Vertical instability growth rate studies with rigid and deformable plasma models and proximity controller development in the TCV tokamak

The control of plasma position and shape is of fundamental importance to achieve high performances in fusion tokamaks. In particular, the control of the vertical position is essential for elongated plasma to avoid vertical displacement events (VDE), which cause the disruption of the plasma column against the tokamak facing components. A proximity controller based on the real-time growth rate estimation has been implemented on the TCV tokamak. The controller tracks the plasma growth-rate to avoid overcoming stability limits. The growth rate estimation is based on the RZIp model (in a similar way as in [Olofsson 2022 PPCF 64 072001]), which proves to be fast enough for an online implementation. The calculations of the RZIp model has been compared to a more accurate one: the deformable free boundary FGE (and its linearised version FGElin) [Carpanese et al. 2020 EPFL PhD thesis n. 7914]. The two models are implemented in the MEQ (Matlab EQuilibrium) suite, a flexible matlab toolbox for tokamak equilibrium calculations. A validation of the FGElin growth rate calculations against the KINX code [Degtyarev et al. 1997 CPC 103 10], a linear ideal MHD growth rates and eigenvectors solver for axysimmetric plasmas with resistive wall and plasma mass included, has been carried out. The codes have been tested for different plasma shapes to inspect the sensitivity of the growth rate calculation on the model adopted and on the details of the equilibrium reconstruction.