托卡马克边缘等离子体带状流及其在L-H模转换过程中作用的实验研究
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摘要
高约束(H)模是1982年在德国ASDEX托卡马克上首次发现的一种改善约束的等离子体放电状态。H模期间,在边缘等离子体区会自发形成边缘输运垒(ETB)。在ETB区内由于湍流及其驱动的输运被抑制了,形成了陡峭的压强梯度区,使总体的等离子体约束得到了改善。因此研究L-H模的转换机制对于降低L-H模的转换阈值功率具有十分现实的意义。理论和实验研究表明流剪切WE×B在L-H模转换过程中扮演十分重要的角色。流剪切主要由平衡流和带状流贡献。其中带状流是一种极向和环向对称的静电涨落结构,分为低频带状流以及测地声模两种。实验和理论表明带状流主要是从湍流得到能量,并反过来能够抑制湍流所导致的反常输运。本论文研究工作主要围绕着带状流的激发、传播、与背景湍流的相互作用关系以及它在L-H模转换过程中可能的作用机制等物理内容展开的。主要的研究结果概述如下：
1)在HL-2A上,我们利用边界探针阵列观察到测地声模的涨落幅度在时序上呈现出一种随机的阵发特性。利用这一阵发特性,我们将等离子体放电时序分成GAM强和GAM弱两种情况,并统计了这两种情况下反常径向粒子输运通量Tr的变化特征。实验结果表明,反常粒子输运主要是由20kHz~100kHz背景湍流所驱动的。较之GAM弱或无GAM的情况,GAM强时的径向粒子通量减小了13%,并且Tr随GAM涨落幅度的增加而单调下降。我们还统计了GAM强和GAM弱时,反常粒子输运计算公式中各项的变化。实验结果表明,GAM主要是通过降低背景湍流的涨落幅度来抑制反常输运的,这其中包括密度涨落幅度｜ne～｜(贡献38%)和电势涨落幅度｜Eθ～｜(15%)的下降,以及电势涨落与密度涨落相关系数γneEθ(38%)的降低。而电势涨落与密度涨落的耦合项cosαneEθ并不随GAM涨落幅度的变化而变化。
2)我们利用静电探针阵列测量了HL-2A边界湍流和带状流在不同ECRH加热功率下的演化特征。ECRH注入功率大于一定阈值时,边界杂质含量开始显著增加。通过比较纯欧姆加热和ECRH加热两种条件下GAM的涨落功率谱变化,我们发现,除了当地的电子温度Te能够影响的GAM峰值频率外,当地的杂质离子含量同样能够改变GAM的峰值频率。通过一些合理的假设,我们发现碳杂质离子含量对GAM频率的影响与考虑杂质效应后GAM的色散关系所预言的GAM本征频率定性符合。我们同时观察了边界平衡径向电场Er、带状流以及背景湍流的演化特征,实验结果表明,当ECRH功率逐渐提高过程中,Er略有变负,低频带状流和测地声模的涨落功率明显增大,而背景湍流占总湍流的功率份额却在这一过程中逐渐减小,这些观察与“捕猎者-猎物”模型所预言的特征是相符的。通过双谱研究,我们发现ECRH注入之后,GAM出现自相互作用。一种可能的原因是ECRH注入之后,GAM的涨落功率超过一定阈值之后出现的一种非线性饱和机制。此外,随着ECRH注入功率的提高,GAM与背景湍流的相互作用强度也在逐渐提高,这可能预示着GAM在触发L-H模转换机制中起到重要的作用。
3)在HL-2A欧姆放电过程中,通过降低等离子放电的弦平均密度,我们利用静电探针在边界观察到双GAM的实验现象。类似的现象在锂化处理后的HT-7边界也有观察到,同时我们还在HT-7观察到多GAM的实验现象。利用静电探针阵列,我们测量了不同径向位置处的电子温度,GAM的涨落幅度,频率以及径向波数的分布特征。HT-7上的实验结果表明,在HT-7上观察到两个不同频率的测地声模LFGAM和HFGAM, LFGAM和HFGAM的中心频率分别为12kHz和21kHz,并且在探针测量的径向范围内(r-α=0～2cm)基本保持不变。同时实验还观察至LFGAM的径向波数接近于0的位置为LFGAM涨落幅度最大的点。利用温度我们求得GAM的本征频率fGAMth随径向的分布,LFGAM波数为O的点同时对应fGAMth等于实际测量LFGAM频率的位置。这一位置对应的是LFGAM的激发点,LFGAM激发后,同时向里和向外传播,向外传播过程中其径向波数逐渐增大。HFGAM的径向分布特征也满足上述基本物理图像。这些实验结果与考虑动理学效应的GAM的色散关系有较好的符合。此外,LFGAM的激发点位置,我们观察至LFGAM与HFGAM的非线性三波相互作用。由于这一径向位置对应LFGAM涨落幅度最强的位置,因此我们有理由相信, LFGAM与HFGAM的非线性耦合是GAM涨落幅度大到一定程度的结果。我们还在HT-7上观察到多GAM的实验现象。其中一些GAM的中心频率存在倍频的关系。利用幅度相关法,我们判断得到倍频的GAM源自于基频GAM的自相互作用。这也暗示着,当GAM的涨落幅度大到一定程度时,存在一种非线性饱和机制,使得GAM的能量能够转移到其他频率的测地声模上。
4)在HL-2A中,当中性束加热功率处于L-H模转换阈值功率附近时,L-H模之间出现一种中间态,既I-phase。I-phase放电期间,我们观察到在最后闭合磁面里面的悬浮电位巧,电子温度Te,密度ne。以及压强Pe上均观察到明显的低频振荡,振荡频率一般为几kHz,并且上述物理参数的低频振荡相位均滞后于径向电场的幅度｜Er｜大概Л/2的相角。利用静电探针阵列,我们测量了I-phase放电期间电势低频扰动的环向模数和极向模数满足n=m=0,即LCO振荡在环向和极向上是一种对称的静电涨落结构。电势涨落上LCO振荡的幅度沿径向向外逐渐衰减,并在最后闭合磁面附近将到一个很低的水平。我们在HL-2A上的观察还表明,径向电场上LCO振荡的幅度｜Er～,LCO｜要超前于背景湍流的涨落幅度,即后者更多的表现为被｜Er～,LC｜｜调制的一种“结果”,这与“捕猎者-猎物”模型所预言的理论结果是完全相反。径向电场的低频振荡豆,Er～,LCO在时序上基本上超前于所有上述提到的物理量而唯独滞后于平衡径向电场Er～的变化。这一实验结果表明,平衡径向电场与低频涨落径向电场之间存在密切的联系,前者可能是激发后者的一个主要的原因。类似的现象R.R.Weynants等人在TEXTOR上的偏压电极实验也有过报道。此外,在等离子体水平位移保持平稳的情况下,我们测量了平衡径向电场和涨落电场在L-I-L模转换过程中完整的演化关系,同时对比了L-I模转换和I-L模反转换过程中平均流的变化。实验结果表明,触发L-I模转换时刻的径向电场要比I-L转换时刻的值要负很多。这一实验现象与早期S-I.Itoh等人的理论预言符合得很好。
Zonal flows (ZFs) are ubiquitous in fluid turbulence, for example, in planetary atmospheres, and the terrestrial jet stream, and are of general interest in turbulence self organization across different scales. Over the last decade, it has been recognized that spontaneously generated ZFs may also play an important role for turbulence or transport self-regulation in magnetically confined plasmas. Considerable attention has focused on their potential role as a trigger mechanism for the transition from low-to high confinement regimes (L-to H-mode transition) in toroidal fusion plasmas, reduc-ing edge plasma turbulence (and transport) possibly in combination with equilibrium E x B flow shear. Our study concentrate at the excitation, propagation and nonlinear interaction with ambient turbulence, as well as the role of the L-H mode transition. The main results are performed as following:
1) Three sets of triple probe arrays (four-tip) are applied to study the transport properties in the edge of HL-2A tokamak. The Geodesic Acoustic Mode (GAM) ex-hibits the intermittency characteristics during the discharge. The radial particle flux has been studied under different phases corresponding to the variable GAM intensity. The experiment results reveal that the radial particle flux has been suppressed by13%during the GAM bursts contrasting to weak GAM cases in the frequency range of am-bient turbulence (20kHz-100kHz). Power of density fluctuations and coherence between density and potential fluctuations contribute most reducing of particle flux, while changing of cross phase between density and potential fluctuations and suppres-sion of power of potential fluctuations contribute few to it. It suggests that the GAM may regulate the turbulent transport mainly by changing the amplitude of ambient turbulence, rather than cross phase between density and potential fluctuations.
2) Geodesic acoustic mode (GAM) and low frequency zonal flow (LFZF) are both observed through Langmuir probe arrays during electron cyclotron resonance heating (ECRH) on the HL-2A tokamak edge. The radial distributions of the ampli-tude and peak frequency of GAM in floating potential fluctuations are investigated through rake probe arrays under different ECRH powers. For the first time it is ob- served that the GAM frequency decreased due to the carbon impurity increasing and the experimental results are qualitatively compared with theoretical dispersion rela-tionship of GAM including the effects of impurities. It is also found that during ECRH phase besides the mean flow, both GAM and LFZF are strengthened. The total fluc-tuation power and the fraction of that power associated with zonal flows power both increase with the ECRH power, consistent with a predator-prey model. The auto-and cross-bicoherence analyses show the coupling between GAM and its second harmon-ic during ECRH phase firstly. Moreover, the results also suggest that the couplings between GAM and the components with multiple GAM frequency are strengthened during ECRH phase. These couplings may be important for the GAM saturation.
3) Multiple GAMs, especially dual GAMs are studied through the Langmuir probe arrays at the edge plasmas of HT-7Tokamak with Lithium coated wall. The dual GAMs are called as low freqeuncy GAM (LFGAM) and high frequency GAM (HFGAM) respectively and it is found that the two modes both have maximum am-plitudes at the location with radial wavenumber close to zero. Within the measur-ing range, HFGAM propagates outwards while LFGAM propagates both inwards and outwards with their central frequencies nearly unchanged. These phenomena could be basically explained by the kinetic GAM theory and quantitative comparison is al-so done on the dispersion relationship of HFGAM. The nonlinear couplings between the kinetic GAMs are also analysed. It is observed that LFGAM strongly interacts with HFGAM near the location with maximum amplitude, additionally, bicoherence and amplitude correlation analyses both suggest that the second harmonic GAMs are probably generated from self interaction of fundamental GAMs.
4) An intermediate stage (I-phase) between L-mode and H-mode has been ob-served on HL-2A when heating power is close to threshold power of L-H mode tran-sition. Langmuir probe arrays have performed to measure the physical parameters inside LCFS as potential Φf, electric field Er, density ne, temperature Te and pressure Pe. The experimental results reveal that an oscillation with frequency of-2kHz can be found in all those parameters which lag with amplitude of electric field|Er|by π/2, implying that the oscillations in ne Te Pe are induced by the time changing of|Er|. The amplitude of ambient turbulence|ΦAT|estimated from envelope analysis is also found lags with|Er|by π/2. The result disagrees with the predictions of "Predator- Prey" model. Moreover, magnetic hystersis loop of mean electric field Er has been found during the L-I mode transition and I-L mode back transition, which is consistent with the prediction of the transition model by S-I. Itoh.
1)在HL-2A上,我们利用边界探针阵列观察到测地声模的涨落幅度在时序上呈现出一种随机的阵发特性。利用这一阵发特性,我们将等离子体放电时序分成GAM强和GAM弱两种情况,并统计了这两种情况下反常径向粒子输运通量Tr的变化特征。实验结果表明,反常粒子输运主要是由20kHz~100kHz背景湍流所驱动的。较之GAM弱或无GAM的情况,GAM强时的径向粒子通量减小了13%,并且Tr随GAM涨落幅度的增加而单调下降。我们还统计了GAM强和GAM弱时,反常粒子输运计算公式中各项的变化。实验结果表明,GAM主要是通过降低背景湍流的涨落幅度来抑制反常输运的,这其中包括密度涨落幅度｜ne～｜(贡献38%)和电势涨落幅度｜Eθ～｜(15%)的下降,以及电势涨落与密度涨落相关系数γneEθ(38%)的降低。而电势涨落与密度涨落的耦合项cosαneEθ并不随GAM涨落幅度的变化而变化。
2)我们利用静电探针阵列测量了HL-2A边界湍流和带状流在不同ECRH加热功率下的演化特征。ECRH注入功率大于一定阈值时,边界杂质含量开始显著增加。通过比较纯欧姆加热和ECRH加热两种条件下GAM的涨落功率谱变化,我们发现,除了当地的电子温度Te能够影响的GAM峰值频率外,当地的杂质离子含量同样能够改变GAM的峰值频率。通过一些合理的假设,我们发现碳杂质离子含量对GAM频率的影响与考虑杂质效应后GAM的色散关系所预言的GAM本征频率定性符合。我们同时观察了边界平衡径向电场Er、带状流以及背景湍流的演化特征,实验结果表明,当ECRH功率逐渐提高过程中,Er略有变负,低频带状流和测地声模的涨落功率明显增大,而背景湍流占总湍流的功率份额却在这一过程中逐渐减小,这些观察与“捕猎者-猎物”模型所预言的特征是相符的。通过双谱研究,我们发现ECRH注入之后,GAM出现自相互作用。一种可能的原因是ECRH注入之后,GAM的涨落功率超过一定阈值之后出现的一种非线性饱和机制。此外,随着ECRH注入功率的提高,GAM与背景湍流的相互作用强度也在逐渐提高,这可能预示着GAM在触发L-H模转换机制中起到重要的作用。
3)在HL-2A欧姆放电过程中,通过降低等离子放电的弦平均密度,我们利用静电探针在边界观察到双GAM的实验现象。类似的现象在锂化处理后的HT-7边界也有观察到,同时我们还在HT-7观察到多GAM的实验现象。利用静电探针阵列,我们测量了不同径向位置处的电子温度,GAM的涨落幅度,频率以及径向波数的分布特征。HT-7上的实验结果表明,在HT-7上观察到两个不同频率的测地声模LFGAM和HFGAM, LFGAM和HFGAM的中心频率分别为12kHz和21kHz,并且在探针测量的径向范围内(r-α=0～2cm)基本保持不变。同时实验还观察至LFGAM的径向波数接近于0的位置为LFGAM涨落幅度最大的点。利用温度我们求得GAM的本征频率fGAMth随径向的分布,LFGAM波数为O的点同时对应fGAMth等于实际测量LFGAM频率的位置。这一位置对应的是LFGAM的激发点,LFGAM激发后,同时向里和向外传播,向外传播过程中其径向波数逐渐增大。HFGAM的径向分布特征也满足上述基本物理图像。这些实验结果与考虑动理学效应的GAM的色散关系有较好的符合。此外,LFGAM的激发点位置,我们观察至LFGAM与HFGAM的非线性三波相互作用。由于这一径向位置对应LFGAM涨落幅度最强的位置,因此我们有理由相信, LFGAM与HFGAM的非线性耦合是GAM涨落幅度大到一定程度的结果。我们还在HT-7上观察到多GAM的实验现象。其中一些GAM的中心频率存在倍频的关系。利用幅度相关法,我们判断得到倍频的GAM源自于基频GAM的自相互作用。这也暗示着,当GAM的涨落幅度大到一定程度时,存在一种非线性饱和机制,使得GAM的能量能够转移到其他频率的测地声模上。
4)在HL-2A中,当中性束加热功率处于L-H模转换阈值功率附近时,L-H模之间出现一种中间态,既I-phase。I-phase放电期间,我们观察到在最后闭合磁面里面的悬浮电位巧,电子温度Te,密度ne。以及压强Pe上均观察到明显的低频振荡,振荡频率一般为几kHz,并且上述物理参数的低频振荡相位均滞后于径向电场的幅度｜Er｜大概Л/2的相角。利用静电探针阵列,我们测量了I-phase放电期间电势低频扰动的环向模数和极向模数满足n=m=0,即LCO振荡在环向和极向上是一种对称的静电涨落结构。电势涨落上LCO振荡的幅度沿径向向外逐渐衰减,并在最后闭合磁面附近将到一个很低的水平。我们在HL-2A上的观察还表明,径向电场上LCO振荡的幅度｜Er～,LCO｜要超前于背景湍流的涨落幅度,即后者更多的表现为被｜Er～,LC｜｜调制的一种“结果”,这与“捕猎者-猎物”模型所预言的理论结果是完全相反。径向电场的低频振荡豆,Er～,LCO在时序上基本上超前于所有上述提到的物理量而唯独滞后于平衡径向电场Er～的变化。这一实验结果表明,平衡径向电场与低频涨落径向电场之间存在密切的联系,前者可能是激发后者的一个主要的原因。类似的现象R.R.Weynants等人在TEXTOR上的偏压电极实验也有过报道。此外,在等离子体水平位移保持平稳的情况下,我们测量了平衡径向电场和涨落电场在L-I-L模转换过程中完整的演化关系,同时对比了L-I模转换和I-L模反转换过程中平均流的变化。实验结果表明,触发L-I模转换时刻的径向电场要比I-L转换时刻的值要负很多。这一实验现象与早期S-I.Itoh等人的理论预言符合得很好。
Zonal flows (ZFs) are ubiquitous in fluid turbulence, for example, in planetary atmospheres, and the terrestrial jet stream, and are of general interest in turbulence self organization across different scales. Over the last decade, it has been recognized that spontaneously generated ZFs may also play an important role for turbulence or transport self-regulation in magnetically confined plasmas. Considerable attention has focused on their potential role as a trigger mechanism for the transition from low-to high confinement regimes (L-to H-mode transition) in toroidal fusion plasmas, reduc-ing edge plasma turbulence (and transport) possibly in combination with equilibrium E x B flow shear. Our study concentrate at the excitation, propagation and nonlinear interaction with ambient turbulence, as well as the role of the L-H mode transition. The main results are performed as following:
1) Three sets of triple probe arrays (four-tip) are applied to study the transport properties in the edge of HL-2A tokamak. The Geodesic Acoustic Mode (GAM) ex-hibits the intermittency characteristics during the discharge. The radial particle flux has been studied under different phases corresponding to the variable GAM intensity. The experiment results reveal that the radial particle flux has been suppressed by13%during the GAM bursts contrasting to weak GAM cases in the frequency range of am-bient turbulence (20kHz-100kHz). Power of density fluctuations and coherence between density and potential fluctuations contribute most reducing of particle flux, while changing of cross phase between density and potential fluctuations and suppres-sion of power of potential fluctuations contribute few to it. It suggests that the GAM may regulate the turbulent transport mainly by changing the amplitude of ambient turbulence, rather than cross phase between density and potential fluctuations.
2) Geodesic acoustic mode (GAM) and low frequency zonal flow (LFZF) are both observed through Langmuir probe arrays during electron cyclotron resonance heating (ECRH) on the HL-2A tokamak edge. The radial distributions of the ampli-tude and peak frequency of GAM in floating potential fluctuations are investigated through rake probe arrays under different ECRH powers. For the first time it is ob- served that the GAM frequency decreased due to the carbon impurity increasing and the experimental results are qualitatively compared with theoretical dispersion rela-tionship of GAM including the effects of impurities. It is also found that during ECRH phase besides the mean flow, both GAM and LFZF are strengthened. The total fluc-tuation power and the fraction of that power associated with zonal flows power both increase with the ECRH power, consistent with a predator-prey model. The auto-and cross-bicoherence analyses show the coupling between GAM and its second harmon-ic during ECRH phase firstly. Moreover, the results also suggest that the couplings between GAM and the components with multiple GAM frequency are strengthened during ECRH phase. These couplings may be important for the GAM saturation.
3) Multiple GAMs, especially dual GAMs are studied through the Langmuir probe arrays at the edge plasmas of HT-7Tokamak with Lithium coated wall. The dual GAMs are called as low freqeuncy GAM (LFGAM) and high frequency GAM (HFGAM) respectively and it is found that the two modes both have maximum am-plitudes at the location with radial wavenumber close to zero. Within the measur-ing range, HFGAM propagates outwards while LFGAM propagates both inwards and outwards with their central frequencies nearly unchanged. These phenomena could be basically explained by the kinetic GAM theory and quantitative comparison is al-so done on the dispersion relationship of HFGAM. The nonlinear couplings between the kinetic GAMs are also analysed. It is observed that LFGAM strongly interacts with HFGAM near the location with maximum amplitude, additionally, bicoherence and amplitude correlation analyses both suggest that the second harmonic GAMs are probably generated from self interaction of fundamental GAMs.
4) An intermediate stage (I-phase) between L-mode and H-mode has been ob-served on HL-2A when heating power is close to threshold power of L-H mode tran-sition. Langmuir probe arrays have performed to measure the physical parameters inside LCFS as potential Φf, electric field Er, density ne, temperature Te and pressure Pe. The experimental results reveal that an oscillation with frequency of-2kHz can be found in all those parameters which lag with amplitude of electric field|Er|by π/2, implying that the oscillations in ne Te Pe are induced by the time changing of|Er|. The amplitude of ambient turbulence|ΦAT|estimated from envelope analysis is also found lags with|Er|by π/2. The result disagrees with the predictions of "Predator- Prey" model. Moreover, magnetic hystersis loop of mean electric field Er has been found during the L-I mode transition and I-L mode back transition, which is consistent with the prediction of the transition model by S-I. Itoh.
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