Nonlinear 2-D effects in the control of magnetic Islands by ECCD

The stabilization of tearing magnetic islands by means of localized current driven by electron cyclotron waves, requires optimizing the efficiency of the injected helical current. The problem is conventionally addressed using 0-D model of the (generalized) Rutherford equation to find the dependence in terms of the island width, wave beam width and deposition scale length, as well as phase tracking requirements. The use of a 2-D reconnection model shows that both the early time response of a tearing unstable system to ECCD and important nonlinear processes lead to irreversible modifications on the 2-D configuration, where 'phase' and 'width' of an island cease to be observable and controllable state variables. In particular the occurrence of a phase instability and of multiple axis and current sheets, may be a serious impediment for feedback control schemes