Study On The Effect Of Resonance Magnetic Perturbation On The Tearing Mode Instability

The development of human economy is inseparable from energy.The rapid growth of economy leads to the increasing consumption of energy.The use of non-renewable energy,such as coal and oil has also caused great harm to the environment.Therefore,human beings urgently need to find new energy to solve this crisis.The discovery of nuclear fusion energy has brought hope to humankind.This new energy is inexhaustible and has no pollution to the environment,but its uncontrollability has been an obstacle to human use.Several devices such as tokamak and stellarator which use the magnetic field to constraint plasma nuclear fusion have been designed.However,a lot of work needs to be done to achieve a sustained and stable energy output.Based on the existing experiments and theories,it is widely believed that tokamak is the most likely to achieve a controlled nuclear fusion reaction,and it has become the mainstream of magnetic confinement nuclear fusion.The level of confinement of the tokamak plasma is primarily dependent on the Magnetohydrodynamic(MHD)instabilities,whose characteristic scales are compareable with the small radius of the device,such as the kink mode instability,the tearing mode instability,the axisymmetric instability.Among these MHD instabilities,the tearing mode instability is one of the most important instabilities,which determines the operating limit that tokamak can achieve.Based on the compressible resistance MHD model under the two-dimensional slab geometry,we study the effects of Resonant Magnetic Perturbation(RMP)on the instability of tearing mode by numerical simulations.The main contents and conclusions are as follows.Firstly,in order to find a better way to suppress the Double Tearing Mode(DTM)instability induced by RMP,the evolution process of the DTM instability is explored.The numerical simulation results show that the growth of the magnetic island will go through three typical stages before the mode reaches saturation.For the outer magnetic island,the development of the mode includes:(I)linearly stable stage;(II)linear growth stage;and(III)exponential growth stage.The inner magnetic island also has three stages,but its second stage is the forced magnetic reconnection stage.Moreover,we also find the following phenomena:(1)in the final phase of the exponential growth stage,the growth of the outer magnetic island is always faster than that of the inner magnetic island,and with the increasing of the amplitude of RMP,the gap between the inner and outer magnetic islands will increase;(2)RMP plays a dominant role in the linear growth stage and has very weak effect on the island development in the exponential growth stage;(3)the outer magnetic island is always generated before the inner one appears,and this phenomenon becomes more obvious with the increasing of the distance between the two rational surfaces;(4)increasing the RMP amplitude and decreasing the spacing between the two rational surfaces can shorten the time for the magnetic island to reach saturation.Secondly,we study the effect of RMP on the DTM induced by asymmetric magnetic perturbation in detail.We have set up four different forms of magnetic perturbation:(1)only the inner rational surface has magnetic perturbation without RMP;(2)only the outer rational surface has magnetic perturbation without RMP;(3)only the inner rational surface has magnetic perturbation with RMP;(4)only the outer rational surface has magnetic perturbation with RMP.For the first two cases,we find that the widths of the inner and outer magnetic islands are the same in the end of the mode,and the evolutions of these two magnetic islands are the same,regardless of which rational surface the magnetic perturbation is set on.In contrast,for the latter two cases,we find that(1)the width of the outer magnetic island is larger than that of the inner magnetic island at the end of the mode;(2)the effect of RMP on the outer rational surface is much greater than that on the inner rational surface;(3)RMP can shorten the time for the magnetic island to reach saturation,no matter which rational surface has been set with the magnetic perturbation.Thirdly,the effects of RMP on the Single Tearing Mode(STM)with a plasma equilibrium flow are studied.The plasma equilibrium flow can change the O-point position of the magnetic island,and the phase between the magnetic island and RMP keeps on changing all the time.Therefore,the driving and suppressing effects of RMP on the STM instability appear alternately,leading to a periodic fluctuation for the growth curve of the magnetic-island width.The main conclusions are as follows:(1)when the flow velocity is small,the period of the O-point change of the magnetic island on the rational surface is relatively large,so the suppressing effect of RMP plays a major role in the development of the mode,and this will cause the width of the saturated magnetic island to decrease;(2)when the flow velocity increases to some value with which the flow can just survive through the whole development of the mode,RMP has the greatest suppressing effect on the tearing mode instability;(3)when the flow velocity increases further,the period become shorter,the driving effect of RMP increases while the suppressing effect decreases,which will lead to a certain increase for the width of the saturated magnetic island;(4)when the flow velocity is so large that the period of the O-point change is close to zero,the suppressing and driving effects will reach an equilibrium,and in this case the width of the saturated magnetic island will not change with the increase of the flow velocity,and the tearing mode will become stable.