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The physical process of tokamak plasma spans a large space-time scale, and the main physical processes differ widely in different spatial regions (such as core, pedestal, scraping-off layer, divertor region), so it is necessary to adopt the integrated modeling method to analyze the physical problems on a global multi-space-time scale. In order to study in depth the transport and confinement during the steady-state or ramp-up of the tokamak discharging experiment, it is necessary to use a variety of physical programs to carry out integrated simulation research and physical analysis. Based on the OMFIT platform, in this paper the integrated simulation verification and analysis of the shot #37012 are conducted, which is a high-
$\beta $ discharge experiment on HL-2A device and verifies the reliability and applicability of those programs. In this process, the experimental parameters are checked and supplemented by selecting appropriate models. The simulation results after evolution are consistent with the experimental results. On this basis, we use the TGLF model to analyze the linear electrostatic drift wave instability in the core region. The reason for the improvement of the H-mode confinement by NBI off-axis heating is that the ETG instability in the NBI power deposition region is suppressed. The transport is dominated by ITG instability in the internal transport barrier (ITB), and the transport is reduced to the level of neoclassical transport.-
Keywords:
- magnetic confinement fusion /
- HL-2A /
- High-β /
- H mode
[1] Ida K, Fujita T 2018 Plasma Phys. Controlled Fusion 60 033001
Google Scholar
[2] Meneghini O, Smith S P, Lao L L, Izacard O, Ren Q, Park J M, Staebler G M 2015 Nucl. Fusion 55 083008
Google Scholar
[3] Artaud J F, Basiuk V, Imbeaux F, Schneider M, Garcia J, Giruzzi G, Turco F 2010 Nucl. Fusion 50 043001
Google Scholar
[4] Artaud J F, Imbeaux F, Garcia J, Giruzzi G, Aniel T, Basiuk V, Urban J 2018 Nucl. Fusion 58 105001
Google Scholar
[5] Imbeaux F, Pinches S D, Lister J B, Buravand Y, Casper T, Duval B, Strand P 2015 Nucl. Fusion 55 123006
Google Scholar
[6] Candy J, Holland C, Waltz R E, Fahey M R, Belli E A 2009 Phys. Plasma 16 060704
Google Scholar
[7] Pan C, Staebler G M, Lao L L, Garofalo A M, Gong X, Ren Q, Smith S P 2013 Phys. Plasmas 20 082503
Google Scholar
[8] Pfeiffer W W, Davidson R H, Miller R L, Waltz R E 1980 GA-A16178 http://fusion.gat.com/THEORY/onetwo
[9] Lao L L, St John H, Stambaugh R D, Kellman A G, Pfeiffer W 1985 Nucl. Fusion 25 1611
[10] Staebler G M, Kinsey J E, Waltz R E 2005 Phys. Plasmas 12 102508
Google Scholar
[11] Meneghini O, Smith S P, Lao L L, Izacard O, Ren Q, Park J M, Staebler G M 2015 Nuclear Fusion 55 083008
[12] McClenaghan J, Garofalo A M, Lao L L, Weisberg D B, Meneghini O, Smith S P, Holcomb C T 2020 Nucl. Fusion 60 046025
Google Scholar
[13] Wu M Q, Li G Q, Chen J L, Du H F, Gao X, Ren Q L 2018 Nucl. Fusion 58 046001
Google Scholar
[14] Gao X, Yang Y, Zhang T, Liu H, Li G, Ming T 2017 Nucl. Fusion 57 056021
Google Scholar
[15] Wu M Q, Pan C K, Chan V S, Li G Q, Garofalo A M, Jian X, Liu L, Ren Q L, Chen J L, Gao X, Gong X Z, Ding S Y, Qian J P 2018 Phys. Plasmas 25 042506
Google Scholar
[16] Meneghini O, G Snoep, B C Lyons, J McClenaghan, C S Imai, B Grierson, S P Smith, G M Staebler, P B Snyder, J Candy, E Belli, L Lao, J M Park, J Citrin, T L Cordemiglia, A Tema, S Mordijck 2021 Nucl. Fusion 61 026006
Google Scholar
[17] Chen J L, Jian X, Chan V S, Li Z, Deng Z, Li G 2017 Plasma Phys. Controlled Fusion 59 075005
Google Scholar
[18] Chen J L, Chan V S, Jian X, Zhang X J, Ren Q L, Li G Q, Zhou C X, CFETR Phys Team 2021 Nucl. Fusion 61 046002
Google Scholar
[19] Jian X, Chen J L, Chan V S, Zhuang G, Li G Q, Deng Z, Shi N, Xu G L, Staebler G M, Guo W F 2017 Nucl. Fusion 57 046012
Google Scholar
[20] Giruzzi G, Artaud J F, Baruzzo M, Bolzonella T 2015 Nucl. Fusion 55 073002
Google Scholar
[21] Lao L L, John H S, Stambaugh R D, Kellman A G, Pfeiffer W 1985 Nuclear Fusion 25 1611
[22] John H S, Taylor T S, Lin-Liu Y R, Turnbull A D 1994 Plasma Phys. Controlled Fusion 3 603
[23] Goldston R J, McCune D C, Towner H H, Davis S L, Hawryluk R J, Schmidt G L 1981 J. Comput. Phys. 43 61
Google Scholar
[24] Jenkins T G, Held E D 2015 J. Comput. Phys. 297 427
Google Scholar
[25] Lin-Liu Y R, Chan V S, Prater R 2003 Phys. Plasmas 10 4064
Google Scholar
[26] Waltz R E, Staebler G M, Dorland W, Hammett G W, Kotschenreuther M, Konings J A 1997 Phys. Plasmas 4 2482
Google Scholar
[27] Staebler G M, Kinsey J E, Waltz R E 2007 Phys. Plasmas 14 055909
Google Scholar
[28] Howard N T, Holland C, White A E, Greenwald M, Candy J 2016 Nucl. Fusion 56 014004
Google Scholar
[29] McClenaghan J, Garofalo A M, Meneghini O, Smith S P, Leuer J A, Staebler G M, Lao L L, Park J M, Ding S Y, Gong X, Qian J 2017 Nucl. Fusion 57 116019
Google Scholar
[30] Belli E A, Candy J 2008 Plasma Phys. Controlled Fusion 50 095010
Google Scholar
[31] Belli E A, Candy J 2009 Plasma Phys. Controlled Fusion 51 075018
Google Scholar
[32] Belli E A, Candy J 2012 Plasma Phys. Controlled Fusion 54 015015
Google Scholar
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图 1 OMFIT芯部等离子体剖面集成模拟流程图
Figure 1. The integrated simulation workflow of core plasma with OMFIT.
图 2 第37012炮放电参数 (a) 等离子体电流
${I_{\text{p}}}$ ; (b) 等离子体储能$ {W}_{\mathrm{E}} $ ; (c) 归一化比压${\beta _{\text{N}}}$ 和极向比压${\beta _{\text{p}}}$ ; (d) 线平均电子密度$\overline {{n_{\text{e}}}} $ ; (e) NBI加热功率; (f)${D_\alpha }$ Figure 2. The dischargement parameters of the shot #37012: (a) Plasma current
${I_{\text{p}}}$ ; (b) stored energy$ {W}_{\mathrm{E}} $ ; (c) normalized beta${\beta _{\text{N}}}$ and poloidal beta${\beta _{\text{p}}}$ ; (d)line-averaged electron density$ {\stackrel{-}{n}}_{\mathrm{e}} $ ; (e) NBI heating power${P_{{\text{NBI}}}}$ ; (f)${D_\alpha }$ .
图 3 第37012炮在1020 ms时的(a)离子温度和(b)旋转速度剖面
Figure 3. The ion temperature profile (a) and rotation profile (b) of the shot #37012 at the 1020 ms.
图 4 第37012炮在1020 ms时的电子密度剖面处理
Figure 4. The treatment of electron density profile of the shot #37012 at the 1020 ms.
图 5 第37012炮在1020 ms时得到的电子温度剖面
Figure 5. The profile of electron temperature of the shot #37012 at the 1020 ms.
图 6 集成模拟计算中各物理量的多次迭代收敛性 (a1), (b1), (c1) 迭代前后对比; (a2), (b2), (c2) TGYRO计算点的收敛过程
Figure 6. The astringency of each physical quantity in the integrated simulation: (a1), (b1), (c1) The comparison between before and after the iteration; (a2), (b2), (c2) the convergence process of the TGYRO calculating points.
图 7 第37012炮在1020 ms时刻的各成分电流剖面
Figure 7. The current profiles of each composition of the shot #37012 at the 1020 ms.
图 8 第37012炮在1020 ms时刻剖面的模拟结果与实验结果对照 (a) 压强剖面; (b) 电子密度剖面; (c) 离子温度剖面; (d) 安全因子
$q$ 剖面Figure 8. The experiment and simulation profiles comparation of the shot #37012 at the 1020 ms: (a) Pressure; (b) electron density; (c) ion temperature; (d) safety factor
$q$ .
图 9 NBI能量密度沉积分布
Figure 9. The distribution of NBI deposed energy density.
图 10 第37012炮放电在1020 ms时刻模拟后得到 (a) 离子能量通量; (b) 电子能量通量
Figure 10. The ion energy flux (a) and electron energy flux (b) of the shot #37012 at the 1020 ms.
图 11 0.2—0.8区域内两支最不稳定的本征模式的频谱
Figure 11. The spectrum of two most unstable eigenmode in the 0.2–0.8 region.
图 12
$ \rho =0.3, 0.5, 0.8 $ 处线性不稳定性的增长率与波数的关系(蓝色为电子抗磁漂移方向, 红色为离子抗磁漂移方向)Figure 12. The relationship between the growth-rate and wavenumber of the linear instabilities in the
$ \rho =0.3, 0.5, 0.8 $ (the blue points represent the electron diamagnetic drift direction and the red points represent the ion diamagnetic drift direction).表 1 第37012炮在1020 ms时的参数
Table 1. The parameters of the shot #37012 at the 1020 ms
物理量 值 $ {I}_{\mathrm{p}}/\mathrm{k}\mathrm{A} $ 175 $ {B}_{\mathrm{t}}/\text{T} $ 1.26 $ {q}_{95} $ 4 $ {P}_{\mathrm{N}\mathrm{B}\mathrm{I}}/\mathrm{k}\mathrm{W} $ 750+680 $ {\beta }_{\mathrm{N}} $ 1.98 ${\bar{n} }_{\mathrm{e} }/{10}^{19}~{\mathrm{m} }^{-3}$ 2.4 $ {W}_{\mathrm{E}} $/kJ 33.3 芯部离子温度/keV 2.07 
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[1] Ida K, Fujita T 2018 Plasma Phys. Controlled Fusion 60 033001
Google Scholar
[2] Meneghini O, Smith S P, Lao L L, Izacard O, Ren Q, Park J M, Staebler G M 2015 Nucl. Fusion 55 083008
Google Scholar
[3] Artaud J F, Basiuk V, Imbeaux F, Schneider M, Garcia J, Giruzzi G, Turco F 2010 Nucl. Fusion 50 043001
Google Scholar
[4] Artaud J F, Imbeaux F, Garcia J, Giruzzi G, Aniel T, Basiuk V, Urban J 2018 Nucl. Fusion 58 105001
Google Scholar
[5] Imbeaux F, Pinches S D, Lister J B, Buravand Y, Casper T, Duval B, Strand P 2015 Nucl. Fusion 55 123006
Google Scholar
[6] Candy J, Holland C, Waltz R E, Fahey M R, Belli E A 2009 Phys. Plasma 16 060704
Google Scholar
[7] Pan C, Staebler G M, Lao L L, Garofalo A M, Gong X, Ren Q, Smith S P 2013 Phys. Plasmas 20 082503
Google Scholar
[8] Pfeiffer W W, Davidson R H, Miller R L, Waltz R E 1980 GA-A16178 http://fusion.gat.com/THEORY/onetwo
[9] Lao L L, St John H, Stambaugh R D, Kellman A G, Pfeiffer W 1985 Nucl. Fusion 25 1611
[10] Staebler G M, Kinsey J E, Waltz R E 2005 Phys. Plasmas 12 102508
Google Scholar
[11] Meneghini O, Smith S P, Lao L L, Izacard O, Ren Q, Park J M, Staebler G M 2015 Nuclear Fusion 55 083008
[12] McClenaghan J, Garofalo A M, Lao L L, Weisberg D B, Meneghini O, Smith S P, Holcomb C T 2020 Nucl. Fusion 60 046025
Google Scholar
[13] Wu M Q, Li G Q, Chen J L, Du H F, Gao X, Ren Q L 2018 Nucl. Fusion 58 046001
Google Scholar
[14] Gao X, Yang Y, Zhang T, Liu H, Li G, Ming T 2017 Nucl. Fusion 57 056021
Google Scholar
[15] Wu M Q, Pan C K, Chan V S, Li G Q, Garofalo A M, Jian X, Liu L, Ren Q L, Chen J L, Gao X, Gong X Z, Ding S Y, Qian J P 2018 Phys. Plasmas 25 042506
Google Scholar
[16] Meneghini O, G Snoep, B C Lyons, J McClenaghan, C S Imai, B Grierson, S P Smith, G M Staebler, P B Snyder, J Candy, E Belli, L Lao, J M Park, J Citrin, T L Cordemiglia, A Tema, S Mordijck 2021 Nucl. Fusion 61 026006
Google Scholar
[17] Chen J L, Jian X, Chan V S, Li Z, Deng Z, Li G 2017 Plasma Phys. Controlled Fusion 59 075005
Google Scholar
[18] Chen J L, Chan V S, Jian X, Zhang X J, Ren Q L, Li G Q, Zhou C X, CFETR Phys Team 2021 Nucl. Fusion 61 046002
Google Scholar
[19] Jian X, Chen J L, Chan V S, Zhuang G, Li G Q, Deng Z, Shi N, Xu G L, Staebler G M, Guo W F 2017 Nucl. Fusion 57 046012
Google Scholar
[20] Giruzzi G, Artaud J F, Baruzzo M, Bolzonella T 2015 Nucl. Fusion 55 073002
Google Scholar
[21] Lao L L, John H S, Stambaugh R D, Kellman A G, Pfeiffer W 1985 Nuclear Fusion 25 1611
[22] John H S, Taylor T S, Lin-Liu Y R, Turnbull A D 1994 Plasma Phys. Controlled Fusion 3 603
[23] Goldston R J, McCune D C, Towner H H, Davis S L, Hawryluk R J, Schmidt G L 1981 J. Comput. Phys. 43 61
Google Scholar
[24] Jenkins T G, Held E D 2015 J. Comput. Phys. 297 427
Google Scholar
[25] Lin-Liu Y R, Chan V S, Prater R 2003 Phys. Plasmas 10 4064
Google Scholar
[26] Waltz R E, Staebler G M, Dorland W, Hammett G W, Kotschenreuther M, Konings J A 1997 Phys. Plasmas 4 2482
Google Scholar
[27] Staebler G M, Kinsey J E, Waltz R E 2007 Phys. Plasmas 14 055909
Google Scholar
[28] Howard N T, Holland C, White A E, Greenwald M, Candy J 2016 Nucl. Fusion 56 014004
Google Scholar
[29] McClenaghan J, Garofalo A M, Meneghini O, Smith S P, Leuer J A, Staebler G M, Lao L L, Park J M, Ding S Y, Gong X, Qian J 2017 Nucl. Fusion 57 116019
Google Scholar
[30] Belli E A, Candy J 2008 Plasma Phys. Controlled Fusion 50 095010
Google Scholar
[31] Belli E A, Candy J 2009 Plasma Phys. Controlled Fusion 51 075018
Google Scholar
[32] Belli E A, Candy J 2012 Plasma Phys. Controlled Fusion 54 015015
Google Scholar
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