Second-Harmonic Generation Of Plasma Waves In The Inner Magnetosphere

Plasma waves play an important role in the energy and momentum transfer through wave-particle interactions.The study of plasma waves is beneficial for understanding the physical processes of earth magnetosphere.In recent years,second harmonics of plasma waves have been widely observed in the inner magnetosphere,and their spatial distribution,fluctuation characteristics,excitation mechanisms,and effects on the space environment have drawn more and more attentions.In this paper,based on Van Allen Probes satellite observations,theoretical analysis and one-dimensional hybrid simulations,the nonlinear generation of plasma second harmonics waves in the inner magnetosphere are investigated.The main research results are as follows.1.A bridge role of the second harmonic of EMIC waves in generation of higher harmonics.Firstly,we report an electromagnetic ion cyclotron（EMIC）harmonic event observed by the Van Allen Probe B,whose generation is demonstrated to result from nonlinear wave-wave resonances through the bicoherence analysis.Hybrid simulation shows that the second to sixth harmonics could be successively generated order by order via nonlinear wave-wave couplings after a pump EMIC wave is initially injected,which is in consistent with the observations of EMIC harmonic.In particular,as the second harmonic grows up to a rather strong level,the third and then higher harmonics emerge more and more clearly,which suggest the important role of the second harmonic（especially its amplitude）.Finally,the statistical distribution for the amplitude of EMIC second harmonic waves indicates that the energy transfer rate from the fundamental wave to the second harmonic is mainly less than 2%,which might be too low to result in third and other higher harmonics above the observational level.2.The first observational evidence of wave-wave coupling between H⁺band and He⁺band EMIC waves.Based on observations of Van Allen Probe A,we provide an observational evidence of nonlinear interaction between H⁺band and He⁺band EMIC waves.By performing hybrid simulation,we investigate the specific nonlinear interaction process,and three nonlinear processes are discussed.Firstly,nonlinear interactions between different band EMIC waves can generate emissions not only at a sum frequency but also at a difference frequency.Secondly,EMIC harmonic waves generated by wave-wave coupling.Third,the second harmonic is involved in the secondary nonlinear process,implying that the second harmonic play an important role in energy transfer in secondary nonlinear processes.Our observations show that by nonlinear wave-wave coupling,fluctuations with a larger wave vector（as well as a higher frequency）can be generated,which effectively reduces the minimum resonance energy into a level below 2 Me V,implying that can play an important role in the dynamics of the radiation belt.3.The preferred condition to excite second harmonics of lower-band chorus waves are proposed and confirmed.The global distributions of chorus second harmonic waves are provided.The effects of thermal electrons in the generation of chorus second harmonic are investigated.The preferred condition for generation of the second harmonic of chorus waves has been derived under the cold plasma assumption,which predicts that chorus waves with a frequency（f）and a normal angle（θ）satisfying f/f_ce=（cosθ）/3 are more likely to excite the second harmonic(f_ce is the local electron gyrofrequency).Based on the Van Allen Probe A observations from 1 September 2012 to 30 June 2018,21338chorus second harmonic events are identified.We found that most chorus second harmonic events fall around the preferred condition,which provide an observational support for our theory.Besides,a group of second harmonic events with the high occupations（>40%）of hot electrons are found away from the preferred condition,which might deform the dispersion curve and make the preferred generation condition derived under the cold plasma assumption invalid.Moreover,our survey shows that chorus second harmonic waves typically occur in L～4.5-6.5,particularly in night-dawn-forenoon sector,in consistent with the distribution of the electron diffuse aurora,implying that chorus second harmonics could play a potential role in the generation of diffuse aurora.It suggests that chorus second harmonics might play a potential role in the generation of diffuse aurora.The amplitude model should also be given and the amplitude of chorus second harmonics is found to mostly be 1.5 p T,which is useful to model their influence in magnetospheric particles.The amplitude ratio of the second harmonic to the fundamental wave is close to 1%,implying that the energy transfer rate from the fundamental wave to the second harmonic is low.It should be responsible for the rare occurrences of observed chorus higher harmonic waves.4.Discuss the nonlinear generation mechanism of the second harmonic of MS waves,verified second-harmonic generation theory by satellite observations.A cold plasma assumption can be adopted to simplify the theoretical model,from which an analytical formula for the amplitude of second harmonics can be explicitly given.Moreover,a typical second harmonic of MS waves observed by the Van Allen Probes has been reproduced through theoretical calculation using the observed fundamental wave.The theoretically calculated amplitude of the second harmonics is consistent with the observational values,demonstrating that the observed second harmonics of MS waves are excited by the nonlinear interaction as predicted in second-harmonic generation theory.Our result is helpful to understand the nonlinear generation mechanism of plasma waves in the magnetosphere,and also give some new insights into the wave-particle interactions of space plasma in the inner magnetosphere.