Particle-in-Cell Simulations Of Nonlinear Interactions Between Electrostatic Waves And Energetic Particles In Plasmas

Wave-particle interactions exist widely in laboratory and space plasmas.The interactions play very important roles in the diagnosis,heating,transportation and instability of plasmas.A sufficient understanding of wave-particle interactions is the key to control these physical processes.At present,the research on the linear phase of wave-particle resonance has been relatively mature.However,the theory of nonlinear behavior in the evolution still needs to be improved and supplemented.The works in this paper are based on the bump-on-tail(BOT)model,and focus on the nonlinear Landau damping during the interaction between energetic electrons and electrostatic waves.In this paper,a simple initial distribution of energetic electrons is adopted,and the wave with specific modulus in the model is retained by filtering.The core physical process is abstracted.Although this simplified model is not common in real plasmas,the study of the nonlinear wave-particle interaction mechanism has a general nature for wave-particle resonance occurring locally in phase space.The theoretical work on BOT mainly calculates the evolution of particle distribution function by solving the Vlasov/Fokker-Planck equations coupled with Maxwell equations.However,some excessively complicated nonlinear terms,such as mode coupling in multi-mode resonance,must be neglected or truncated in this quasilinear method.Therefore,this paper studies the simplified BOT model using the particle simulation.A code using Particle-in-Cell(PIC)method has been made to analyze the nonlinear wave-particle resonance process.This thesis is divided into six chapters.The first chapter is the introduction.The physical model and the numerical methods are described in the second chapter.Furthermore,the convergence of numerical parameters such as spatial and temporal step size in the PIC code is analyzed to verify the rationality and reliability of the code.Chapter 3 focuses on the nonlinear process of wave-particle resonance in a non-dissipative system.In the collisionless cases,the results of single mode simulation agree well with the classical theory.Some new results are obtained in the case of double resonances.The investigations show that,when the mode is excited by EPs and nearly grows to saturation,the secondary resonant phase islands will be formed between the main resonant phase islands.The secondary phase islands are caused by the coupling of these two waves which resonate with EPs,thus forming a virtual wave which can capture some original passing EPs.Even if the two main resonance islands do not overlap,the formation of the secondary phase island is observed.These secondary phase island structures can provide a new way of energy exchange between waves and EPs,and allows EPs to transfer more energy to the wave field in the case without damping.In chapter 4,the nonlinear behavior of wave particle resonance in a dissipative system is discussed.The damping effects are the background dissipation and the kinetic friction(drag).After introducing these two effects,the process of frequency sweeping and hole-clump structure formation are successfully simulated.The research shows the results as follows.(1)Background dissipation makes the frequency sweeping.The sweeping can occur both near to and far from the instability threshold,and the width of frequency sweeping increases with the increase of damping,while the saturation amplitude of the mode decreases with the increase of damping.(2)The frequency sweeping cannot be caused by drag alone.However,in the presence of background dissipation,the drag effect can enhance the frequency sweeping,and the closer to the instability threshold,the more obvious the enhancement effect will be.(3)The physical image of hole-clump structure formation is illustrated by observing the evolution of EPs phase space.It is found that when two waves resonate with EPs,the nonlinear coupling effect between different modes will increase the damping of each wave,reduce the saturation amplitude of the waves,and reduce the energy exchange efficiency between EPs and waves.When the damping is large,the effect of decreasing wave-particle energy exchange is greater than that of increasing energy exchange owing the formation of secondary phase islands.In chapter 5,the interaction between the excited electrostatic solitary wave and the energetic electrons with a certain velocity distribution is studied.The simulation results show the physical process of generating an electrostatic solitary wave and modulating the background electron and energetic electron velocity.The unstable wave-number and corresponding maximum growth rate of electrostatic solitary wave excited by EPs with different velocities are given.It is found that,electrostatic solitary wave driven by EPs has a higher saturation level and longer duration in BOT mode.The last chapter summarizes the whole paper and prospects the future work.