Study Of Poloidal Flow In Tokamak Plasma And Its Application In The Magnetohydrodynamic Instability

Tokamak is a typical device for magnetic confinement fusion.Its steady state operation is the fundamental of self-sustained burning of the plasma in the future tokamaks.It is a long-term research of suppressing various instabilities in tokamaks,which is in order to ensure the steady state operation.In this thesis,the influence of equilibrium flow with dominantly poloidal flow on the classical tearing mode and the effect of radial electric field on the geodesic acoustic mode(GAM)are investigated.It is different from the previous researches which are only focus on the effect of toroidal flow.And the anisotropy is taken into consideration in the analysis of the influence of radial electric field on GAM.In the past researches on the effect of equilibrium flow,most studies are focused on the influence of toroidal flow.The effect of poloidal flow is neglected.As there is no pure poloidal flow which satisfies the continuity equation,in this thesis,the influence of poloidal flow is investigated on the assumption that the poloidal flow and the toroidal flow are in the same ordering and it is also shown that the poloidal flow is predominant on this assumption.Usually near the edge of tokamak plasmas,there is a radial equilibrium electric field.As the toroidal part of equilibrium magnetic field is much more larger than the poloidal part in tokamak,consequently,sometimes an poloidal equilibrium flow may appear(ExB flow).Its value is approximately equal to the poloidal part of equilibrium flow on the equal magnitude assumption.For this reason,the influence of radial electric field is investigated.Based on the equal magnitude assumption,the vorticity equation including the influence of poloidal equilibrium flow is derived from the ideal magnetohydrodynamic equations.Regarding the poloidal mode number as a large number and using the confluent hypergeometric functions,the solutions of the simplified vorticity equation can be derived from the asymptotic matching of outer solutions to the inner limit.Then the stability index ?' which is the sign of instabilities for resistive classical tearing modes can be derived.The expression of stability index indicates that the stability of classical tearing mode is closely related to the profile of safety factor.To study the influence of poloidal flow on the tearing modes with arbitrary poloidal mode numbers,we numerically solve the vorticity equation.With the given profiles of typical safety factors and poloidal flows,the results show that(1)comparing the case of predominant poloidal flow with the case of pure toroidal flow which is investigated by others before,when the poloidal Mach number and the toroidal Mach number are in the same ordering,the changes of stability index are approximately equal.It means that the effect of poloidal flow on the classical tearing mode is comparable to the effect of toroidal flow.(2)The flow shear at the mode rational surface plays the dominant role.The poloidal equilibrium flow with positive flow shear at the rational surface has beneficial influence on the stabilization of classical tearing modes.If the flow shear at the rational surface is negative,the effect of the poloidal equilibrium flow would be adverse.(3)Comparing with the cylindrical case,the stabilizing effect of poloidal equilibrium flow on classical tearing mode is better in toroidal plasmas.Considering the existence of radial electric field near the edge of tokamak plasma and neglecting the magnetic perturbation which is related to the finite beta effect,the dispersion relation including the influence of radial electric field is derived.Only considering the standard GAMs,which means the normalized frequency ?>>1(where ?=qR?/?T),we analytically and numerically solve the dispersion relation,respectively.The results show that(1)both frequencies and damping rates increase with respect to the Mach number which indicates the radial electric field.(2)The analytical result is more accurate in the case of high ratio of the parallel temperature to the perpendicular temperature.(3)The real frequencies of GAM decrease with the increasing value of ratio of the parallel temperature to the perpendicular temperature.But the increasing value of ratio dramatically promotes the damping rates of GAM.When the parallel temperature is lower than the perpendicular temperature,i.e.T?/Tl<1,the enhanced anisotropy tends to enlarge the real frequency but reduces the damping rate.When the parallel temperature is higher than the perpendicular temperature,i.e.T?/T?>1,the enhanced anisotropy tends to reduce the real frequency but enlarges the damping rate.(4)Comparing with the radial electric field,the frequency and damping rate are more sensitive to the ratio of the parallel temperature to the perpendicular temperature.And the increasing radial electric field can enhance the real frequency more effectively for the case with the parallel temperature higher than the perpendicular temperature than for the case with the parallel temperature lower than the perpendicular temperature.While the change of the damping rate versus the radial electric field is not so different for both anisotropic cases.