The effect of nonlinear mode coupling on the stability of toroidal Alfv{acute e}n eigenmodes

Journal Article · Mon Sep 01 04:00:00 EDT 1997 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.872466· OSTI ID:538470

Lashmore-Davies, C N; Thyagaraja, A ^[1]; Cairns, R A ^[2]

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1. UKAEA Fusion, Culham, Abingdon, Oxon, OX14 3DB, United Kingdom (UKAEA/Euratom Fusion Association)
2. School of Mathematical and Computational Sciences, University of St. Andrews, St. Andrews, Fife, KY16 9SS (United Kingdom)

A cylindrical model of a tokamak is used to describe the nonlinear coupling between Alfv{acute e}n waves and sound waves. The model is applied to the case of a toroidal Alfv{acute e}n 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 Alfv{acute e}n 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.

• OSTI ID: 538470
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 9 Vol. 4; ISSN 1070-664X; ISSN PHPAEN
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ALFVEN WAVES
ALPHA PARTICLES
DISPERSION RELATIONS
FUSION YIELD
INHOMOGENEOUS PLASMA
MAGNETIC SURFACES
PLASMA INSTABILITY
STABILITY
TOKAMAK DEVICES