Numerical Simulations Of The Multiple Alfvén Eigenmodes Under Weak Shear And Reversed Shear Equilibrium

The magnetic perturbations caused by the Alfven eigenmodes can transport the energetic particles out of the plasma center region before they are thermalized,thus reducing the efficiency of the burn.Therefore,it is very important to study these Alfven eigenmodes on present machines and model them accurately,so as to predict the rapid alpha particle loss in ITER burning plasma and the device method to suppress harmful Alfven activity.In advanced tokamak operations,scenarios with weak central magnetic shear or re-versed shear has been proposed.It is necessary to study the Alfvenic mode activities in such scenarios.Theoretical researches have predicted the multiplicity of core-localized toroidicity-induced Alfven eigenmodes fort/s>1,where e is the inverse aspect ra-tio and s is magnetic shear.We numerically investigate the existence of multiplicity of core-localized toroidicity-induced Alfven eigenmodes(TAEs)and mode characteristics using NOVA code(non-variational magnetohydrodynamic code)in the present work.We firstly verify the existence of the multiplicity for zero beta plasma and the even mode at the forbidden zone.For the finite beta plasma,the mode parities become more distin-guishable,and the frequencies of odd modes are close to the upper tip of the continuum,while the frequencies of even modes are close to the lower tip of the continuum.Their frequencies are well separated by the forbidden zone.With the increasing of e/s,more modes with multiple radial nodes will appear,which is in agreement with the theoretical prediction.The discrepancy between theoretical prediction and our numerical simula-tion is also discussed in the main text.Because the reversed shear Alfven eigenmode(RSAE)and even the RSAE associated with the non-circular triangularity Alfven gap(NAE-RSAE)usually reside near the shear-reversal point,the condition that the inverse aspect ratio is larger than the magnetic shear is naturally satisfied.Therefore,it is sug-gested that RSAE modes in each gap should also have multiplicity.So,we numerically investigate the existence of multiplicity of core-localized NAE-RSAEs and mode char-acteristics using NOVA code in the present work.We firstly verify the existence of the multiplicity for zero beta plasma by using a D-shaped equilibrium.It is pointed out that,for a given toroidal mode number,the Alfven cascade spectrum accommodates down sweeping and up sweeping modes above and below the NAE range of frequencies.An analytical model for the existence of multiple RSAE modes is in good agreement with the simulation results.One notices that the triangularity has a greater effect on the odd-type modes than that on the even-type modes.And negative triangularity will inhibit the multiplicity of NAE-RSAE modes.In the course of the study,not only the existence of multiple RSAEs modes was confirmed,but also multiple non-circular triangularity Alfven eigenmodes were found in the process of frequency scanning,and even all kinds of Alfven eigenmodes will have multiplicity under the weak shear or reverse shear equilibrium satisfying e/s>1.Although the device parameters we selected do not depend on the specific parameters of an existing tokamak,the physical quantities used in the NOVA code are normalized,which shows that our results can be generalized universally.