First demonstration of real-time kinetic equilibrium reconstruction on TCV by coupling LIUQE and RAPTOR

Abstract

Kinetic Equilibrium Reconstruction (KER) in tokamaks is the solution of the free-boundary MHD equilibrium that best fits the external magnetic measurements and the internal plasma profiles as imposed from modeling and/or available internal measurements. In this paper, for the first time, the KER has been performed in real-time by coupling the free-boundary equilibrium code LIUQE to the 1.5D transport code RAPTOR, during a TCV discharge. The transport code is used as a dynamic state observer evolving the current diffusion equation, the electron heat and particle diffusion equations and correcting the prediction with the measurements available in real-time, making use of the Extended Kalman Filter (EKF) method. The simple coupling strategy, based on a matching of the free functions (p and T T) on the right-hand-side of the Grad Shafranov equation, is shown to be effective in providing consistency of pressure and current density profiles between the two codes. We also show that, despite this highly non-linear system, this technique does not require significant additional computational time with respect to the running times of the two independent codes and does not require a tight coupling of the two codes allowing therefore their independent development. The KER is compared to standard real-time equilibrium reconstruction, performed routinely in TCV, where only the external magnetic measurements are taken into account. The following cases are considered: flat central ne, current density broadening due to applied electron cyclotron current drive and neoclassical tearing mode causing a temperature drop. The KER reproduces the expected changes of the internal profiles, tracking their dynamic evolution in their physical timescales.

A Data-Assimilation Based Method for Equilibrium Reconstruction of Magnetic Fusion Plasma and its Application to Reversed Field Pinch

“…In the tokamak the toroidal magnetic field is much stronger than the poloidal field, and the equilibrium is described by the GS equation under the assumption of the existence of magnetic flux surfaces, which assumption is appropriate under strong toroidal field. Many works have been done on the equilibrium reconstruction problems based on the GS equation [9]- [14], [25]- [27].…”

“…This choice of parametrization of the unknown parts has the advantage that with the use of Picard iteration scheme [28] the solution to the GS equation can be expressed as a product of a vector whose components are the unknown parameters and a response matrix. The solution of the optimization problem for the equilibrium reconstruction can be obtained by solving a matrix equation, for example, by the use of the singular value decomposition (SVD) method, which reduces computational time drastically [10], [12]- [14], and equilibrium reconstruction has become used for real-time plasma control [11], [27]. More recently similar parametrization is widely used in equilibrium reconstruction for detailed studies of equilibrium and for real time control of the tokamak plasma [26].…”

Summary report of the 3rd IAEA technical meeting on fusion data processing validation and analysis (FDPVA)

“…The present approaches for KER were reviewed and introduced in detail. Specifically, KER has been demonstrated in real-time for the first time, where the application was delivered by coupling free boundary equilibrium reconstruction (LIUQE) [10] and radial transport code (RAPTOR) [11][12].…”

Integrated real-time supervisory management for off-normal-event handling and feedback control of tokamak plasmas

“…This layer thus converts specific plant signals to generic continuous-value states of the plasma and actuators which are used by the tokamakagnostic layer and vice-versa. For example, on TCV, the RT kinetic plasma equilibrium reconstruction can provide realistic pressure and current density profiles [6]; and the RT measures, combined with models, of heating sources provide the states of EC and NBI actuators [7], [8]. The tokamak-agnostic layer specifically deals with the ONEs and the execution of control tasks according to the pulse-schedule.…”