托卡马克边缘等离子体中测地声模带状流的实验研究
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摘要
本论文主要研究了托卡马克等离子体涨落流中一种非常重要的静电涨落结构：带状流(zonal flows)。托卡马克等离子体中的带状流是极向上环向上对称的静电涨落，并且它在径向上有传播。理论研究表明带状流在调节背景湍流幅度、改善输运以及触发低约束模到高约束模转换(L-H转换)方面都有着重要的作用。它共有两个分支：低频带状流(Low Frequency Zonal Flow，LFZF)和有限频率的测地声模(Geodesic Acoustic Mode，GAM)，本论文的重点是测地声模的实验测量，研究它的模特征、同背景湍流之间相互作用以及和输运的关系。
本论文中测量测地声模的实验是在中国环流器2号A(Huanliuqi-2A，HL-2A成都)托卡马克上完成的。在国际上首次使用了特殊构造的三台阶静电Langmuir探针阵列，在托卡马克的极向、环向和径向三个方向上同时对测地声模的三维谱特征进行了测量，第一次同时给出了测地声模的三维谱特征。使用两点法计算了测地声模的三维谱功率谱密度S(k_θ，k_φ，k_r，f_(GAM))，结果表明测地声模在极向和环向对称，m=n=0；在径向上测地声模向外传播，径向波数为k_r=+1．8cm~(-1)，宽度为Δk_r=1．5cm~(-1)，用离子回旋半径ρ_i归一化后得到k_rρ_i=0．05，Δk_rρ_i=0．04；测地声模的径向波数谱S(k_r，f_(GAM))表明测地声模径向上向外传播，主要是行波成分，驻波分量非常少，它的群速度等于相速度，都是向外传播。
本论文通过对实验数据详细地双谱分析和包络分析，首次澄清了在实验中观察到的测地声模同背景湍流两种相互作用：第一种相互作用对应于测地声模从背景湍流产生的能量守恒过程，表现为测地声模对高频背景湍流的直接幅度调制，是测地声模的产生过程；第二种相互作用反映测地声模对背景湍流的剪切效应，在这个过程中背景湍流通过测地声模把能量从低频向高频级联，是在测地声模产生之后和背景湍流的相互作用。本论文还研究了测地声模同高频湍流之间非线性耦合的共振现象。实验结果表明测地声模的相速度接近高频背景湍流的群速度，在两种速度最接近的时候共振现象最明显。本论文得出结论，测地声模由背景湍流通过非线性三波相互作用产生，并且反作用于背景湍流。
本论文首次研究了测地声模对径向粒子输运的影响。分析结果表明测地声模的极向对称性能够抑制径向输运，并且测地声模密度涨落的极向不对称性引起输运通量在极向上的不对称。
此外本论文还对测地声模进行了非线性动力学的相关分析，初步结果表明测地声模相对幅度越大非线性维数就越小。
The zonal flows in tokamak plasma, which are toroidally and poloidally symmetric with finite radial wavenumber, play a very import role in regulating the turbulence and enhancing the confinement. Zonal flows have two branches: the Low Frequency Zonal Flow (LFZF) and Geodesic Acoustic Mode (GAM). The experimental study of GAM is the subject of this thesis.
The three-dimensional wavenumber and frequency spectrum for the geodesic acoustic mode (GAM) has been measured in the HuanLiuqi-2A tokamak for the first time. The spectrum provides definite evidence for the GAM, which is characterized by k_θ=k_φ= 0 and k_rρ_i≈0.04 - 0.09 with the full width at half-maximum k_rρ_i≈0.03 - 0.07. The localized GAM packet is observed to propagate outward in the radial direction with nearly the same phase and group velocity. A single peak feature is observed in S(k_r) spectrum, which implies there only exists traveling wave component in the GAM, with little standing wave component.
The envelopes of the radial electric field and density fluctuations are observed to be modulated by the GAM. By comparing the experimental result with that of the envelope analysis using model signals, the mechanism of the envelope modulation has been identified. The results strongly suggest that the envelope modulation of the E_r fluctuations is dominantly caused by the direct regulation of the GAM during the GAM generation in the energy-conserving triad interaction, and the envelope modulation of the density fluctuations is induced by the GAM shearing effect, which transfers the fluctuation energy from low to high frequencies.
In addition, all the cross- and auto-bicoherences for interactions between the GAM and turbulent fluctuations show a similar peaked feature that may reflect the resonant property in the nonlinear coupling between the GAM and turbulent fluctuations.
The radial particle flux associated with GAM is studied in the thesis. The GAM can reduce the radial particle flux and the asymmetry in the density fluctuation of GAM possibly leads to the asymmetry of the radial particle flux.
The nonlinear dynamics analysis is also applied to GAM. The nonlinear dimension decreases with the increasing of the relative amplitude of GAM.
本论文中测量测地声模的实验是在中国环流器2号A(Huanliuqi-2A，HL-2A成都)托卡马克上完成的。在国际上首次使用了特殊构造的三台阶静电Langmuir探针阵列，在托卡马克的极向、环向和径向三个方向上同时对测地声模的三维谱特征进行了测量，第一次同时给出了测地声模的三维谱特征。使用两点法计算了测地声模的三维谱功率谱密度S(k_θ，k_φ，k_r，f_(GAM))，结果表明测地声模在极向和环向对称，m=n=0；在径向上测地声模向外传播，径向波数为k_r=+1．8cm~(-1)，宽度为Δk_r=1．5cm~(-1)，用离子回旋半径ρ_i归一化后得到k_rρ_i=0．05，Δk_rρ_i=0．04；测地声模的径向波数谱S(k_r，f_(GAM))表明测地声模径向上向外传播，主要是行波成分，驻波分量非常少，它的群速度等于相速度，都是向外传播。
本论文通过对实验数据详细地双谱分析和包络分析，首次澄清了在实验中观察到的测地声模同背景湍流两种相互作用：第一种相互作用对应于测地声模从背景湍流产生的能量守恒过程，表现为测地声模对高频背景湍流的直接幅度调制，是测地声模的产生过程；第二种相互作用反映测地声模对背景湍流的剪切效应，在这个过程中背景湍流通过测地声模把能量从低频向高频级联，是在测地声模产生之后和背景湍流的相互作用。本论文还研究了测地声模同高频湍流之间非线性耦合的共振现象。实验结果表明测地声模的相速度接近高频背景湍流的群速度，在两种速度最接近的时候共振现象最明显。本论文得出结论，测地声模由背景湍流通过非线性三波相互作用产生，并且反作用于背景湍流。
本论文首次研究了测地声模对径向粒子输运的影响。分析结果表明测地声模的极向对称性能够抑制径向输运，并且测地声模密度涨落的极向不对称性引起输运通量在极向上的不对称。
此外本论文还对测地声模进行了非线性动力学的相关分析，初步结果表明测地声模相对幅度越大非线性维数就越小。
The zonal flows in tokamak plasma, which are toroidally and poloidally symmetric with finite radial wavenumber, play a very import role in regulating the turbulence and enhancing the confinement. Zonal flows have two branches: the Low Frequency Zonal Flow (LFZF) and Geodesic Acoustic Mode (GAM). The experimental study of GAM is the subject of this thesis.
The three-dimensional wavenumber and frequency spectrum for the geodesic acoustic mode (GAM) has been measured in the HuanLiuqi-2A tokamak for the first time. The spectrum provides definite evidence for the GAM, which is characterized by k_θ=k_φ= 0 and k_rρ_i≈0.04 - 0.09 with the full width at half-maximum k_rρ_i≈0.03 - 0.07. The localized GAM packet is observed to propagate outward in the radial direction with nearly the same phase and group velocity. A single peak feature is observed in S(k_r) spectrum, which implies there only exists traveling wave component in the GAM, with little standing wave component.
The envelopes of the radial electric field and density fluctuations are observed to be modulated by the GAM. By comparing the experimental result with that of the envelope analysis using model signals, the mechanism of the envelope modulation has been identified. The results strongly suggest that the envelope modulation of the E_r fluctuations is dominantly caused by the direct regulation of the GAM during the GAM generation in the energy-conserving triad interaction, and the envelope modulation of the density fluctuations is induced by the GAM shearing effect, which transfers the fluctuation energy from low to high frequencies.
In addition, all the cross- and auto-bicoherences for interactions between the GAM and turbulent fluctuations show a similar peaked feature that may reflect the resonant property in the nonlinear coupling between the GAM and turbulent fluctuations.
The radial particle flux associated with GAM is studied in the thesis. The GAM can reduce the radial particle flux and the asymmetry in the density fluctuation of GAM possibly leads to the asymmetry of the radial particle flux.
The nonlinear dynamics analysis is also applied to GAM. The nonlinear dimension decreases with the increasing of the relative amplitude of GAM.
引文
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