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等离子体自发旋转对托卡马克装置的约束性能和稳定性十分重要. 能否有效地诱导等离子体自发旋转来致稳电阻壁模对国际热核聚变实验堆(International Thermonuclear Experimental Reactor, ITER)的稳定运行尤为关键. 在韩国先进超导托卡马克(Korea Superconducting Tokamak Advanced Research, KSTAR)装置上首次实验证明了在特定参数下, 共振磁扰动(resonant magnetic perturbation, RMP)产生的新经典环向黏滞(neoclassical torodial viscosity, NTV)力矩能够驱动等离子体旋转. 先前在东方超环托卡马克(Experimental Advanced Superconducting Tokamak, EAST)的RMP实验中同样也观测到了RMP加入后等离子体旋转在同电流方向增加的实验现象, 然而与KSTAR不同, EAST上模拟计算的NTV力矩比中性束力矩小两个量级, 无法解释环向旋转速度的增加. 本文开展了进一步的研究, 首先通过实验方法测得了RMP产生的力矩分布, 与之前模拟得到的NTV力矩相比要大两个量级, 说明存在NTV以外的机制驱动等离子体旋转. 其次, 在实验中观察到旋转速度增大的同时也伴随有${\boldsymbol{E}}\times{\boldsymbol{B}}$速度的明显变化, 并且, 与实验测量得到的RMP产生的力矩分布一致, 表明${\boldsymbol{E}}\times{\boldsymbol{B}}$剪切的变化产生的残余应力可能是导致RMP加入后旋转速度增大的原因. 为了解释RMP加入后环向旋转速度的增大, 本文分析了RMP加入后随机磁场对大尺度湍流的影响, 发现各尺度湍流在随机磁场的背景下, 为了维持准中性条件, 小尺度湍流的增长可能会导致雷诺应力的增大. 在RMP加入期间, 雷诺应力驱动$ \boldsymbol{E}\times\boldsymbol{B} $剪切的增大会破坏湍流对称性, 产生残余应力驱动环向旋转. 最后，实验的统计结果也表明, RMP对环向旋转的驱动效果与湍流强度有关, 进一步验证了RMP加入${\boldsymbol{E}}\times{\boldsymbol{B}}$剪切产生的残余应力是驱动环向旋转变化的主要机制.Plasma spontaneous rotation significantly affects confinement performance and stability in tokamaks. Effectively inducing this rotation is essential for stabilizing resistive wall modes (RWMs) and ensuring the stable operation of the International Thermonuclear Experimental Reactor (ITER). Recent experiments conducted on the Korea Superconducting Tokamak Advanced Research (KSTAR) device demonstrated that resonant magnetic perturbations (RMPs) can induce neoclassical toroidal viscosity (NTV) torque under certain conditions, successfully driving plasma rotation. Similarly, on the Experimental Advanced Superconducting Tokamak (EAST), an increase in plasma rotation in the direction of the plasma current has been observed following RMP application. However, unlike the KSTAR findings, the NTV torque simulations for EAST are two orders of magnitude lower than experimental measurements, indicating additional mechanisms beyond NTV may drive the observed plasma rotations. In this paper, to investigate these mechanisms, momentum balance, causality, and statistical analyses are performed at EAST. An increase in rotation velocity is found to correlate with significant changes in the ${\boldsymbol{E}}\times{\boldsymbol{B}}$ flow, matching the RMP-induced torque distribution. This alignment suggests that residual stress, arising from variations in ${\boldsymbol{E}}\times{\boldsymbol{B}}$ shear, may cause the observed rotation to increase. The effects of stochastic fields on multi-scale turbulence are considered as a possible explanation for correlations between ${\boldsymbol{E}}\times{\boldsymbol{B}}$ velocity and toroidal rotation. Stochastic fields appear to enhance the inertia of large-scale turbulence while driving small-scale turbulence to maintain quasi-neutrality. The resulting turbulent Reynolds stress, generated by small-scale turbulence, may account for the increases of the observed ${\boldsymbol{E}}\times{\boldsymbol{B}}$ velocity during RMP application. Statistical analysis further highlights the importance of island width in understanding the threshold RMP current in ramping-up RMP experiments, supporting the conclusion that turbulence-driven ${\boldsymbol{E}}\times{\boldsymbol{B}}$ shear-related residual stress is the key mechanism of driving plasma rotation following RMP application.
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Keywords:
- tokamak /
- momentum transport /
- intrinsic rotation /
- resonant magnetic perturbation
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图 1 EAST上, (a) CXRS和NBI的布局俯视图; (b) CXRS测量位置和RMP线圈的极向分布
Fig. 1. (a) Top view of the CXRS and NBI layout on the EAST tokamak; (b) poloidal distribution of RMP coils on the EAST tokamak.
图 2 (a), (b)上、下RMP线圈电流环向分布的时间演化; (c)线平均密度${\bar n}_{\rm e} $的时间演化; (d)芯部电子温度${ T}_{\rm e 0} $的时间演化; (e)芯部旋转速度$V_{\phi 0} $的时间演化; (f)芯部离子温度${ T}_{\rm i 0} $的时间演化
Fig. 2. Time evolutions of toroidal distribution for (a) upper and (b) lower RMP coil currents; time evolutions of (c) line-averaged density, (d) central electron temperature, (e) central rotation velocity and (f) central ion temperature.
图 3 不同RMP相位加入前后的电子密度剖面(上)、电子温度和离子温度剖面(中)、环向旋转速度剖面(下). 蓝色对应RMP加入前的时刻, 红色对应RMP加入后的时刻
Fig. 3. Electron density (top), electron and ion temperature (middle), and toroidal rotation velocity profiles (bottom) before and after the application of RMP with different phases. The blue curves represent the conditions before RMP application, while the red curves correspond to the conditions after RMP application.
图 4 (a) $ {\text{δ}} B_{{\mathrm{r}}} $环向分布的时间演化; (b) $ {\text{δ}} B_{{\mathrm{r}}} $$ n=1 $分量的时间演化
Fig. 4. Time evolutions of (a) toroidal distribution of $ {\text{δ}} B_{{\mathrm{r}}} $ and (b) $ n = 1 $ component of $ {\text{δ}} B_{{\mathrm{r}}} $.
图 5 (a)不同频率微波密度涨落反射计的截止密度; (b) 79.2 GHz密度剖面反射计测量的复信号功率谱; (c)—(e) 79.2 GHz, 85.2 GHz以及91.8 GHz三道使用重心法从复信号双边功率谱中计算得到的多普勒频移的时间演化
Fig. 5. (a) Cutoff densities of microwave density fluctuation reflectometry at different frequencies; (b) power spectrum of the complex signal measured by the 79.2 GHz density fluctuation reflectometry; (c)–(e) Doppler shifts deriving from center of gravity of the double-sided power spectrum of 79.2, 85.2, and 91.8 GHz channels.
图 6 (a)在普朗特常数为1的假设下, 根据离子功率平衡得到的离子热扩散系数(黑)以及动量对流速度(红)分布; (b)估算得到的RMP产生的力矩分布
Fig. 6. (a) Ion heat diffusivity (black) and momentum convection velocity (red), obtained from ion power balance using TRANSP/NUBEAM under the assumption of a Prandtl number of 1; (b) estimated torque distribution generated by the RMP.
图 7 (a) RMP线圈电流(黑)以及线平均密度(蓝)、(b) 4.6 GHz低杂波(黑)和内感(蓝)、(c)电子温度、(d)电子温度梯度以及(e) R ≈ 2.2 m处环向旋转速度(红)和$ {\boldsymbol{E}}\times{\boldsymbol{B}} $速度(蓝)的时间演化
Fig. 7. Time evolutions of (a) the RMP coil current (black) and line-averaged density (blue), (b) 4.6 GHz lower hybrid wave power (black) and internal inductance (blue), (c) electron temperature and (d) their gradients at various locations, (e) toroidal rotation (red) and $ {\boldsymbol{E}}\times{\boldsymbol{B}} $ (blue) velocities at R ≈ 2.2 m.
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