Nonlinear stability analysis of external hydromagnetic modes in a tokamak
Nonlinear stability analysis of external hydromagnetic modes in a tokamak
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托卡马克外部水磁模式的非线性稳定性分析
DOI：
10.1088/0741-3335/39/6/003
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发表时间：
1997
影响因子：
2.2
通讯作者：
C. Wahlberg
中科院分区：
文献类型：
--
作者：
H. G. Eriksson;C. Wahlberg
本文研究了托卡马克中具有螺旋对称性的理想磁流体动力学（MHD）外模的非线性稳定性。基于对圆柱几何中分叉平衡的分析，研究了非共振的、具有极向模数的近边缘模。该分析在很大程度上是分析性的，并且基于螺旋模式振幅的扩展。然而，最后的结果，得到数值。系统地研究了非线性效应对极向模数、电流分布和壁距的依赖关系，包括离轴峰值电流分布。结果表明，螺旋模式与现实的壁距离，在原则上，非线性稳定，即分叉是超临界的，所有研究的电流剖面。稳定效果随m的增加而增加，并强烈依赖于模式数。对于高m，即使在非常小的模式振幅下，非线性效应也是显著的，因此，具有高m的螺旋状态的振幅非常小。此外，稳定效果强烈地依赖于电流分布，并在分布达到峰值时增加。然而，如果太多的电流在等离子体边缘附近的区域中流动，则分叉仍然是超临界的，但是分叉平衡的幅度非常大，从而指示在实践中不会获得非线性稳定性的情况。这一发现可能与高性能托卡马克与一个大的自举电流的一部分操作的兴趣。对于m = 2模式，等离子体边缘附近的电流密度降低的要求是最严格的。
This paper deals with the nonlinear stability properties of external, ideal magnetohydrodynamic (MHD) modes with helical symmetry in a tokamak. Based on an analysis of bifurcated equilibria in cylindrical geometry, the investigation is concerned with non-resonant, nearly marginal modes with poloidal mode numbers . The analysis is to a large extent analytical and based on an expansion in the helical mode amplitude. The final results, however, are obtained numerically. A systematic investigation of the dependence of the nonlinear effect on poloidal mode number, current profile and wall distance is performed, including current profiles which are peaked off-axis. The results show that helical modes with with realistic wall distances are, in principle, nonlinearly stable, i.e. the bifurcation is supercritical, for all studied current profiles. The stabilizing effect increases with m and depends strongly on the mode number. For high m, the nonlinear effect is significant even at very small mode amplitude and, consequently, the amplitudes of helical states with high m are very small. Also, the stabilizing effect depends strongly on the current profile and increases when the profile is peaked. However, if too much current is flowing in a region near the plasma edge, the bifurcation is still supercritical but the amplitudes of the bifurcated equilibria are very large, thus indicating a situation where nonlinear stability would not be obtained in practice. This finding may be of interest in connection with high-performance tokamaks operating with a large fraction of bootstrap current. The requirement of reduced current density near the plasma edge is most stringent for the m = 2 mode.