ITER具有内部输运垒方案中的离散阿尔芬本征模

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

摘要/Abstract

摘要：

基于国际热核聚变实验堆(ITER)装置具有内部输运垒(ITB)的方案, 研究了离散阿尔芬本征模(αTAE)的物理特征, 其中α是等离子体压强梯度的标度参数。采用基于负离子的中性束注入(NNBI)加热和电流驱动能获得一个大且强的ITB以实现更高的性能, 并讨论该方案中αTAE的不稳定性。在纯射频方案中, 探究了ITB的收缩、维持和坍塌过程中的αTAE。模拟结果表明: αTAE发生于具有陡峭压强梯度的ITB区域, 形成的ITB越强会存在越多的αTAE, 且该模式的频率也越高。在高能量粒子条件下αTAE的多个分支容易变得不稳定, 被激发的αTAE其频率随着束能量的增加而增加。ITB作为高β_p方案的关键, 具有ITER稳态的许多理想特征, 因此关联性地探究了DIII-D高β_p方案中αTAE。

关键词: 阿尔芬本征模, 托卡马克, 等离子体不稳定性, 高能量粒子

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

中图分类号:

TL631.24

欧阳思杰, 胡双辉, 欧阳学峰, 朱万坡, 兰源丹, 黄旋格. ITER具有内部输运垒方案中的离散阿尔芬本征模[J]. 计算物理, 2023, 40(6): 677-688.

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.

图/表 14

图1 (a)(s, α)参数和(b)压力沿ρ方向的剖面；(c)ωr/ωA0和log(-γ/ωA0)沿ρ方向的剖面分别用正方形(□)和加号(+)来表示；(d)为势阱结构

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

图2 (a) 势阱V以及MHD中s=0.61、α=5.98时的(b)(1, 0)模，(c)(1, 1)模，(d)(2, 0)模的模结构(图中δψ的实部和虚部分别用实线和虚线表示。)

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.)

图3 ρ=0.65，ωr/ωA0(—)和γ/ωA0(- - -)随kθρA0的变化

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

图4 ρ=0.65，ωr/ωA0(—)和γ/ωA0(- - -)随vE/vA0的变化

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

图5 ρ=0.65，θb∈[70°, 110°]，ωr/ωA0(—)和γ/ωA0(- - -)随vE/vA0的变化

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

图6 ρ=0.65，ωr/ωA0(—)和γ/ωA0(- - -)随βE0的变化

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

图7 (a) t=2 000 s，(s, α)参数沿着ρ方向的剖面；(b)ωr/ωA0和log(-γ/ωA0)沿着ρ方向的剖面，分别用正方形(□)和加号(+)表示

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

图8 (a) s=-0.56，ωr/ωA0和log(-γ/ωA0)随α的变化情况；(b)α=4.8，ωr/ωA0和log(-γ/ωA0)随s的变化情况(ωr/ωA0和log(-γ/ωA0)分别用实线(—)和虚线(-)表示。)

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.)

图9 (a) α和(b)s沿ρ方向的剖面；在t=2 000 s撤掉ECCD后(c)ωr/ωA0和(d)log(-γ/ωA0)沿着ρ的剖面

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

图10 在去除12 MW的ICH和LH系统和加入12 MW的NBI加热后，(a)t=2 300 s，(s, α)参数沿ρ方向的剖面和(b)t=2 300 s，αTAE沿ρ方向的发生区域(正方形(□)和加号(+)分别代表ωr/ωA0和log(-γ/ωA0)。)

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.)

图11 t=2 000 s时，ρ=0.65处ωr/ωA0(—)和γ/ωA0(- - -)随kθρA0的变化

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

图12 t=2 000 s时，ρ=0.65处(a)ωr/ωA0(—)和γ/ωA0(- - -)随vE/vA0变化的情况；(b)势阱，混合模型下的αTAE；(c)(3, 0)模；(d)(4, 0)模

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

图13 (a)、(b)和(c)分别是方案1、方案2和方案3中(s, α)沿ρ方向的剖面；(d)、(e)和(f)分别是方案1、方案2和方案3中αTAE (1, 0)模沿ρ方向发生的区域(ωr/ωA0和log(-γ/ωA0)分别用正方形(□)和加号(+)表示。)

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.)

图14 方案3中，ρ=0.66, (a)ωr/ωA0(—)和γ/ωA0(- - -)随着vE/vA0变化的情况；(b)势阱；在混合模型下的αTAE(c)(3, 0)模和(d)(3, 1)模

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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