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

The effect of nonlinear mode coupling on the stability of toroidal Alfvén eigenmodes 150 150 UKAEA Opendata

The effect of nonlinear mode coupling on the stability of toroidal Alfvén eigenmodes

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.

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11/06/1997