Theories And Simulations Of Geodesic Acoustic Modes In Tokamak Plasma

In tokamak plasma,various instabilities are produced due to the spatial inhomogeneity of temperature and density as well as magnetic field.Further development of these instabilities will lead to turbulent transport,thus affecting the confinement performance of the plasma.Therefore,how to suppress turbulent transport has become a very important issue in the research of magnetic confinement fusion.Research findings show that the zonal flows can effectively reduce the turbulent transport level through E×B shear,thus improving the confinement performance of plasma.Therefore,it is very important to study the physics of zonal flows.As a high-frequency branch of zonal flows,geodesic acoustic modes(GAMs)can be driven by drift wave turbulence through non-linear interaction,which in turn can suppress drift wave turbulence,so they have also received extensive attention.In this thesis,the effects of rotation and impurities in tokamak plasma on GAM and the magnetic components of electromagnetic GAM are studied by using the gyrokinetic theory.At the same time,the electromagnetic GAM is simulated by using the gyrokinetic code GEM.First,we study the effect of plasma poloidal rotation induced by the radial equilibrium electric field on collisional damping of GAM.Starting from the gyrokinetic equation including poloidal rotation and Krook collision operator,and using quasi-neutral conditions,we obtain the dispersion relation of GAM.By solving the dispersion relation theoretically and numerically,we studied the influence of poloidal rotation on the collisional damping of GAM at different ion collision rates.The results show that:(1)when the safety factor is small and the ion collision rate is small or medium,the poloidal rotation will gradually reduce the collisional damping rate of GAM;when the ion collision rate is high,the poloidal rotation will first decrease and then increase the collisional damping rate of GAM.(2)When the safety factor is large,the poloidal rotation always decreases the collisional damping rate of GAM,and the larger the collision rate,the more obvious the impact is.In addition,by comparing the collisional damping and collisionless damping of GAM,the critical collision rate is obtained and compared with the experimental parameters.At the same time,the reason why the poloidal rotation affects the collisional damping of GAM is simply analyzed.Then,we study the impurity effects on collisionless damping of GAM in toroidally rotating plasma.For convenience,we only consider two typical impurities,carbon and tungsten,to study the effects of non-trace impurities and trace impurities on GAM,respectively.The results show that:(1)For non-trace impurity,without rotation,the impurity concentration and mass number can significantly reduce the frequency of GAM and increase its damping rate,while the impurity charge number has little effect on GAM,which is consistent with previous results.In the presence of rotation,impurity concentration still has a significant effect on GAM,and the greater the rotation speed,the more obvious the effect.On the other hand,in the presence of impurities,rotation will still increase the frequency of GAM and reduce its damping rate.However,with the increase of impurity concentration,the effect of rotation on GAM decreases gradually.(2)Without rotation,trace impurities have little effect on GAM.In the case of weak rotation,trace impurities still have no effect on GAM,but in the case of strong rotation,trace impurities will significantly increase the frequency of GAM and reduce its damping rate.On the other hand,the effect of rotation on GAM is obviously enhanced by trace impurities.(3)Isotope effect can significantly reduce the frequency and damping of GAM.At the same time,the isotope effect can also weaken the effect of impurities on GAM,while enhance the effect of rotation on GAM.Finally,we first theoretically study the magnetic components of the electromagnetic GAM.The expressions of magnitudes of various magnetic components are derived,in which the coupling between the inverse aspect ratio and the transit frequency is mainly considered.The results show that:(1)The magnitude of all magnetic components is related to many plasma parameters.(2)The sine and cosine component of the m=1 and m=2 harmonic magnetic components all exist,and both of them are dominated by sine components.(3)The inverse aspect ratio has a significant influence on the m=1 and m=2 magnetic components.When the inverse aspect ratio is small,the magnitude of m=2 magnetic component will be much larger than that of m=1,which is consistent with previous results.When the inverse aspect ratio is large enough,the magnitude of m=1 magnetic component is comparable to or even close to that of m=2 magnetic component.This is also the biggest difference between this paper and previous results.Then we simulated the electromagnetic GAM by using the gyrokinetic code GEM and make a simple comparison with the theoretical results,the results show that the simulation results are in good agreement with the theoretical results qualitatively.It is also found that the electromagnetic effect has little effect on the frequency and damping of GAM.