Theoretical And Numerical Study On Dispersion Relation Of Geodesic Acoustic Mode And Drift Wave In Tokamak

Achieving effective plasma confinement in magnetically confined fusion devices has always been the fundamental and essential topic in the field.Unfortunately,there lacks solid transport theories for high-temperature magnetized plasmas.Specifically,the classical transport theory fails to explain the high transport coefficients observed in experiments.The neo-classical theory,with the global geometric effect included,also pridicts much lower transports coefficients.It is now widely accepted that the transport in Tokamak is closely related to the boundary turbulence,the whole transport process is determined by the complex interaction between the macroscopic flows and the microscopic turbulence.In Tokamaks,the turbulence is primarily excited by the drift instabilities,whereas for the macroscopic flows,a global structure called zonal flow is found to have strong interactions with boundary turbulence,and thus has received much attention.To conclude,the study of drift turbulence and zonal flows are crucial to the improvement of the plasma confinement in Tokamaks.This thesis is developed to explore the temporal and spatial characteristics of the drift wave and the zonal flows under practical parameters,with multiple non-ideal effects included.The content of this thesis starts by introducing the development and the current status in the field of magnetically confined fusion,providing a primitive understanding of the background the practical significance.The drift waves and the geodesic acoustic mode(GAM,a branch of zonal flow)is introduced in detail to give a clear picture of the existing developments and unresolved topics.The introductions serve as a comprehen-sive picture of the topic of this thesis.This thesis first investigated the GAM under practical parameters.Being a branch of the zonal flows,the GAM plays an important role in the surpression of the turbulence and the anomalous transport.In Tokamak experiments,the plasma is usually in a differ-ent regime from the ideal theories.Neglecting the collisions between the ions and the existence of the impurities,the ideal theories sometimes fail to explain the experiment data.In this thesis,a gyro-kinetic model with co-existing collisions and impurities is developed.The derived dispersion relation confirmed the non-monotonic relation be-tween the damping rate and the collision frequency.Meanwhile,the critical point of this non-monotonic relation is found to shift towards the low-collision end as the impu-rity level increases.The model also gives a comparison among the effect of different collisions and the Landau damping.From the results,the Landau damping effect is relatively small,while teh ion-ion collision and the impurity-induced collision give ap-proximate corrections to the damping rate of GAM.Specifically,the impurity-induced collision helps reducing the real frequency of GAM,while the effect on the damping rate is relatively complicated.When the collision is low,the impurity-induced collision increase the damping rate,while for high collisions,the damping rate is decreased as the collision rate increses.In a word,the the combined effect of the collisions and the impurities cannot be treated as the sum of each individual effects.This thesis also studied the linear theory of the drift wave in the 2-fluid MHD pro-cess.The field of drift waves has long been a hot topic because the drift turbulence is closely related to the formation and evolution of the zonal flows in Tokamak devices.Over the past decades,great progress have been made about the drift wave theories.Nontheless,there still are some topics that are worth further attention,one of which be-ing the drift wave under the MHD framework.The classical theories of drift waves often adopt the 2-fluid representaion,with the local approximation and the electro-static ap-proximation assumed,whereas experiments have often found regimes where the spatial scales and the magnetic components of drift waves approach those of MHD processes.In this thesis such a drift wave regime is studied in a cylindrical magnetized plasma us-ing a full two-fluid MHD model implemented in the NIMROD code.The investigation first derived the analytical dispersion of the drift wave under the cylindrical geome-try,and the same model is numerically studied using code NIMROD.The comparison between the numerical results and the classical theories show a qualitative agreement,implying the key factor of the drift wave is included in the NIMROD simulations.On the premise of the MHD equilibrium,the full 2-fluid MHD model gives the complete magnetic effects on the drift waves,which is absent in traditional drift wave theories.The simulation also reveals a "non-classic" drift wave branch,which is believed to be corresponding to the exited state of the drift wave eigenmode.