| Both the International Thermonuclear Experimental Reactor(ITER)and the China Fusion Engineering Test Reactor(CFETR)need to achieve self-sustained heating of plasma,in which the fusion reaction of deuterium and tritium will produce 3.5 MeV α particles.These α particles may excite various instabilities in the frequency range of 10 Hz-109 Hz.On the contrary,these instabilities will enhance the transport of α particles,resulting in lower self-sustained heating efficiency,and even cause damage to the first wall and the divertor targets of the device due to excessive heat flux.In addition,some auxiliary heating,such as Neutral Beam Injection(NBI)and Ion Cyclotron Resonance Heating(ICRH),will also produce a large number of energetic particles.Therefore,it is very important to study the energetic particle instabilities.In this dissertation,the codes(NIMROD and M3D-K)based on the kinetic-MagnetoHydroDynamics(MHD)hybrid physical model are used to simulate two important energetic particle instabilities(ion fishbone mode and Reversed Shear Alfven Eigenmode(RSAE)).First,we used the NIMROD code to conduct a numerical simulation study on the resistive internal kink mode and the ion fishbone mode on HL-2A.The purpose is to better understand the stabilizing effect of ECRH on the ion fishbone mode in the experiment.We focused on the effect of resistivity on internal kink mode and ion fishbone mode.When S≤105(S is the magnetic Reynolds number),the growth rate of the modes decreases with increasing S and their scaling relationship is γ∝ S-1/3.However,when S>105,the growth rate hardly changes with the increase of S.As S increases,the frequency of the fishbone mode increases first and then remains almost unchanged.In addition,the effect of energetic ions on the fishbone mode is analyzed in detail by scanning the beta fraction(βfrac)and cut off velocity(vcutoff)of energetic ions.The simulation results show that the m/n=1/1 mode gradually transforms from an internal kink mode to a fishbone mode with the increase of βfrac,and energetic ions have a stabilizing effect on the internal kink mode.Except that the stabilizing effect of energetic ions on the internal kink mode is not reflected in the analytical results,the simulation results are basically consistent with the theoretical analysis.In addition,both the growth rate and the frequency have a linear dependence on the cut off velocity.Then,we used the M3D-K code to simulate the down-sweeping RSAE on HL-2A.The equilibrium profiles and some key simulation parameters are all derived from the experimental data in the HL-2A.The purpose of this part is to identify the three main theories about the down-sweeping RSAE through numerical simulation.We scanned qmin by shifting the q profile up and down as a whole while keeping the shape unchanged.With the decrease of qmin,the frequency of RSAE decreases first,and reaches the minimum value when qmin=m/n,and then starts to sweep up just like the common RSAE.The structure of the down-sweeping RSAE is highly localized near qmm so the simulation results do not support the theory that the down-sweeping RSAE is the Infernal Alfven Eigenmode(IAE).The frequency and structure of the mode obtained by our simulation are consistent with the observations of the HL-2A experiment.For the same |qmin-m/n|,the growth rate of down-sweeping RSAE is smaller than that of up-sweeping RSAE,and the threshold of energetic ion beta to excite down-sweeping RSAE is larger.This may be the reason why down-sweeping RSAE is rarely found in tokamaks and stellarators all around the world,and this is also consistent with the prediction of the theory that the down-sweeping RSAE is a quasimode.Since M3D-K does not contain the Finite Larmor Radius(FLR)effect of the background plasma,this indicates that the FLR effect of thermal ions is not necessary for the existence of the down-sweeping RSAE.Then we also studied in detail the impact of the energetic ions on RSAE by scanning three parameters(βfrac,ρh/α and v0/vA0),and explored the mechanism of the energetic ions destabilizing the RSAE.Finally,we studied the nonlinear resonance between energetic ions and RSAE.We choose a mode with relatively small linear growth rate(n=3,qmin=1.06)and the other mode with relatively large linear growth rate(n=3,q,min=1)as the research objects.We identified integer resonance and fractional resonance between RSAE and fast ions through a detailed analysis of the energy perturbation distribution(δE)of energetic ions.For the mode with n=3,qmin=1.06,integer resonance is dominant no matter in the linear phase or in the nonlinear phase,and no obvious wave-particle fractional resonance is found in the nonlinear phase.For the mode with n=3,qmin,=1,the frequency chirps up and down during the nonlinear phase,and the upper branch in the later nonlinear stage is dominant.The clump and hole of δE correspond to the upper and lower branches of the frequency,respectively.As the frequency gradually divides into two branches,the clump and hole of δE correspondingly move in opposite directions and eventually separate from each other.We selected the ions with large energy increase and count the distribution of their p-values(p=(3ωΦ-ωhigh)/ωθ),where ωhigh is the upper branch of the frequency.It is found that the p value of the ions with E/E0>0.5 is highly localized around 2.5.At the same time,the characteristic frequency of the ions with a large energy reduction mainly satisfies 3ωΦ-2.5ωθ=ωlow,that is,a fractional resonance is also found,where ωlow is the lower branch of the frequency.We argue that the nonlinear wave-particle resonance causes the bounce harmonic p to be a half-integer and the nonlinear harmonics p’=l=1.These results provide new evidences for the recently proposed wave-particle nonlinear resonance theory. |
