BALLOONING INSTABILITIES OF TOKAMAKS WITH SHEARED TOROIDAL FLOWS
The ballooning-mode eikonal representation is applied to the linearised incompressible magnetohydrodynamic (MHD) equations in axisymmetric systems with toroidal mass flows to obtain a set of initial value partial differential equations in which the time t and the extended poloidal angle chi are the independent variables. To derive these equations, the eikonal function S is assumed to satisfy the usual condition "bf B" cdot nabla S = 0 to guarantee that the modes vary slowly along the magnetic fields. In addition, to resolve the "bf V" cdot nabla operator acting on perturbed quantities, the eikonal must also satisfy the conditions "rm d"S/"rm d"t = 0. This induces a Doppler shift in S. In a flux coordinate system (s,chi, phi) with straight magnetic field lines, we have that S=phi - q(S)chi -Omega(s)t + k(s), where q, Omega and k are functions only of the radial coordinate s and represent the safety factor, the plasma rotation frequency and the radial wave number, respectively. This description of the instability, however, is incompatible with normal mode solutions of the MHD equations because the wave vector "bf k" equiv nabla S becomes time dependent when the velocity shear is finite. Nevertheless, we are able to investigate the effects of sheared toroidal flows on localised ballooning instabilities because the initial value formulation of the problem we have developed does not constrain the solutions to evolve as exp(iomega t). Fixed boundary MHD equilibria with isothermal toroidal flows that model the JET device are generated numerically with a variational inverse moments code. As the initial value equations are evolved in time, periodic bursts of ballooning activity are observed. Each subsequent burst is correlated with the formation of a mode structure at the outside edge of the torus with noticeable ballooning characteristics, but displaced by 2pi in the extended popoidal angle domain. An instability growth rate that is remarkably linear is extracted from the peak values of these ballooning bursts. The frequency of the bursts is a function of the velocity shear and is independent of the magnitude of the rotation.
Bibliographic Reference: 15TH EUROPEAN CONFERENCE ON CONTROLLED FUSION AND PLASMA HEATING, DUBROVNIK (YUGOSLAVIA), MAY, 16-20, 1988, AVAILABILITY: CEC-LUXEMBOURG, DG-XIII-C-3, POB 1907, MENTIONING PAPER EN 34066 ORA
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Record Number: 1989126118300 / Last updated on: 1989-06-01
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