Continuum damping of toroidal Alfven eigenmodes in finite-[beta] tokamak equilibria
A general theoretical approach for the study of the two-dimensional structure of high-n Toroidal Alfven Eigenmodes (TAE) in finite-[beta], large aspect ratio (R[sub o]/a [much gt] 1) tokamak equilibria is presented. Here, n is the toroidal mode number, [beta] = plasma/magnetic pressure, and a(R[sub o]) is the minor (major) radius of the torus. It is shown how the general pseudo-differential boundary value problem for the radial eigenmode structure can be systematically constructed from the local dispersion relation; which is obtained using the ballooning formalism. The TAE modes are characterized by a broad radial envelope, the width of which is independent on the mode number in the general case of monotonic equilibrium profiles. The results on the two-dimensional eigenmode structure are expected to be applicable to drift-type waves. The ballooning transform is generalized here to handle singular eigenfunctions typical of the continuous shear Alfven spectrum, and, thereby, facilitates the computation of the TAE resonant damping rate due to the finite coupling to the shear Alfven continuum. Due to the radial localization of the modes in the high-n limit, the (s,[alpha]) model equilibrium is adopted, without loss of qualitative generality, to study high-[beta] ([beta] = 0(a/R[sub o])) tokamak equilibria with circular magnetic surfaces (s = magnetic shear and [alpha] = R[sub o]q[sup 2][beta][prime], q being the safety factor). An analytical expression for the damping rate is then derived for arbitrary values of s and [alpha]; which recovers the previously obtained results in the s [much lt] 1, [alpha] [much lt] 1 limit. In the more general case, the analytical expression must be evaluated numerically. Finite pressure (or [alpha]) is shown to have important effects on TAE stability. A critical value [alpha][sub c](s) is found, above which TAE modes strongly couple to the continuous spectrum, leading to strong mode damping and, possibly, mode stabilization.
- Research Organization:
- Princeton Univ., NJ (United States)
- OSTI ID:
- 7041623
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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Theory of continuum damping of toroidal Alfven Eigenmodes in finite-{beta} tokamaks
Theory of continuum damping of toroidal Alfven Eigenmodes in finite-[beta] tokamaks