EAST通行高能粒子激发的非共振鱼骨模不稳定性模拟

doi:10.19596/j.cnki.1001-246x.8565

摘要/Abstract

摘要：

用磁流体动理学混合模拟程序M3D-K研究反剪切安全因子剖面下的非共振鱼骨模不稳定性。非共振鱼骨模指的是q_min略大于1的反剪切安全因子剖面下高能粒子激发的鱼骨模。分析能量共振关系，得到不同抛射角高能粒子激发非共振鱼骨模的物理机制。为了确定非共振鱼骨模稳定的参数阈值和鱼骨模不稳定性的变化趋势，在抛射角0.6时扫描非共振鱼骨模的参数，如注入能量E、高能粒子比压P_hot/P_total等，分析非线性过程中高能粒子的慢化分布、模结构的演化和鱼骨模扫频。抛射角在0.6、0.7和1.0时非线性的慢化分布变平趋势和实验中高能粒子变化一致，抛射角在0.6时非线性模结构由非共振鱼骨模模结构向其他高频模模结构演化，非线性过程的鱼骨模出现向上扫频符合经典鱼骨模的扫频。

关键词: 鱼骨模不稳定性, 反剪切安全因子剖面, 通行高能粒子, 共振关系

Abstract:

A hybrid simulation of non-resonant fishbone (NRF) instabilities with reversed safety factor profile is investigated with a global kinetic-magnetohydrodynamic (MHD) code (M3D-K). With EAST parameters, NRF instability can be driven by energetic particles as minimum safety factor is a little greater than unity. With analysis on energy resonance, physical mechanism of NRF excited by energetic particles at different angles is studied. Parameters such as injection energy E, P_hot/P_total, are scanned to find parameter thresholds and change of fishbone instability. In addition, we analyze slowing-down distribution of energetic particles, evolution of mode structure and fishbone mode sweep in nonlinear process. A flattening trend of nonlinear slowing-down distribution at Λ = 0.6, 0.7, 1.0 is consistent with that of energetic particles in experiments. Mode structure evolves from that of NRF mode to those of other high-frequency modes at Λ = 0.6. The upward sweep frequency of fishbone is consistent with the sweep frequency of classical fishbone at Λ = 0.6.

Key words: non-resonant fishbone instability, reversed safety factor profile, passing energetic particles, energy resonance relation

徐敬坤, 汪卫华. EAST通行高能粒子激发的非共振鱼骨模不稳定性模拟[J]. 计算物理, 2023, 40(3): 291-300.

Jingkun XU, Weihua WANG. Hybrid Simulation of Non-resonant Fishbone Instabilities Excited by Passing Energetic Particles in EAST Tokamak[J]. Chinese Journal of Computational Physics, 2023, 40(3): 291-300.

图/表 14

图1 平衡剖面P和q

Fig.1 Equilibrium profiles of total pressure and safety factor q

图2 高能粒子慢化分布函数

Fig.2 Slowing-down function of energetic particles

图3 频率ω、增长率γ在不同高能粒子比压Phot/Ptotal下随着抛射角的变化

Fig.3 Linear growth rate and mode frequency as functions of Λ at different pressure fraction Phot/Ptotal

图4 速度流函数在不同抛射角对应的310 τA的模结构(a) Λ = 1.0；(b) Λ = 0.9；(c) Λ = 0.8；(d) Λ = 0.7

Fig.4 Velocity stream function U at 310 τA (a) Λ = 1.0; (b) Λ = 0.9; (c) Λ = 0.8; (d) Λ = 0.7

图5 高能粒子激发鱼骨模共振关系(图中红色的“.”为能量变化点，背景图片上的黄色区域和蓝色区域为高能粒子的分布，红色的线为能量变化的主要区域。) (a) Λ =1.0；(b) Λ = 0.9；(c) Λ = 0.8；(d) Λ = 0.7

Fig.5 Energy resonance excited by energetic particles (The red '.' represents energy change. The yellow and blue areas are the distribution of energetic particles. The red line is the main area of energy change.) (a) Λ = 1.0; (b) Λ = 0.9; (c) Λ = 0.8; (d) Λ = 0.7

图6 高能粒子激发鱼骨模的共振关系(Λ = 0.6，红色的线代表能量变化主要分布，背景中黄色和蓝色区域为高能粒子的分布。) (a) Phot/Ptotal = 0.4；(b) Phot/Ptotal = 0.5；(c) Phot/Ptotal = 0.6；(d) Phot/Ptotal = 0.7

Fig.6 Energy resonance excited by energetic particles at Λ = 0.6 (The red line represents the main area of energy change. The yellow and blue areas are the distribution of energetic particles.) (a) Phot/Ptotal = 0.4; (b) Phot/Ptotal = 0.5;(c) Phot/Ptotal = 0.6; (d) Phot/Ptotal = 0.7

图7 抛射角Λ = 0.6，注入能量E0=18.25 keV时频率ω、增长率γ和注入能量E的关系

Fig.7 At Λ = 0.6, linear growth rate and mode frequency as functions of injection energy E (The initial injection energy E0=18.25 keV.)

图8 不同抛射角的能量演化

Fig.8 Energy evolution at different pitch angles

图9 抛射角1.0时，不同高能粒子比压的能量演化

Fig.9 At a pitch angle 1.0, energy evolution with different Phot/Ptotal

图10 抛射角Λ = 0.6时，不同时刻的慢化分布

Fig.10 Slowing-down distributions (Λ = 0.6) at different time

图11 抛射角Λ = 0.7时, 不同时刻的慢化分布

Fig.11 Slowing-down distributions (Λ = 0.7) at different time

图12 (a) 抛射角1.0时，不包含磁流体能量演化过程；(b) 抛射角1.0时，不同时刻的慢化分布

Fig.12 (a) Energy evolution at Λ = 1.0; (b)Slowing-down distribution at Λ = 1.0 at different time

图13 非线性演化的模结构(Λ = 0.6) (a) 660 τA; (b) 1 460 τA; (c) 2 010 τA; (d) 2 710 τA

Fig.13 Mode structures of nonlinear evolution (Λ = 0.6) at (a) 660 τA; (b) 1 460 τA; (c) 2 010 τA; (d) 2 710 τA

图14 抛射角Λ = 0.6时，非共振鱼骨模扫频

Fig.14 Upward sweep frequency of non-resonant fishbone at Λ = 0.6

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