Hybrid simulations of beta-induced Alfvén eigenmode with reversed safety factor profile

Abstract

Based on the experimental parameters in HL-2A tokamak, hybrid simulations have been carried out to investigate the linear stability and nonlinear dynamics of BAE. It is found that the (m/n=3/2) beta-incuced Alfvén eigenmode (BAE) is excited by co-passing energetic ions with qmin=1.5 in linear simulation, and the mode frequency is consistent with experimental meuasurement. The simulation results show that the energetic ions βh, the injection velocity v0 and orbit width parameter ρh of energetic ions are important parameters determining the drive of BAE. Furthermore, the effect of qmin (with fixed shape of q profile) is studied, and it is found that: when qmin ≤ 1.50, the excited modes are BAEs, which are located near q=1.50 rational surfaces; when qmin > 1.50, the excited modes are simillar to the reversed-shear Alfvén eigenmodes (RSAEs), which are mainly localized around q=qmin surfaces. Nonlinear simulation results show that the nonlinear dynamics of BAE is sensitive to the EP drive. For strongly driven case, firstly, redistribution and transport of engetic ions are trigged by (m/n=3/2) BAE, which raised the radial gradient of energetic ions distribution function near q=2 rational surface, and then an EPM (m/n=4/2) is driven in nonlinear phase. Finally, these two instabilities triggered significant redistribution of energetic ions, which results in the twice-repeated and mostly-downward frequency chirping of (m/n=3/2) BAE. For weakly driven case, there are no (m/n=4/2) EPM being driven and twice-repeated chirping in nonlinear phase, since the radial gradient near q=2 rational surface is small and almost unchanged.

Destabilization of low-frequency modes (LFMs) driven by a thermal pressure gradient in EAST plasmas with q min ⩽ 2

“…In the present case, for the basic-frequency case, Ω * pi = 0.6051 and f ti = 9.7674 kHz; then, the theoretically predicted frequency is about f = 0.7441 f ti = 7.2680 kHz, which is consistent with the frequency ( f LFM1 ∼ 8.0 kHz) in the plasma frame in the experiment. Similarly, for the higher-frequency branch (12,6), Ω * pi = 1.2102 and f ti = 9.7674 kHz; then, the theoretically predicted frequency is about f = 1.1387 f ti = 11.1220 kHz, which is consistent with the frequency ( f LFM2 ≈ 12.5 kHz) in the plasma frame in the experiment. It is also clearly shown that the mode frequency jumps from 7.3 kHz to 11.1 kHz, which is of the same order as the experimental observations.…”

“…We now investigate the LFMs' instabilities by adopting the local equilibrium parameters of the EAST discharge #60223 evaluated at R = 2.018 m, and are B 0 = 2.0612 T, τ = 3.2204, β i = 0.0014, η i = 1.1455, r = 0.0635, δW f = −0.0056 and ni ≡ L ni /R = 0.4138. Figure 11(b) shows the dependence of mode frequencies and growth rates on Ω * pi = ω * pi /ω ti for the basic-frequency branch (6, 3) with k θ ρ Li = 0.1171 and k θ ρ Le = 0.0035, and the higher-frequency branch (12,6) with k θ ρ Li = 0.2341 and k θ ρ Le = 0.0069. The other equilibrium parameters are fixed.…”

“…The so-called appellation of LFMs is proposed in [1], which was first given the name beta-induced Alfvén-acoustic eigenmode (BAAE) [2,3]. LFMs often occur in plasmas where the betainduced Alfvén eigenmodes (BAEs) [4][5][6] and reversed shear Alfvén eigenmodes (RSAEs) [7][8][9][10] are also unstable. The LFMs and BAEs are excited concurrently, and the frequencies of LFMs and RSAEs sweep upward synchronously as q min (minimum of the safety factor) decreases, and are reproduced periodically during the oscillation of the central collapse event, as observed in the experimental advanced superconducting tokamak (EAST) [11].…”

Modeling of the effects of impurity seeding on plasma detachment and impurity screening of snowflake divertor on HL-2M tokamak by SOLPS-ITER

“…It should be noted that strictly speaking the SF-magnetic configuration we used should be identified as XD according to reference [48] due to the secondary X-point being located outside the plasma domain. However, a similar configuration has been named SF in HL-2M [46,49], NSTX [50,51] as well as DIII-D [17], therefore, we still keep naming it as 'SFD', which is consistent with previous works. Nevertheless, the naming of the configuration does not influence the conclusions.…”

Simulations of nonlinear interaction between beta-induced Alfvén eigenmode and tearing mode

“…In M3D-K, the bulk plasma is described by the resistive MHD equations and the energetic ions (EPs hereafter) are described by the drift-kinetic equations, and the kinetic effects of EPs are coupled into the momentum equation through the EPs pressure tensor P h [36,37]. This hybrid model is widely applied to study the problems of the interaction between EP and MHD instabilities [3][4][5][38][39][40][41][42][43][44][45]. The main parameters are as follows.…”