A limit-cycle model for internal transport barrier oscillations

A 0-D model for the time evolution of the electron temperature T and current density j is derived (following a systematic procedure) from the cylindrical 1-D electron heat transport and current density diffusion equations. The stationary regimes (stable fixed points) of the deduced dynamical system are analysed and it is shown that the model reproduces well the cases of total diffusion (no sources), of a pure Ohmic (OH) discharge and of a constant external heating scenario. Moreover, it is seen that, as the fraction of externally driven non-inductive current applied off-axis is increased, the system moves from an OH regime into an internal transport barrier (ITB) regime, where j is reversed and the negative magnetic shear reduces the heat diffusivity, thus increasing T at the core. When the external power deposition is made proportional to both T and j, limit-cycle oscillations, which resemble those of the O-regime at Tore Supra, are found. The 1-D transport equations are also solved numerically and an ITB oscillatory regime with features similar to the experiments is found, namely, a period of oscillation that is of the order of the resistive time scale, along with a decrease of the oscillation's amplitude with increasing frequency.