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The high-confinement mode (H-mode) significantly enhances the energy and particle confinement in fusion plasma compared with the low-confinement mode (L-mode), and it is the basic operation scenario for ITER and CFETR. Edge localized mode (ELM) often appears in H-mode, helping to expel impurities to maintain a longer stable state. However, the particle burst and energy burst from ELM eruptions can severely damage the first wall of fusion device, so, it is necessary to control the ELM. Experiments on EAST tokamak and HL-2A tokamak have been conducted with ELM mitigation by lower hybrid wave (LHW), confirming the effect of LHW on ELMs, but the physical mechanism of ELM mitigation by LHW is still not fully understood. In this paper, the influences of LHW injection on the linear and nonlinear characteristics of peeling-ballooning mode (P-B mode) are investigated in the edge pedestal region of H-mode plasma in tokamakby using the BOUT++ code. The simulations take into consideration both the conventional main plasma current driven by LHW and the three-dimensional perturbed magnetic field generated by the scrape-off layer helical current filament (HCF) on the P-B mode. The linear results show that the core plasma current driven by LHW moves the linear toroidal mode spectrum towards higher mode numbers and lower growth rates by reducing the normalized pressure gradient and magnetic shear of the equilibrium. Nonlinear simulations indicate that due to the broadening of the linear mode spectrum, the core current driven by LHW can reduce the pedestal energy loss caused by ELM through globally suppressing different toroidal modes of the P-B mode, and the three-dimensional perturbed magnetic field generated by LHW-driven HCF can reduce the energy loss caused by ELMs through promoting the growth of modes other than the main mode and enhancing the coupling between different modes. It is found in the study that the P-B mode promoted by the three-dimensional perturbed magnetic field generated by HCF has a mode number threshold, and when the dominant mode of the P-B mode is far from the mode number threshold driven by the three-dimensional perturbed magnetic field, the energy loss due to ELMs is more significantly reduced. These results contribute to a more in-depth understanding of the physical mechanism in ELM control experiment by LHW.
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Keywords:
- magnetic confinement fusion plasma /
- edge localized modes /
- lower hybrid wave /
- peeling-ballooning modes
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图 1 模拟中采用的平衡截面.
Figure 1. Cross-section of equilibrium used in the simulation.
图 2 初始平衡的压强和电流剖面.
Figure 2. Pressure and current profiles of the original equilibrium.
图 3 不同LHW驱动电流下的(a)平行电流剖面和(b)安全因子剖面
Figure 3. Parallel current profiles (a) and safety factor profiles (b) with different LHW-driven currents.
图 4 LHW驱动的HCF的三维结构示意图
Figure 4. Schematic diagram of the three-dimensional structure of LHW-driven HCF.
图 5 (a) P-B模归一化线性增长率, 其中$ {\omega }_{{\mathrm{A}}}=1/{\tau }_{{\mathrm{A}}} $为阿尔芬频率; (b)平衡的归一化压强梯度, 其中$ \alpha = $ $\left(2{\mu }_{0}{R}_{0}{q}^{2}{\mathrm{d}}p\right)/\left({B}^{2}{\mathrm{d}}r\right) $
Figure 5. (a) Linear growth rates of the P-B mode; (b) normalized pressure gradient of the equilibrium with different $ {J}_{{\mathrm{L}}{\mathrm{H}}{\mathrm{W}}} $. Here, $ \alpha =\left(2{\mu }_{0}{R}_{0}{q}^{2}{\mathrm{d}}p\right)/\left({B}^{2}{\mathrm{d}}r\right) $.
图 6 LHW驱动的不同大小$ {J}_{{\mathrm{L}}{\mathrm{H}}{\mathrm{W}}} $对ELMsize时间演化的影响, 插图为0—75$ {\tau }_{{\mathrm{A}}} $时刻的放大
Figure 6. Influence of different $ {J}_{{\mathrm{L}}{\mathrm{H}}{\mathrm{W}}} $ driven by LHW on the time evolution of ELMsize, The inset in the lower right corner is an enlargement of the from 0 to 75$ {\tau }_{{\mathrm{A}}} $.
图 7 P-B模非线性模式演化(图中红色虚线为ELMsize) (a)初始平衡; (b) JLHW = 0.2 MA ; (c) JLHW = 0.3 MA $ {J}_{{\mathrm{L}}{\mathrm{H}}{\mathrm{W}}} $; (d) JLHW = 0.4 MA $ {J}_{{\mathrm{L}}{\mathrm{H}}{\mathrm{W}}} $
Figure 7. Temporal evolutions of the P-B mode spectrum: (a) Original equilibrium; (b) JLHW = 0.2 MA ; (c) JLHW = 0.3 MA $ {J}_{{\mathrm{L}}{\mathrm{H}}{\mathrm{W}}} $; (d) JLHW = 0.4 MA. The red dashed line represents ELMsize.
图 8 不同大小HCF产生的$ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $对ELMsize随时间演化的影响
Figure 8. Influence of $ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $ generated by different amplitudes of HCF on the time evolution of ELMsize.
图 9 P-B模非线性模式演化, 分别对应未加入$ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $ (a), 以及300 A HCF (b), 450 A HCF (c), 600 A HCF (d) 产生的$ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $下的模拟, 图中红色虚线为ELMsize
Figure 9. Temporal evolutions of the P-B mode spectrum, for cases without $ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $ (a) and with $ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $ generated by 300 A (b), 450 A (c), 600 A (d) HCF. The red dashed line represents ELMsize.
图 10 环向平均的$ E\times B $剪切流随时间的演化, 分别为未加入$ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $(a) 以及加入300 A (b), 450 A (c), 600 A (d) HCF. 图中白色虚线为$ \psi =1 $的位置, 红色虚线为平衡压强梯度最大位置$ \psi =0.871 $
Figure 10. Temporal evolutions of the toroidal averaged $ E\times B $ shear flow, for cases without $ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $ (a) and with $ {A}_{\left|\right|{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $ generated by 300 A (b), 450 A (c), 600 A HCF (d). The white and red dashed lines represent locations of $ \psi =1 $ and the maximum pressure gradient location $ \psi =0.871 $, respectively.
图 11 不同$ {J}_{{\mathrm{L}}{\mathrm{H}}{\mathrm{W}}} $电流条件下600 A HCF对ELMsize时间演化的影响
Figure 11. Influence of 600 A HCF on the time evolution of ELMsize under different $ {J}_{{\mathrm{L}}{\mathrm{H}}{\mathrm{W}}} $ current conditions.
图 12 考虑HCF后的P-B模谱结构随时间的演化, 其中, 从上到下依次为初始平衡 (a), (b); JLHW = 0.2 MA (c), (d); JLHW = 0.3 MA (e), (f); JLHW = 0.4 MA (g), (h)下的平衡. 左侧的一列(a), (c), (e), (g)为未加入$ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $的模拟; 右侧(b), (d), (f), (h)为加入600 A HCF产生的$ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $的模拟
Figure 12. Temporal evolutions of the P-B mode spectrum structure considering HCF. From top to bottom, the sequences are the orginal equilibrium (a), (b); equilibrium with JLHW = 0.2 MA (c), (d); JLHW = 0.3 MA (e), (f); JLHW = 0.4 MA (g), (h), respectively. The left column (a), (c), (e), (g) represent cases without $ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $; the right column (b), (d), (f), (h) represent cases with $ {A}_{//{\mathrm{H}}{\mathrm{C}}{\mathrm{F}}} $ from 600 A HCF.
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