Long‐term development of elongated tokamak plasmas after failure of feedback stabilization

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Abstract
Tokamaks with cross sections elongated in the axial direction are subject to an instability that basically involves an axial displacement of the plasma. This instability can be stabilized by a feedback circuit. This Brief Communication deals with the long‐term development of the plasma after a failure of the feedback circuit during an otherwise normal discharge. The short‐term (linear) development of such a plasma was considered earlier by Yokomizo et al. [Nucl. Fusion 2 3, 1593 (1 9 8 3)]. During the long‐term development, the plasma makes intimate contact with the surrounding conducting shell (vacuum vessel). The timescale for this development is long compared to the Alfvèn time, so that it is appropriate to consider the plasma in a magnetohydrodynamic (MHD) equlibrium which evolves slowly. This equilibrium (assumed axisymmetric) is unusual in that currents and forces are exchanged between the shell and the plasma. The dynamics of the equilibrium is determined by Ohmic dissipation associated with the plasma currents and the toroidal and poloidal currents of the shell. For a ‘‘typical’’ large tokamak, it is found that dissipation in the shell may dominate. Modeling of such long‐term development may be important because the forces acting on the shell due to the shell currents may be large. It may be important that dissipation in the plasma can be neglected or that it is small in such modeling since the uncertainty of the results, due to uncertainties associated with the plasma, is absent or may be small.