The effect of nonlinear mode coupling on the stability of toroidal Alfvén eigenmodes
The effect of nonlinear mode coupling on the stability of toroidal Alfvén eigenmodes
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非线性模式耦合对环形阿尔芬本征模稳定性的影响
DOI：
10.1063/1.872466
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发表时间：
1997
影响因子：
2.2
通讯作者：
R. A. Cairns
中科院分区：
文献类型：
--
作者：
C. Lashmore;A. Thyagaraja;R. A. Cairns
本文用托卡马克的圆柱模型来描述阿尔芬波与声波之间的非线性耦合。该模型适用于一个环形阿尔芬本征模（TAE）驱动不稳定的融合α粒子的情况下，探索其相关性的非线性饱和的这种模式，它可以产生的α粒子在燃烧等离子体的损失。该机制是调制不稳定性的有限振幅波，在这种情况下，TAE模式，其中密度波动和阿尔芬边带自发激发时，有限振幅波超过阈值振幅。一般来说，在有界非均匀等离子体中的这种非线性计算需要数值解。然而，在这种情况下，一个近似的解析解是通过利用这一事实，即声波在一个特定的磁性表面上是几何奇异的。因此，进行计算的磁表面上的TAE不稳定性的中心和非线性色散关系的推导。调制不稳定性的阈值产生一个值的扰动的径向分量的磁场的平衡磁场，这是可比的饱和振幅的TAE不稳定性得到的其他工人的比率。此外，非线性色散关系还包括谐振情况，对于该谐振情况，阈值可以显著更低。目前，启发式计算表明，调制不稳定性可能确实是相关的TAE不稳定性的演变和最终饱和。本文用托卡马克的圆柱模型来描述阿尔芬波与声波之间的非线性耦合。该模型被应用到一个环形阿尔芬本征模（TAE）的情况下，不稳定的聚变α粒子驱动，探索其相关性的非线性饱和的这种模式，它可以产生一个损失的α粒子在燃烧等离子体。该机制是调制不稳定性的有限振幅波，在这种情况下，TAE模式，其中密度波动和阿尔芬边带自发激发时，有限振幅波超过阈值振幅。一般来说，在有界非均匀等离子体中的这种非线性计算需要数值解。然而，在这种情况下，一个近似的解析解是通过利用这一事实，即声波在一个特定的磁性表面上是几何奇异的。因此，计算是在TAE不稳定性集中的磁表面上进行的，并且在磁表面上存在非线性色散。
A cylindrical model of a tokamak is used to describe the nonlinear coupling between Alfven waves and sound waves. The model is applied to the case of a toroidal Alfven eigenmode (TAE) driven unstable by fusion alpha particles to explore its relevance to the nonlinear saturation of such modes, which can produce a loss of alpha particles in a burning plasma. The mechanism is the modulational instability of a finite-amplitude wave, in this case a TAE mode, in which a density fluctuation and Alfven sidebands are spontaneously excited when the finite-amplitude wave exceeds a threshold amplitude. In general, such a nonlinear calculation in a bounded inhomogeneous plasma would require a numerical solution. However, in the present case, an approximate analytic solution is derived by making use of the fact that the sound wave is logarithmically singular on a particular magnetic surface. The calculation is therefore carried out on the magnetic surface on which the TAE instability is centered and a nonlinear dispersion relation is derived. The threshold for the modulational instability yields a value for the ratio of the perturbed radial component of the magnetic field to the equilibrium magnetic field, which is comparable to the saturated amplitude of a TAE instability obtained by other workers. In addition, the nonlinear dispersion relation also includes a resonant case for which the threshold can be significantly lower. The present, heuristic calculation suggests that the modulational instability may indeed be relevant to the evolution and eventual saturation of a TAE instability. A cylindrical model of a tokamak is used to describe the nonlinear coupling between Alfven waves and sound waves. The model is applied to the case of a toroidal Alfven eigenmode (TAE) driven unstable by fusion alpha particles to explore its relevance to the nonlinear saturation of such modes, which can produce a loss of alpha particles in a burning plasma. The mechanism is the modulational instability of a finite-amplitude wave, in this case a TAE mode, in which a density fluctuation and Alfven sidebands are spontaneously excited when the finite-amplitude wave exceeds a threshold amplitude. In general, such a nonlinear calculation in a bounded inhomogeneous plasma would require a numerical solution. However, in the present case, an approximate analytic solution is derived by making use of the fact that the sound wave is logarithmically singular on a particular magnetic surface. The calculation is therefore carried out on the magnetic surface on which the TAE instability is centered and a nonlinear dispers...