托卡马克中电磁离子尺度湍流的带状流生成与饱和
Zonal-flow generation and saturation of electromagnetic ion-scale turbulence in tokamaks
AI总结：
研究托卡马克中离子尺度湍流的带状流生成与饱和，通过局部通量管陀螺动力学模拟，对安全因子q和电子β\(_e\)参数扫描，发现非线性转变边界，给出低\(\beta_e\)标度，为预测非线性转变阈值提供实用方法。
AI中文摘要：
在有限等离子体β条件下，对托卡马克等离子体中离子尺度湍流进行了局部通量管陀螺动力学模拟，以研究通过湍流应力产生带状流的情况。对安全因子q和电子β\(_e\)进行参数扫描发现，当有效β\(\beta_{\mathrm{eff}} \equiv q^2\beta_e\)超过某个临界值\(C_{\mathrm{nl}}\)时，会从低输运状态转变为高输运状态。动力学和理想气球模的线性稳定性极限也与\(\beta_e \propto 1/q^2\)成比例，但它们位于观测到的转变之上，表明该效应不是由于线性不稳定性，而是由于非线性动力学。在低\(\beta_{\mathrm{eff}}\)时，雷诺应力占主导并驱动带状流。在较高值时，麦克斯韦应力变得相当，抑制带状流形成并导致发散输运。确定了旋风基础案例和球形托卡马克（ST40）配置的这种非线性转变边界，表明\(\beta_{\mathrm{eff}} = C_{\mathrm{nl}}\)关系可能具有更广泛的适用性，尽管\(C_{\mathrm{nl}}\)似乎与配置有关。对于旋风基础案例，经验观察到，对于低于临界值\(\beta_{e,\mathrm{sb}}\)（标度崩溃）的\(\beta_e\)，麦克斯韦和雷诺应力导致的能量转移速率进入带状流的比率与\(\beta_e\)成比例。发现\(\beta_{e,\mathrm{sb}}\)的值随着纵横比的减小而增加，这表明对于更紧凑的磁平衡，线性标度在更宽的\(\beta_e\)范围内仍然有效。这种低\(\beta_e\)标度为一种实用方法提供了基础，该方法以最少依赖高度电磁非线性模拟来预测非线性转变阈值。
英文摘要：
Local flux-tube gyrokinetic simulations of ion-scale turbulence in tokamak plasmas at finite plasma beta are conducted to investigate the generation of zonal flows via turbulent stresses. A parameter scan in the safety factor $q$ and electron beta $β_e$ reveals a transition from low- to high-transport states when $β_{\mathrm{eff}} \equiv q^2β_e$ exceeds a certain critical value $C_{\mathrm{nl}}$. While the linear stability limits for kinetic and ideal ballooning modes also scale as $β_e \propto 1/q^2$, they lie above the observed transition, indicating that the effect is not due to linear instabilities but to nonlinear dynamics. At low $β_{\mathrm{eff}}$, Reynolds stress dominates and drives zonal flows. At higher values, Maxwell stress becomes comparable, suppressing zonal-flow formation and leading to divergent transport. This nonlinear-transition boundary is determined for both the Cyclone Base Case and a spherical tokamak (ST40) configuration, suggesting that the relation $β_{\mathrm{eff}} = C_{\mathrm{nl}}$ may have broader applicability, though $C_{\mathrm{nl}}$ appears to be configuration-dependent. For the Cyclone Base Case, the ratio of energy transfer rates into zonal flows due to Maxwell and Reynolds stresses is observed empirically to scale as $β_e$ for $β_e$ below a critical value $β_{e,\mathrm{sb}}$ (scaling breakdown). The value of $β_{e,\mathrm{sb}}$ is found to increase with decreasing aspect ratio, suggesting that the linear scaling remains valid over a wider range of $β_e$ for more compact magnetic equilibria. This low-$β_e$ scaling provides the basis for a practical method to predict the nonlinear-transition threshold with minimal reliance on highly electromagnetic nonlinear simulations.
