Physics and control of external kink instabilities with realistic 3D boundaries: a challenge for modern modeling and experimentation

The external kink ideal MHD instability has been one of the first and most severe limiting instabilities encountered in magnetic confinement of fusion plasmas [1]. In present day devices it establishes hard operational boundaries for both the tokamak and the Reversed Field Pinch (RFP) configurations. An interesting feature of it is that its growth rate critically depends on the device passive boundary characteristics and this can slow it down to time scales accessible to modern real time feedback control systems, normally using external active coils as actuators. The external kink instability evolving in presence of a resistive wall surrounding the plasma is often referred to as Resistive Wall Mode (RWM). After briefly reviewing the different factors that affects RWM stability, we will concentrate on the role of 3D passive structures and external fields. In fact, moving from the qualitative cylindrical assumptions to a fully quantitative investigation under realistic 3D boundary conditions is a very hard challenge for both modern experiments and modeling tools, especially when the closed loop analysis including feedback control is tackled. On the numerical side, the need for including detailed and realistic description of the device structure to be then coupled to multi-modal plasma stability analyses leads to the implementation of advanced simulation techniques. On the other hand, designing experiments able to give clear and robust data for detailed benchmarking of numerical codes to be then used in view of the design of future devices is a non-trivial experimental task. To discuss all these aspects we will present recent data and simulations from RFX-mod [2], a medium size (R=2 m, a=0.459 m) device able to confine RFP plasmas with currents up to 2 MA. Given the intrinsic instability of multiple RWMs in the RFP configuration, RFX-mod has been equipped with a very powerful and flexible system made up 192 active coils that can be feedback controlled to study RWM stability under different actuator configurations [3]. Modeling these experiments for a direct, quantitative comparison between numerical tools and experimental data involves dynamic representation of toroidal plasma equilibrium and stability, 3D passive boundary, 3D active external field distribution and feedback control software algorithms. This task has been recently successfully accomplished by appropriate upgrading and tuning the CarMa code [4,5]. Interestingly enough, cross-configuration considerations can give substantial insight on problems common also to present and future tokamak devices. Considerations on this subject will conclude the work. [1] M.S. Chu and M. Okabayashi, Plasma Phys. Control. Fusion 52 (2010) 123001. [2] P. Sonato et al, Fusion Eng. Des. 66-68 (2003) 161. [3] Baruzzo M., et al., Nucl. Fusion 52 (2012) 103001. [4] Albanese R. et al., IEEE Trans. Magn. 44 (2008) 1654. [5] Marchiori G. et al,. Nucl. Fusion 52 (2012) 023020.