Metastable states in tokamaks

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Abstract
A situation is considered such that the thermal conductivity of the electrons depends on the safety factor q and is much larger in an outer zone characterized by q>qa where qa is a critical value of q, thus simulating the existence of a cold boundary region dominated by losses related to stochastic magnetic effects and to resonant instabilities around rational q-surfaces. The solution of the coupled system of the Ohm-Maxwell and transport equations is such that the interface with q=qa can equivalently be defined as a surface conserving the poloidal flux. For initial perturbations cooling the boundary the interface moves inwards. At the same time the temperature on the interface remains approximately constant and cold. The total current decays linearly in time with a decay rate depending on the degree of peaking and scaling with electric dissipation time in the boundary zone, but independent of the confinement time. The system is also linearly unstable with respect to heating perturbations, e.g. generated by an outward heat pulse widening the warm zone. The nonlinear behaviour in this case exhibits a bifurcated character.

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