Theoretic Research On Global Geodesic Acoustic Modes In Tokamak

Geodesic Acoustic Modes(GAMs)are the high frequency branch of turbulencedriven zonal flows(ZFs)and are widely observed in L-mode and I-mode plasmas in most of the toroidal magnetic confinement fusion devices.They are brought into intensive interest due to their ability of modulating drift wave turbulence by their flow shearing effects and the important roles they play in the L-H and L-I mode transitions.Although the discrete eigenmode structures of the global GAMs have been widely observed in experiments and numerical simulations recently,the theoretic research on the origins and the concrete structures of these modes is still in its early stage.In this thesis,we have developed the linear theories on global GAMs based on several fluid-type models as well as the more thorough gyrokinetic model.First of all,a linear theory of ion finite-Larmor-radius(FLR)—induced global GAMs based on the ideal electrostatic two-fluid model is developed,in which modest ion FLR effects are encompassed through the polarization drifts.The radial differential equation obtained for the eigenmodes is a type of generalized Schrodinger equation,in which the eigenfrequency is mixed with the equilibrium profiles in a complex manner into a“potential”function.By numerically solving this equation as a genuine boundaryvalue problem,it is found that,for typical equilibrium profiles,there exists a series of global GAMs,with relatively higher frequencies that intersect with the GAM continuum.Those with frequencies in the intermediate range are forbidden by the singularity of the“potential”function.When restricting the poloidal θ harmonics up to m=±1,we have successfully interpreted the bound-state-like mode profiles of global GAMs discovered in the simulation performed by Miyato et al and have also pointed out the limitation of their model.Then a more realistic theory of global GAMs with short wavelengths,based on the framework of an electrostatic gyro-fluid model,has been developed,in which the more thorough sorts of ion FLR effects resulting from ion gyro-average are encompassed,in comparison with the two-fluid model,while the radial differential equation of the eigenmodes still comes up in a compact form of a generalized Schrodinger equation.By solving the corresponding boundary value problem numerically with typical equilibrium profiles,a multitude of global GAMs with quantized eigen-frequencies have been found.In particular,as the consequence of the plasma model improvement,we have obtained multiple edge-localized global GAMs with the features resembling those observed experimentally.Meanwhile several wide internal global GAMs and global acoustic modes are also found.Furthermore,we have developed the theory of global GAMs based on the more complete electrostatic gyrokinetic model with the edge localized equilibrium radial electric field(Er-well)included,in which the ion FLR effects are captured via both gyro-average and magnetic drift velocities.Upon solving the boundary value problem,the global zonal flow modes with zero real eigenfrequencies,the global acoustic modes and wide internal global GAMs with Landau damping rates that are comparable in magnitude with the real mode frequencies,and a family of edge-localized global GAMs with negligible Landau damping rates are uncovered.The equilibrium radial electric field Er has small squeezing effects on the mode structure of the global GAMs throught the poloidal rotation(poloidal Mach number Mp)caused by Er×B drift.We have also investigated the variations of two branches of the local dispersion function with Mp and the variations of the frequencies and turning points of the edge-localized global GAMs with Mp through iteration method.It is revealed that both the local and global GAM frequencies up-shift with the depth of Er-well,which also has a squeezing effect on the spatially oscillating radial extensions of the edge-localized global GAMs.Finally,we have developed the theory of the electromagnetic global GAMs with long wavelengths approximation based on the ideal MHD model with toroidal rotation included.Toroidal rotaion brings the extra cos 20 component besides the base sin 20 cmponent in the perturbed geodesic displacement of the fluid element and results in two coupled second-order differential equations for the global GAMs.These two equations degrade to single differential equation that has been reported in literature when the toroidal rotation is absent.This theory successfully predicts the-π/8 phase shift of the electromagnetic GAMs induced by the toroidal rotation on EAST.