Ion Polarization Density Correction In Tokamak Pedestal

Turbulent transport is a critical physics process that affects the confinement of high temperature plasmas in magnetic fusion device.Massively parallel gyrokinetic simulation has become a major tool for studying linear and nonlinear physics in the microinstability that leads to turbulence and turbulent transport.One important component of the gyrokinetic simulation is to accurately solve gyrokinetic Poisson equation,in which a critical step is to precisely calculate ion polarization density.The ion polarization density is composed of two parts:one part is caused by the change in ion gyroradius,which is retained in the conventional gyrokinetic formulation.Another part is cause by the change in the ion density.The latter part is a higher order term comparing to the first part under weak plasma gradient and thus is generally ignored.However,this part becomes equally important under strong gradient,which can affect linear instability and zonal flow response and shall not be ignored.Based on these observations,we carry out a series of gyrokinetic simulations in this thesis and accomplish the following innovative results.(1)We illuminated for the origin of the two parts of the polarization density by a single particle picture.The relative importance of these two parts is compared for different parameter regimes.To show the existence of this high order correction of the polarization density,we developed an effective algorithm to calculate fully kinetic particle orbit in toroidal geometry,with which we are able to verify the correctness and necessity of the higher order polarization density.(2)We modified the flagship fusion simulation code GTC(Gyrokinetic Toroidal Code)to include the high order polarization density,which enables GTC to accurately solve the perturbed gyrokinetic Poisson equation under the strong plasma gradient in the pedestal.Based on the code development,we studied the effect of high order polarization density on ion temperature gradient(ITG)turbulence.We first employ a 1-D ballooning eigen equation for the ITG instability to study this effect in the weak gradient regime,and then use the GTC code to study this effect on the ITG mode in the strong gradient regime.In both weak and strong gradient regimes,if only including adiabatic electrons,we find that the high order polarization density has little effect on the linear ITG frequency and growth rate,but it has a significant effect on the mode structure in the parallel direction.The further nonlinear ITG simulation with adiabatic electrons shows that the high order polarization density leads to a significant decrease in the thermal diffusivity.Meanwhile,we find that under strong gradient,the kinetic electrons can enhance the effect of high order polarization density significantly.The most unstable mode jumps between different branches of the roots of the linear dispersion,which leads to completely different mode structures.(3)We modified and implemented a novel numerical method to solve the flux-surface averaged Poisson equation in the GTC,and then studied the effect of the high order polarization on the zonal flow especially the geodesic acoustic mode(GAM).It is found that under strong gradient,the high order polarization density makes no difference in the residual zero-frequency zonal flow,but it can significantly change the linear properties of GAM,e.g.,the stronger gradient yields a lower GAM frequency and damping rate,which helps regulating the turbulent transport.