Discrete Alfvén Eigenmodes in ITER with the Internal Transport Barrier Scenario

doi:10.19596/j.cnki.1001-246x.8672

Abstract

Abstract:

The physical features of discrete Alfvén eigenmodes (αTAEs) bounded by the α-induced potential wells are investigated in ITER (International Thermonuclear Experimental Reactor) with the ITB (internal transport barrier) scenario, where α denotes a measure of the pressure gradient. The use of the negative-ion-based neutral beam injection (NNBI) heating and current driving can obtain a large and strong ITB for higher performance, and the instability of αTAE in this scheme is discussed. The αTAEs during sustaining, shrinking and erosion of ITB are discussed upon the pure radio frequency scenario. It is found that αTAEs exist in the ITB region due to the steep pressure gradient. More αTAEs exist in scenarios with strong ITB and the frequencies of these eigenmodes are higher. Multiple αTAEs are readily destabilized in the presence of energetic particles. The frequency of the excited αTAEs increases with increasing beam energy. The high β_p scenario with ITB on DIII-D has many of the desired properties of ITER steady-state. The αTAEs in high β_p scenarios are also studied.

Key words: Alfvén eigenmodes, tokamak, plasma instabilities, energetic particle

CLC Number:

TL631.24

Sijie OUYANG, Shuanghui HU, Xuefeng OUYANG, Wanpo ZHU, Yuandan LAN, Xuange HUANG. Discrete Alfvén Eigenmodes in ITER with the Internal Transport Barrier Scenario[J]. Chinese Journal of Computational Physics, 2023, 40(6): 677-688.

Figures/Tables 14

Fig.1 (a) The parameters (s, α) and (b) pressure profile versus ρ; (c) squares (□) and crosses (+) are used to describe ωr/ωA0 and log(-γ/ωA0) versus ρ, respectively; (d) structure of potential wells

Fig.2 (a) Potential V and (b) δψ(1, 0), (c) δψ(1, 1) and (d) δψ(2, 0) versus θ for α=5.98, s=0.61 in MHD (Real and imaginary δψ is plotted by solid and dashed line, respectively.)

Fig.3 Real frequencies ωr/ωA0 (—) and growth rates γ/ωA0 (- - -) versus kθρA0 at ρ=0.65

Fig.4 Real frequencies ωr/ωA0 (—) and growth rates γ/ωA0 (- - -) versus vE/vA0 at ρ=0.65

Fig.5 Real frequencies ωr/ωA0 (—) and growth rates γ/ωA0 (- - -) versus vE/vA0 for θb∈[70°, 110°] at ρ=0.65

Fig.6 Real frequencies ωr/ωA0 (—) and growth rates γ/ωA0 (- - -) versus βE0 at ρ=0.65

Fig.7 (a) The parameters (s, α) versus ρ at t=2 000 s; (b) Squares (□) and crosses (+) are used to describe the real frequencies ωr/ωA0 and the parameter relating to imaginary frequencies log(-γ/ωA0) versus ρ at t=2 000 s, respectively

Fig.8 (a) Real frequencies ωr/ωA0 and the parameter relating to imaginary frequencies log(-γ/ωA0) versus α for s=-0.56; (b) ωr/ωA0 and log(-γ/ωA0) versus s for α=4.8 (ωr/ωA0and log(-γ/ωA0) are plotted by solid lines (—) and dashed lines (-), respectively.)

Fig.9 The parameters of (a) α and (b) s versus ρ; (c) real frequencies ωr/ωA0 and (d) the parameter relating to imaginary frequencies log(-γ/ωA0) versus ρ after the ECCD removed at t=2 000 s

Fig.10 After the addition of 12 MW of NBI heating by removing 12 MW of ICH and the LH system, (a) the parameters (s, α) versus ρ at t=2 300 s and (b) the range of αTAEs at t=2 300 s (Real frequencies ωr/ωA0 and the parameter relating to imaginary frequencies log(-γ/ωA0) are plotted by square (□) and crosses (+), respectively.)

Fig.11 (a) Real frequencies ωr/ωA0 (—) and growth rates γ/ωA0 (- - -) versus kθρA0 at ρ=0.45 at t=2 000 s

Fig.12 (a) Real frequencies ωr/ωA0 (—) and growth rate γ/ωA0 (- - -) versus vE/vA0 at ρ=0.45 at t=2 000 s; (b) potential well, (c) αTAEs (3, 0) and (d) (4, 0) verse θ in hybrid model

Fig.13 (a), (b) and (c) the parameters (s, α) versus ρ, corresponding to Case 1, Case 2 and Case 3; (d), (e) and (f) the frequency profiles of αTAE (1, 0), corresponding to Case 1, Case 2 and Case 3, respectively (Real frequencies ωr/ωA0 and the parameter relating to imaginary frequencies log(-γ/ωA0) are plotted by square (□) and crosses (+), respectively.)

Fig.14 In case 3, (a) real frequencies ωr/ωA0 (—) and growth rates γ/ωA0 (- - -) versus vE/vA0 at ρ=0.66; (b) potential well; (c) αTAE (3, 0) and (d) (3, 1) verse θ in hybrid model

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