Resonant MHD modes with toroidal coupling

Technical Report · Sun Jul 01 00:00:00 EDT 1990

DOI:https://doi.org/10.2172/6691315· OSTI ID:6691315

Connor, J W; Hastie, R J ^[1]; Taylor, J B ^[2]

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1. Commission of the European Communities, Abingdon (UK). JET Joint Undertaking
2. Texas Univ., Austin, TX (USA). Inst. for Fusion Studies

This is part 2 of a study of resonant perturbations, such as resistive tearing and ballooning modes, in a torus. These are described by marginal ideal mhd equations in the regions between resonant surfaces; matching across these surfaces provides the dispersion relation. In part 1 we described how all the necessary information from the ideal mhd calculations could be represented by a so-called E-matrix. We also described the calculation of this E-matrix for tearing modes (even parity in perturbed magnetic field) in a large aspect ratio torus. There the toroidal modes comprise coupled cylinder tearing modes and the E-matrix is a generalization of the familiar {Delta}{prime} quantity in a cylinder. In the present paper we discuss resistive ballooning, or twisting-modes, which have odd-parity in perturbed magnetic field. We show that, unlike the tearing modes, these odd-parity modes are instrinsically toroidal and are not directly related to the odd-parity modes in a cylinder. This is evident from the analysis of the high-n limit in ballooning-space, where a transition from a stable {Delta}{prime} to an unstable {Delta}{prime} occurs for the twisting mode when the ballooning effect exceeds the interchange effect, which can occur even at large aspect ratio (as in a tokamak). Analysis of the high-n limit in coordinate space, rather than ballooning space, clarifies this singular behaviour and indicates how one may define twisting-mode {Delta}{prime}. It also yields a prescription for treating low-n twisting modes and a method for calculating an E-matrix for resistive ballooning modes in a large aspect ratio tokamak. The elements of this matrix are given in terms of cylindrical tearing mode solutions.

• Research Organization: Texas Univ., Austin, TX (USA). Inst. for Fusion Studies; Commission of the European Communities, Abingdon (UK). JET Joint Undertaking
• Sponsoring Organization: DOE/ER
• DOE Contract Number: FG05-80ET53088
• OSTI ID: 6691315
• Report Number(s): DOE/ET/53088-439; IFSR--439; ON: DE90015185
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
BALLOONING INSTABILITY
CLOSED PLASMA DEVICES
EQUILIBRIUM
INSTABILITY
MAGNETIC FIELDS
MHD EQUILIBRIUM
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
TEARING INSTABILITY
THERMONUCLEAR DEVICES
TOKAMAK DEVICES