Numerical modeling, combining the toroidal ideal MHD code GPEC and the nonlinear two-fluid MHD code TM1, was used for comprehensive studies of the plasma response to resonant magnetic perturbations (RMPs) with toroidal mode number n = 1–5 for controlling edge-localized modes (ELMs) in ITER for the standard operation scenario (15 MA Q = 10). Several issues related to RMP ELM control are investigated, including the optimization of the RMP coils configuration, the evaluation of the magnitude of density pump-out and the q95 windows of ELM suppression. GPEC calculates the magnetic response, which consistently includes the very important edge kink/peeling response to static magnetic perturbations. GPEC two-dimensional scans of the relative coil current phasing among the three rows of internal coils, at fixed coil current amplitude, reveal the optimal phasing for the RMP coil configuration with n = 1–5, respectively. The poloidal half wavelength of resonant mode at the edge of plasma calculated by GPEC indicates that the midplane row coils have the best resonant coupling with the plasma for n = 2, while the upper and lower row coils have the best resonant coupling with the plasma for n = 3. Based on the plasma kinetic equilibrium and the GPEC calculations of the magnetic response, TM1 was used to simulate the conditions for RMP field penetration in the ITER pedestal. TM1 shows magnetic island formation at the foot of ITER pedestal with RMP coil current threshold ranging from 4 kAt to 8 kAt with n = 2 to 4. These magnetic islands at the pedestal-foot lead to density pump-out, the magnitude of which scales as and ranges from 5% to 20% at the pedestal-top when scanning the coil current from 4 to 60 kAt. The density pump-out is found to be weaker for higher n RMP. The nonlinear TM1 simulations also show field penetration at the pedestal-top, where the threshold of RMP coil current depends on the q95. The alignment of the magnetic island and the location of the pedestal-top decreases the height and width of the pedestal to suppress ELMs. Simulations by two-dimensional scans of RMP coil current and q95 reveal the accessible q95 windows of ELM suppression for both n = 3 and 4 RMPs. The predicted q95 windows of ELM suppression are very similar to the ones in currently operating tokamaks and the required RMP coil current for ELM suppression is less than 40–50 kAt, which is well within the designed capability for ITER. In addition, the simulations indicate that wide q95 windows of ELM suppression may be accessible in ITER by operating with dominant n = 4 (or n = 5) RMPs.
摘要：结合环形理想磁流体力学代码GPEC与非线性双流体代码TM1，对ITER标准运行方案（15 MA Q = 10）中环向模数n = 1–5的共振磁扰动（RMP）等离子体响应进行了综合研究。针对RMP边缘局域模（ELM）控制的若干问题进行了探讨，包括RMP线圈配置的优化、密度泵出幅度的评估以及ELM抑制的q95窗口。GPEC计算了磁响应，该响应一致地包含了重要的边缘扭曲/剥离响应。GPEC对三排内部线圈在固定线圈电流幅度下相对电流相位的二维扫描表明，对于n = 1–5，最优的RMP线圈配置分别对应特定的相位组合。由GPEC计算的边缘共振模极向半波长表明，对于n = 2，中平面线圈排与等离子体耦合最佳；而对于n = 3，上、下线圈排耦合最佳。基于等离子体动理学平衡及GPEC计算结果，TM1模拟了ITER台基中RMP场穿透的条件。TM1显示，在n = 2–5且线圈电流阈值约为4–8 kAt时，ITER台基底部形成磁岛。这些台基底部磁岛导致密度泵出，其幅度随线圈电流从4扫描至60 kAt时，在台基顶部约为5%–20%。研究发现，较高n的RMP产生的密度泵出较弱。非线性TM1模拟还表明，在台基顶部发生场穿透，其RMP线圈电流阈值依赖于q95。磁岛与台基顶部位置的对准会降低台基高度和宽度，从而抑制ELM。对RMP线圈电流和q95的二维扫描揭示了n = 3和n = 4 RMP均可实现ELM抑制的q95窗口。预测的ELM抑制q95窗口与当前运行中的托卡马克装置非常相似，且所需RMP线圈电流低于40–50 kAt，完全在ITER设计能力范围内。此外，模拟表明，通过使用主导的n = 4（或n = 5）RMP，ITER可能获得更宽的ELM抑制q95窗口。