study the wave-wave interaction of magnetosonic waves. The power spectrum obtained by PIC simulation shows discrete peaks at lower harmonic frequencies which are not predicted by the linear theory. Since the frequency of magnetosonic waves generated by ring distribution proton is usually located at harmonics of the proton gyro frequency and the dispersion curve below the half of low hybrid frequency is approximately a straight line, the modes of magnetosonic waves is easy to satisfy the wave-wave interaction condition. We diagnose the dispersion relation and the bicoherence index of the waves, and find that the low frequency magneto sonic waves are excited by the higher ones through the wave-wave interaction.5. Magnetosonic waves in a dipole magnetic fieldWe perform a 2-D general curvilinear PIC simulation model to study the excitation of magnetosonic waves in a dipole magnetic field, and here the plasma have three components: cool electrons, protons and localized protons of ring distribution. The magnetosonic waves, which propagate almost perpendicular to the dipole magnetic field, are excited by ring distribution protons in source region.When the magnetosonic waves propagate to the boundary of source region along the radial direction, some waves are reflected, while the others propagate through the boundary. The cool protons and electrons are energized during the excitation of the magnetosonic waves, therefore, the magnetosonic waves are heavily damped when they leave the source region with the existence of the ring distribution protons. The magnetosonic waves are confined near the localized source region.