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A cylindrical model of a tokamak is used to describe the non-linear coupling between Alfvén waves and sound waves. The model is applied to the case of a toroidal Alfvén eigenmode (TAE) driven unstable by fusion alpha-particles. The mechanism is the modulational instability of a finite amplitude wave, in this case a TAE mode, in which a density fluctuation and Alfvén sidebands are spontaneously excited when the finite amplitude wave exceeds a threshold amplitude. An appropriate 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 centred and a non-linear dispersion relation 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. The present, heuristic calculation suggests that the modulational instability may indeed be relevant to the evolution and eventual saturation of a TAE instability.

Additional information

Authors: LASHMORE-DAVIES C N, AEA Fusion, Culham Laboratory, Abingdon, Oxon (GB);THYAGARAJA A, AEA Fusion, Culham Laboratory, Abingdon, Oxon (GB);CAIRNS R A, University of St Andrews, School of Mathematical and Computational Sciences (GB)
Bibliographic Reference: Report: UKAEA FUS 361 EN (1997) 21 pp.
Availability: Available from the Librarian, UKAEA, Culham Laboratory, Abingdon, Oxon, OX14 3DB (GB)
Record Number: 199711285 / Last updated on: 1997-10-10
Original language: en
Available languages: en