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聚变等离子体中快离子分布函数的速度空间层析反演(tomography)是研究磁约束核聚变装置中快离子分布和输运的重要手段. 在东方超环(experimental advanced superconducting tokamak, EAST)中性束注入(neutral beam injection, NBI)与离子回旋共振加热(ion cyclotron range of frequencies heating, ICRF)协同加热实验中, 快离子诊断测量信号以及TRANSP模拟获得的快离子分布函数中观测到协同效应产生的高于中性束注入能量的高能粒子. 为了研究快离子分布行为, 获得不同加热条件下诊断测量的快离子分布函数, 采用不同的正则化方法, 增加先验信息以及将快离子Dα光谱诊断(fast-ion Dα spectroscopy, FIDA)与中子发射谱仪(neutron emission spectrometers, NES)相结合等方式, 有效提高快离子诊断信噪比以及在速度空间权重覆盖率, 实现在单独NBI加热以及NBI和ICRF协同加热条件下基于诊断测量的层析反演, 获得真实可靠的快离子分布函数. 这为下一步提高NBI与ICRF协同加热效率, 研究协同加热机制以及相关的快离子分布和输运行为奠定基础.In magnetic confinement fusion devices, velocity-space tomography of fast-ion velocity distribution function is crucial for investigating fast-ion distribution and transport. In the neutral beam injection (NBI) and ion cyclotron resonance heating (ICRF) synergistic heating experiments in Experimental Advanced Superconducting Tokamak (EAST), high-energy particles with energy exceeding the particle energy in NBI are observed. Simulations of synergistic effect on fast-ion velocity distribution function given by TRANSP also show the existence of particles with energy higher than the particle energy in NBI. To investigate the behaviors of fast ion distribution and calculate the velocity distribution functions under different heating conditions, the first-order Tikhonov regularization tomographic inversion method with higher inversion accuracy is introduced by comparing various regularization techniques. The limitations of the dual-view fast-ion Dα (FIDA) diagnostic measurements in velocity space are addressed by incorporating prior information such as null measurement and the known peaks and effectively mitigate the occurrence of artifacts. This method is first employed in the case of NBI heating. The NBI peak is successfully reconstructed at the expected location in velocity space, which shows significant improvement in the inversion results. In order to further validate the synergistic effect of NBI-ICRF heating and study the mechanism of fast ion distribution under synergistic heating, the combination of FIDA and neutron emission spectrometer (NES) is applied to the first-order Tikhonov regularization tomographic inversion method for enhancing the coverage of velocity space, through which the issue of artifacts in the inversion results is significantly improved, and thus the precision of the obtained fast-ion velocity distribution functions is enhanced. Based on the benefit described above, the method of combining NES diagnosis and FIDA diagnosis is used to obtain fast-ion velocity distribution functions in the NBI and ICRF synergistic heating discharge. The synergistic heating effect is manifested in the fast-ion velocity distribution. The availability of this inversion method in reconstructing fast-ion velocity distribution functions during high-performance operation of NBI-ICRF synergistic heating in the EAST experiment is confirmed. In the next-step EAST research, high performance discharge will demand more efficiency NBI and ICRF synergistic heating, the present work builds the stage for investigating the underlying mechanism of synergistic heating and the intricate behaviors associated with fast ion distribution and transport.
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Keywords:
- velocity-space tomography /
- fast-ion Dα spectroscopy /
- neutral beam injection /
- ion cyclotron resonance heating.
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图 1 EAST托卡马克上四条中性束束线位置、O和B窗口FIDA视图以及NES的布局 (a)俯视图; (b) 极向截面图. 视场中的红线是本文所分析的信号的观测位置
Fig. 1. Layout of four neutral beams, the O and B-port view of FIDA, the location of the NES on EAST: (a) Top view; (b) poloidal view. The red lines-of-sight are analyzed in this paper for shot #113648.
图 2 归一化的权重函数总和 (a) NES H窗口; (b) FIDA O窗口; (c) FIDA B窗口
Fig. 2. Normalized weight function coverage: (a) NES H-port; (b) FIDA O-port; (c) FIDA B-port.
图 3 #113648放电参数时序演化图 (a) 中子产额; (b) 极向比压; (c) 中性束注入功率; (d) ICRF加热功率
Fig. 3. Time traces of shot #113648: (a) Neutron yield; (b) poloidal beta; (c) neutral beam injection power; (d) ICRF heating power.
图 4 单独NBI以及NBI-ICRF协同加热时双视图FIDA测量光谱 (a) 切向FIDA信号; (b)垂直FIDA信号; 误差棒为诊断束打开区间测量光谱的整体标准差
Fig. 4. Dual view FIDA measurement spectrum of NBI only and NBI-ICRF synergetic heating: (a) Tangential view; (b) vertical view.
图 5 单独NBI以及NBI-ICRF协同加热时NES能谱
Fig. 5. NES spectrum of NBI only and NBI-ICRF synergetic heating.
图 6 TRANSP模拟的快离子分布函数 (a)单独NBI加热; (b) NBI-ICRF协同加热; 黑色虚线为NBI能量, 黑色实线为单独NBI加热时快离子能量上限
Fig. 6. TRANSP simulation of fast ion distribution function: (a) NBI only heating; (b) NBI-ICRF synergetic heating. Black dashed line is the NBI injection energy, black solid line is the upper limit of fast ion energy for NBI only.
图 7 沿负俯仰角积分的快离子分布能谱图.
Fig. 7. Fast ion distribution energy spectrum integrated along the negative pitch angle.
图 8 单独NBI时基于FIDA诊断测量的快离子分布函数层析反演 (a)零阶Tikhonov正则化; (b) 一阶Tikhonov正则化; (c) 一阶Tikhonov正则化, 空值测量区域; (d) 一阶Tikhonov正则化, 已知峰值位置
Fig. 8. Reconstructions of the fast ion distribution function based on FIDA diagnostic measurements during NBI only heating: (a) Zero-order Tikhonov regularization; (b) first-order Tikhonov regularization; (c) first-order Tikhonov regularization, null measurement; (d) first-order Tikhonov regularization, known peak.
图 9 NBI-ICRF协同加热阶段基于TRANSP模拟合成信号的层析反演 (a) 零阶Tikhonov正则化; (b) 一阶Tikhonov正则化; (c) 一阶Tikhonov正则化, 空值测量区域
Fig. 9. Reconstructions of synthetic signal based on the TRANSP distributions: (a) Zero-order Tikhonov regularization; (b) first-order Tikhonov regularization; (c) first-order Tikhonov regularization, null measurement.
图 10 基于快离子诊断数据的分布函数层析反演 (a), (b) 不添加先验信息; (c), (d) TRANSP模拟的快离子能量上限作为先验信息; 其中(a), (c)仅使用FIDA测量; (b), (d) FIDA与NES测量结合
Fig. 10. Reconstructions based on fast ion diagnostic data: (a), (b) Without adding a priori information; (c), (d) fast ion energy upper bounds for TRANSP simulations as prior information. Only FIDA measurement is used in panel (a) and (c); FIDA in combination with NES measurements are used in panel (b) and (d).
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[1] Fasoli A, Gormenzano C, Berk H L, Breizman B, Briguglio S, Darrow D S, Gorelenkov N, Heidbrink W W, Jaun A, Konovalov S V, Nazikian R, Noterdaeme J M, Sharapov S, Shinohara K, Testa D, Tobita K, Todo Y, Vlad G, Zonca F 2007 Nucl. Fusion 47 S264
Google Scholar
[2] Heidbrink W W, Luo Y, Burrell K H, Harvey R W, Pinsker R I, Ruskov E 2007 Plasma Phys. Control. Fusion 49 1457
Google Scholar
[3] Reisner M, Fable E, Stober J, Bock A, Bañon Navarro A, Di Siena A, Fischer R, Bobkov V, McDermott R 2020 Nucl. Fusion 60 082005
Google Scholar
[4] Huynh E A L P, Van Eester D, Bilato C R, Varje J, Johnson T, Sauter O, Villard L, Ferreira J, JET contributors and the EUROfusion-IM Team 2020 AIP Conf. Proc. 2254 060003
Google Scholar
[5] Hillairet J, Gallart D, Mantsinen M, Challis C, Frigione D, Graves J, Hobirk J, Belonohy E, Czarnecka A, Eriksson J, Goniche M, Hellesen C, Jacquet P, Joffrin E, Krawczyk N, King D, Lennholm M, Lerche E, Pawelec E, Sips G, Solano E, Tsalas M, Valisa M 2017 EPJ Web Conf. 157 02006
Google Scholar
[6] Heidbrink W W 2010 Rev. Sci. Instrum. 81 10D727
Google Scholar
[7] Michael C A, Conway N, Crowley B, Jones O, Heidbrink W W, Pinches S, Braeken E, Akers R, Challis C, Turnyanskiy M, Patel A, Muir D, Gaffka R, Bailey S 2013 Plasma Phys. Control. Fusion 55 095007
Google Scholar
[8] Nielsen S K, Stejner M, Rasmussen J, Jacobsen A S, Korsholm S B, Leipold F, Maraschek M, Meo F, Michelsen P K, Moseev D, Salewski M, Schubert M, Stober J, Suttrop W, Tardini G, Wagner D 2015 Plasma Phys. Control. Fusion 57 035009
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[29] Pankin A, McCune D, Andre R, Bateman G, Kritz A 2004 Comput. Phys. Commun. 159 157
Google Scholar
[30] Salewski M, Geiger B, Nielsen S K, Bindslev H, Garcia-Munoz M, Heidbrink W W, Korsholm S B, Leipold F, Meo F, Michelsen P K, Moseev D, Stejner M, Tardini G, Team A U 2012 Nucl. Fusion 52 103008
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