Simulation Of M/n=1/1 Modes Driven By Energetic Passing Particles In Tokamaks

Energetic particle physics is one of several key issues in tokamak fusion research.Interactions of energetic particles with plasma can excite various types of instabilities.These unstable modes can in turn cause large radial transport of energetic particles.This is not conducive to the confinement of energetic particles,which results in reduction of energetic particle heating of the background plasma.Fishbone instability is one of these important instabilities with m/n=1/1.Both energetic trapped particles and energetic passing particles can drive fishbone instability.Compared to the energetic trapped particle-driven fishbone,the energetic passing particle-driven fishbone has not been studied extensively.Previous studies mainly include the original work of Betti in 1993 which showed that energetic passing particles can excite a low frequency fishbone mode.Its frequency is similar to the diamagnetic drift frequency of thermal ions.Therefore this instability is called the ωi branch of fishbone.In recent years,it was found in the HL-2A tokamak experiment that energetic passing particles can excite a low frequency fishbone mode.In 2019,Yu et al developed the analytical theory for energetic passing particle-driven low frequency fishbone of EPM branch(EPM=Energetic Particle Mode)whose frequency is determined by the wave particle resonance condition.In addition to the low frequency fishbone modes,a scholar pointed out in 2001 that the energetic passing particles can also excite a high frequency fishbone mode.In this thesis work,the energetic passing particle-driven m/n=1/1 mode is studied systematically via linear and nonlinear simulations by using the MHD-kinetic hybrid code M3D-K.First,a systematic linear simulation study showed that the m/n=1/1 mode driven by energetic co-passing particles is a low frequency fishbone mode.The main wave particle resonance is ωφ+ωθ=ω.The simulated mode frequency is similar to that of analytic theory of Yu.In particular,when the beta value of the background plasma is small,the simulated mode frequencies agree quite well with the analytic mode frequencies.Nonlinear simulation results show that,after the low frequency fishbone is saturated,a new high frequency mode of m/n=1/1 appears with mode structure localized near the magnetic axis,and it is accompanied by a frequency jump.Second,a systematic simulation study is also carried out for the energetic counterpassing particle-driven m/n=1/1 mode.Results show,for typical parameters and profiles,a high frequency EPM is excited with its mode structure localized near the magnetic axis.Furthermore,a high frequency mode similar to the global Alfvén eigenmode(GAE)can also be destabilized for certain parameters.The mode structures of all these modes are localized at the magnetic axis,and the resonance relation is ωφ+2ωθ=ω.There is no low-frequency fishbone mode with a resonance relationship of ωφ+ωθ=ωin the linear stage.This indicates that in the linear simulation phase,the mode with resonance relationship of ωφ+2ωθ=ω among all the unstable modes of m/n=1/1 is the most unstable.In the nonlinear stage,the high-frequency EPM persists for a long time after initial mode saturation and is accompanied by an upward frequency chirping.During the upward frequency chirping,the region in which the resonant particles are located in the phase space also changes accordingly.After a long period of sustained high frequency mode,the EPM transits to a low frequency fishbone with its frequency jumps down from the value of EPM.Correspondingly,the resonance relationship of the low fishbone mode that appears at this time is ωφ+ωθ=ω.The instabilities driven by the co-passing and the counter-passing energetic particles both cause significant radial redistribution of particle distribution during nonlinear saturation.This shows that the energetic passing particles have significant outward transport in the radial direction.Finally,the study showed that under the condition of the particle distribution function we are currently using,the finite orbit width(FOW)of the energetic co-passing particles has a great influence on the simulation results.In particular,if the FOW is simplified to a constant,the energetic co-passing particles will excite high-frequency fishbone-like modes with a wave particle resonance ω=ωφ.If the FOW effect is included with time,the energetic co-passing particles will excite the low-frequency fishbone mode with a resonance relationship of ωφ+ωθ=ω.Theoretically.it can be proved that the driving term of the co-passing energetic particles becomes very small when the FOW is included with time in the distribution function we are currently using.Therefore,the high frequency fishbone is not found in our simulations including this FOW effect.Regardless of whether this FOW effect is considered,the energetic counterpassing particles excite the m/n=1/1 mode whose resonance relation is ωφ+2ωθ=ω.In conclusion,the understanding of the m/n=l/1 instability driven by energetic passing particles has been enriched by simulation studies.Particle transport phenomena caused by m/n=1/1 mode in nonlinear simulation results may throw some light on experimental research.