Resistive-wall instability of external kink modes in a tokamak
- Institute of Nuclear Fusion, Kurchatov Institute Russian Research Centre, pl. Kurchatova, Moscow, 123182 (Russian Federation)
An analytical theory of the resistive-wall instability of external kink modes in a tokamak allowing for toroidal effects is developed. It is assumed that each mode is a set of a number of poloidal harmonics, one of which is the main harmonic while the others are side-band ones. It is allowed for that some of the side-band harmonics can possess singular points inside the plasma. In describing the interaction of each of these types of harmonics with the remaining ones, the local and nonlocal ballooning effects are taken into account. In addition, the magnetic well/hill related to each singular harmonic is allowed for. A set of approximate (model) equations are derived, which allow for the separate study of the nonlocal ballooning effects and the local effects typical for the Mercier modes (joint action of the magnetic well and local ballooning effects). A general expression for the growth rate, which consists of cylindrical and toroidal parts, is found. The cylindrical part of the growth rate for the case of a parabolic distribution of the longitudinal current is calculated. The contribution to the toroidal part of the growth rate due to both nonsingular and singular side-band harmonics is obtained. It is shown that, in both cases, the side-band harmonics play a destabilizing role and make the instability more sensitive to the value of the plasma pressure, as is observed in experiments. The case when the singular point of the main harmonic is sufficiently close to the plasma boundary is discussed. It is shown that, in this case, the instability can be sensitive to the presence of a magnetic well and to the local ballooning effects related to this harmonic.
- OSTI ID:
- 172260
- Journal Information:
- Plasma Physics Reports, Vol. 21, Issue 10; Other Information: PBD: Oct 1995
- Country of Publication:
- United States
- Language:
- English
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