Particle-in-cell Simulations Of Whistler Waves In The Earth's Inner Magnetosphere

Whistler waves are common and important electromagnetic emissions in the Earth's inner magnetosphere.Whistler waves in the high density magnetospheric plasma,such as plasmasphere,are typically incoherent and called as hiss.Whistler waves between the plasmapause and magnetopause are commonly coherent and named as chorus waves.Chorus waves are usually composed of discrete elements,and single element typically exhibits rising-tone or falling tone structure.Whistler waves is the primary source of relativistic electrons in the outer radiation belt,which can acceler-ate?100 keV electrons to relativistic electrons through local stochastic acceleration in several hours to one day.Whistler waves play a pivotal role in controlling electron dy-namics in the Van Allen radiation belts.Through satellite observations and numerical simulations,a lot of studies about whistler waves have been done.In this paper,using particle-in-cell(PIC)simulation codes,we study several nonlinear physical processes associated with whistler waves,including parametric decay of a whistler wave,excita-tion and evolution of rising-tone chorus waves,and the dependence of properties of a rising-tone chorus on hot electron parameters.Our main conclusions are as following:1.Parametric decay of a whistler waveWith one-dimensional(1-D)and two-dimensional(2-D)PIC simulations,we in-vestigate parametric decay of whistler waves.1-D PIC simulation results show that a parallel whistler wave can experience the parametric decay,and decay into a backward daughter whistler wave and a forward ion acoustic wave.The whistler wave with larger frequency or amplitude will experience stronger parametric decay.The parametric de-cay can also take place for intense daughter whistler wave.2-D PIC simulation results show that both parallel and oblique whistler wave can experience the parametric de-cay.And a whistler wave first decays into a backward whistler wave and a forward ion acoustic wave along its propagation direction.Then it decays into a family of daugh-ter whistler waves with nearly same parallel wave number but different perpendicular wave number and a similar family of ion acoustic waves.Some daughter whistler waves are highly oblique,and these excited ion acoustic waves can accelerate a part of ions through Landau resonance.Besides,the parametric decay tends to be stronger for the whistler wave with a larger frequency or amplitude.And the intense daughter whistler waves can also experience the similar parametric decay.2.The dependence of properties of a rising-tone chorus on hot electron parametersUsing 1-D PIC simulations in a mirror field,we study the effect of the number density and the temperature anisotropy of hot electrons on main properties of a rising-tone chorus in the Earth's inner magnetosphere.The simulation results reveal that the saturated amplitude,the duration,and the frequency span of a rising-tone chorus in-crease with increasing number density of hot electrons,while its frequency chirping rate first increases and then saturates.With the increase of temperature anisotropy of hot electrons,the frequency chirping rate of a rising-tone chorus increases,but the cho-rus duration decreases.However,clear rising-tone chorus waves can't be excited for too small or too large number density and temperature anisotropy of hot electrons.Be-sides,when a rising-tone chorus propagates from the magnetic equator to the pole,its frequency span remains nearly constant,but its duration and frequency chirping rate change perhaps due to dispersion.3.Excitation and evolution of rising-tone chorus waves in a mirror fieldWith the 2-D general curvilinear PIC(gcPIC)code,we investigate the excitation and evolution of rising-tone chorus waves in a mirror field.The simulation results present that whistler waves are excited by anisotropic hot electrons in the magnetic equa-torial regions.Then they propagate toward the polar region and obtain more growth.Some whistler waves can develop into rising-tone chorus waves near the magnetic equa-torial regions.Based on analysis of Poynting vector and wave normal angle,the rising-tone chorus waves are confirmed to propagate nearly along the magnetic field.During propagation,the wave normal angles of chorus waves along the straight magnetic field line are nearly constant,however,the wave normal angles of chorus waves along the curved field line gradually increase.In addition,the frequency chirping rate tends to be smaller for the rising-tone chorus wave excited along the more curved field line.4.Generation and evolution of rising-tone chorus in a dipole fieldUsing the 2-D gcPIC code,we also study the generation and evolution of rising-tone chorus waves in the Earth's dipole field.The simulation results show that whistler waves driven by anisotropic hot electrons first appear around the magnetic equator,and their source mainly locates within |?|<3°.Some whistler waves can form rising-tone chorus waves near the magnetic equator.Rising-tone chorus waves are found to be nearly field-aligned.During propagating toward high-latitude regions,their wave normal angles gradually increase with increasing magnetic latitude.At high latitude,chorus waves become very oblique with wave normal angles up to 50°.However,chorus amplitude first enhances and then decays,reaching the maximum value at ??10°.Their decay in high-latitude regions may be due to Landau damping.