Theoretical-Numerical Study Of Drift Wave-Zonal Flow System And Intermittency Experiments In L-mode Discharge In Tokamaks

Zonal flow is the fluid velocity field with one-dimensional spatiotemporal structure.Drift wave is the high mode number wave in inhomogeneous media driven by pressure gradient free energy.It is generally accepted that these two are basic components of the so-called drift wave-zonal flow system.Specifically,the zonal flow in tokamak refers to E×5B velocity arising from radial variation of band-like electrostatic potential fluctuations;the drift wave in axi-symmetric tokamak is the localized standing wave in radial direction pertaining to a certain rational surface,and the travelling wave propagating in poloidal direction.While zonal flow is in mesoscale,there are two distinct scales in drift wave:the linear eigenmode in microscale and the drift wave energy in mesoscale.The nonlinear interaction between zonal flow and drift wave consists of two aspects:(1)zonal flow is driven by Reynolds stress of drift wave and the drift wave energy is modulated by zonal flow;the modulation could be in amplitude and/or in phase;(2)the shear of zonal flow suppresses amplitude of drift wave turbulence.In this dissertation,we focus on the zonal flow excitation mechanism by phase modulation.Although the system in disparate scale is routine in plasma physics,its application to the tokamak configuration is quite a kind of challenging.The reliable calculations of two nonlinear quantities in mesoscale-Reynolds stress and drift wave group velocity demand knowledge of two-dimensional(2D)eigenmode structure in real space.This task is done by making use of the weakly asymmetric ballooning theory(WABT)and multiple scale derivative expansion method,and further refined by iterative finite difference method satisfying the natural boundary condition as provided by WABT solution.After substituting the obtained Reynolds stress and drift wave group velocity into the slab zonal flow equation and drift wave energy equation respectively,the theoretical model of pure phase modulation has to be inevitably studied within the nonlinear framework,well posed as an initial value problem in real space that is solved numerically.As shown in numerical results there are two consecutive phases in the periodic evolution of drift wave energy-the caitvon:a slowly breathing spatial local structure of 'negative' energy,and the instanton:a fine radial structure of short lifetime in rapid propagation.The phase transition from cavition into instantons is triggered by zero-crossing of radial group velocity.For slab zonal flow model,many features of low frequency zonal flow(LFZF)are found similar to experimental observations.For torus zonal flow model there are two branches of zonal flow:the torus-modified low frequency zonal flow(TLFZF)and geodesic acoustic mode(GAM).As a result,the two-equation system in slab zonal flow model becomes three-equation system;the new one arises from toroidal coupling of zonal flow to sinusoidal sound wave via geodesic curvature.The phase transition from caviton to instantons is found highly correlated with the GAM onset as soon as TLFZF grows up to a certain level.The numerical results display a lot of intermittent characteristics observed in up to ten tokamak experiments.Then,we conclude that the intermittency of GAM is deterministic.