Particle-in-cell Simulations Of Whistler Waves And Magnetosonic Waves In The Earth’s Inner Magnetosphere

Both whistler mode waves and magnetosonic(MS)waves are common electromagnetic emissions in the Earth’s inner magnetosphere,which play important roles in regulating electron dynamics in the Van Allen radiation belt.Whistler waves not only accelerate the seed electrons(hundreds of keV)up to relativistic energies(approximately MeV)but also scatter the lower energy(0.1-30 keV)into the atmosphere.MS waves can accelerate the electrons via Landau resonance and scatter equatorially mirroring electrons.Therefore,the study of excitation and propagation of these waves and wave-electron interactions plays key roles in radiation belt dynamics.With linear theory and particle-in-cell(PIC)simulations,we have studied the effects of background cold electrons and the drift velocity of hot electrons on the excitation of whistler waves.By using test particle simulations and PIC simulations,we have investigated the electron stochastic motions driven by MS waves and the effects of the density structure on the MS wave propagation,respectively.Our main conclusions are summarized as follows:1.The effects of background cold electrons on the excitation of whistler mode wavesBy combining both the linear theoretical and 2-D PIC simulation models,we have investigated the effects of background cold electrons on the whistler waves,which are excited by anisotropic hot electrons.If β‖h(parallel plasma beta of hot electrons)is larger than 0.025,the wave normal angle of the dominant whistler mode with the largest linear growth rate is 0 degree,which is not affected by background cold electrons,while its growth rate decrease with the density and temperature of background cold electrons.If β‖h is smaller than 0.025,with the increase of the density and temperature of background cold electrons,the wave normal angle of the dominant whistler mode turns to zero from a large value.This change could be due to the stronger damping caused by background cold electrons for oblique whistler mode.PIC simulations also show the consistent results.In the simulation cases with low β‖h,background cold electrons with large parallel velocities are resonantly accelerated in the perpendicular direction,while parts of hot electrons are trapped and accelerated in the parallel direction.2.Whistler mode waves excited by drifting anisotropic hot electronsWith linear theory and 1-D PIC simulations,we have studied the effects of the drift velocity of hot electrons on the excitation of whistler waves.Liner theory shows that the forward and backward propagating whistler waves excited by drifting anisotropic hot electrons have distinct properties.When β‖h is larger than 0.025,the wave normal angle of the dominant whistler mode is 0 degree,which is not affected by the drift velocity.As the drift velocity increases,the frequency of parallel propagating whistler waves increases,while that of antiparallel propagating waves is found to decline.Furthermore,the growth rate of parallel wave is small for large drift velocities.When β‖h is smaller than 0.025,with the increase of the drift velocity,the wave normal angle of the forward propagating waves gradually declines until reaching 0 degree,while that of the backward propagating waves continues to increase.PIC simulations point out that,if drift velocities are small,the saturated amplitudes of whistler waves excited by drifting anisotropic hot electrons in the parallel and antiparallel propagating direction are comparable.If drift velocities are large,only antiparallel whistler waves exist in simulation system.3.Electron stochastic motions driven by MS wavesWith the test particle simulations,we have investigated the electron motion driven by a monochromatic MS wave.We find that electron motion can become stochastic when wave amplitude exceeds a certain threshold.When an electron initially resonates with the MS wave via bounce resonance,as the bounce resonance order increases,the amplitude threshold of electron stochastic motion firstly increases,then slowly dencreases.The coexistence of bounce and Landau resonances between electrons and MS waves will significantly reduce the amplitude threshold.In some cases,the electron motion can become stochastic in the field of an MS wave with amplitudes below 1 nT,which suggests that the quasi-linear theory assumption will be violated when strong MS waves(amplitude up to～1 nT)are present in the inner magnetosphere.If neither the bounce nor Landau resonance condition is satisfied initially,the amplitude threshold of electron stochastic motion is always very large(>5 nT).4.The effects of the density structure on the MS wave propagationWith 1-D PIC simulations,we have studied the effects of the plasma density structure on the MS wave propagation.We find that plasma density variation leads to partial reflection of MS waves.The MS wave propagation from low density region to high density region leads to the change of MS wave polarization characteristics,the magnetic and the electric fields are enhanced and weakened respectively,and the phase velocity decreases.Besides,for quantifying the effects of plasma density structure on the MS wave propagation,we calculate the reflection efficiency,damping rate,and transmission efficiency by using magnetic amplitude.The reflection efficiency increases with the increase of the structure height and the decrease of the structure width,for the density structure with the same size,the reflection efficiency of lower frequency MS wave is larger.As the increase of the height and width of the density structure,the damping rate gradually increases,and lower frequency MS waves have a large value.As the increase of the density structure height,the transmission efficiency decreases,while it firstly increases and then decreases with the increase of the density structure width.