Tokamak equilibrium reconstruction code LIUQE and its real time implementation

Abstract

Highlights.• Algorithm vertical stabilisation using a linear parametrisation of the current density • Experimentally derived model of the vacuum vessel to account for vessel currents• Real-time contouring algorithm for flux surface averaged 1.5D transport equations• Full real time implementation coded in SIMULINK runs in less than 200µs• Applications: shape control, safety factor profile control, coupling with RAPTOR Abstract. Equilibrium reconstruction consists in identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. The LIUQE code adopts a computationally efficient method to solve this problem, based on an iterative solution of the Poisson equation coupled with a linear parametrisation of the plasma current density. This algorithm is unstable against vertical gross motion of the plasma column for elongated shapes and its application to highly shaped plasmas on TCV requires a particular treatment of this instability. TCV's continuous vacuum vessel has a low resistance designed to enhance passive stabilisation of the vertical position. The eddy currents in the vacuum vessel have a sizeable influence on the equilibrium reconstruction and must be taken into account. A real time version of LIUQE has been implemented on TCV's distributed digital control system with a cycle time shorter than 200µs for a full spatial grid of 28 by 65, using all 133 experimental measurements and including the flux surface average of quantities necessary for the real time solution of 1.5D transport equations. This performance was achieved through a thoughtful choice of numerical methods and code optimisation techniques at every step of the algorithm, and was coded in MATLAB and SIMULINK for the off-line and real time version respectively.

Control-oriented modeling of the plasma particle density in tokamaks and application to real-time density profile reconstruction

“…It is assumed that ρ(ψ) and ψ(R, Z) are known from real-time 2D equilibrium reconstruction (see [51][52][53]). …”

Profile control simulations and experiments on TCV: a controller test environment and results using a model-based predictive controller

“…as well as the scalar Φ b (toroidal flux enclosed by plasma) can be timevarying and provided by a real-time (RT) equilibrium reconstruction codes such as LIUQE [21].…”

“…While we expect the true q-profile to globally follow the trends reported here, we do not claim that the core q-profile estimate accurately represents the situation in the plasma. A comparison of the real-time reconstructed q-profiles used for control with reconstructed profiles from the equilibrium reconstruction code LIUQE [21] as well as interpretative ASTRA [35] simulations is given in section 8.…”

“…Automatic detection and correction for diagnostic artefacts like fringe jumps in FIR channels is included. LIUQE A 2D Grad-Shafranov equilibrium reconstruction code that uses magnetic measurements [21]. It supplies equilibrium geometry information to the RAPTOR-observer, the RAPDENS-observer and the profile controller.…”

“…the density, temperature and current distribution requires knowledge of these quantities in real-time. These quantities can be reconstructed using real-time equilibrium reconstruction [20,21] or dynamic state observers [22] that integrate the available (noisy) diagnostic signals into an estimate of the plasma state.…”