Abstract
Vertical displacement normal modes in shaped tokamak plasmas are studied analytically, based on the reduced ideal-magnetohydrodynamic model. With the help of quadratic forms, and using the appropriate eigenfunction for vertical displacements with toroidal mode number
$n=0$
and dominant elliptical-angle mode number
$m=1$
, a dispersion relation is derived, including the effects of ideal or resistive walls through a single parameter,
$D_w(\gamma )$
, which is, in general, a function of the complex eigenfrequency
$\gamma = -{\rm i}\omega$
. For the resistive-wall case, the dispersion relation is cubic in
$\gamma$
. One root corresponds to the well-known, non-rotating resistive-wall vertical mode, growing on the resistive-wall time scale. The other two roots are weakly damped by wall resistivity, but oscillate with a frequency below the poloidal Alfvén frequency, which makes them immune to continuum damping, but subject to possible instability due to resonant interaction with fast ions.
Funder
Euratom Research and Training Programme
National Magnetic Confinement Fusion Program of China
National Natural Science Foundation of China
Publisher
Cambridge University Press (CUP)
Cited by
4 articles.
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