Fast parallel Grad–Shafranov solver for real-time equilibrium reconstruction in EAST tokamak using graphic processing unit

Huang, Yao; Xiao, Bingjia; Luo, Z.P.

doi:10.1088/1674-1056/26/8/085204

Cited by 13 publications

(9 citation statements)

References 20 publications

(37 reference statements)

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“…In the axisymmetric tokamak configuration, plasma equilibrium is described by the Grad-Shafranov (GS) equation derived from the steady state ideal magneto-hydrodynamic (MHD) equations, [12] and is given by…”

Section: Fixed Boundary Equilibrium Solvermentioning

confidence: 99%

Plasma shape optimization for EAST tokamak using orthogonal method

Chen¹,

Bao²,

Fu³

et al. 2019

Chinese Phys. B

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It is necessary to reduce the currents of poloidal field (PF) coils as small as possible, during the static equilibrium design procedure of Experimental Advanced Superconductive Tokamak (EAST). The quasi-snowflake (QSF) divertor configuration is studied in this paper. Starting from a standard QSF plasma equilibrium, a new QSF equilibrium with 300 kA total plasma current is designed. In order to reduce the currents of PF6 and PF14, the influence of plasma shape on PF coil current distribution is analyzed. A fixed boundary equilibrium solver based on a non-rigid plasma model is used to calculate the flux distribution and PF coil current distribution. Then the plasma shape parameters are studied by the orthogonal method. According to the result, the plasma shape is redefined, and the calculated equilibrium shows that the currents of PF6 and PF14 are reduced by 3.592 kA and 2.773 kA, respectively.

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Section: Fixed Boundary Equilibrium Solvermentioning

confidence: 99%

Plasma shape optimization for EAST tokamak using orthogonal method

Chen¹,

Bao²,

Fu³

et al. 2019

Chinese Phys. B

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“…Great efforts have been made previously to develop numerical solvers for the Grad-Shafranov equation. The applications for these numerical solvers are diverse, ranging from the interpretation of experimental observations [6,7] to the design of operation scenarios [8], real-time control of experiments [7,9,10], the analysis of the stability and transport properties of various configurations [11], and the optimization of machine designs [3,12].…”

Section: Introductionmentioning

confidence: 99%

ATEQ: Adaptive toroidal equilibrium code

et al. 2022

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A radially adaptive numerical scheme is developed to solve the Grad–Shafranov equation for axisymmetric magnetohydrodynamic equilibrium. A decomposition with independent solutions is employed in the radial direction, and Fourier decomposition is used in the poloidal direction. The independent solutions are then obtained using an adaptive shooting scheme together with the multi-region matching technique in the radial direction. Accordingly, the adaptive toroidal equilibrium (ATEQ) code is constructed for axisymmetric equilibrium studies. The adaptive numerical scheme in the radial direction improves considerably the accuracy of the equilibrium solution. The decomposition with independent solutions effectively reduces the matrix size in solving the magnetohydrodynamic equilibrium problem. The reduction of the matrix size is about an order of magnitude as compared with the conventional radially grid-based numerical schemes. Also, in this ATEQ numerical scheme, no matter how accuracy in the radial direction is imposed, the size of matrices basically does not change. The small matrix size scheme gives ATEQ more flexibility to address the requirement of the number of Fourier components in the poloidal direction in tough equilibrium problems. These two unique features, the adaptive shooting and small matrix size, make ATEQ useful to improve tokamak equilibrium solutions.

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“…Grad-Shafranov solvers aimed at real-time implementation are optimized to satisfy the computational time requirements [3] e.g. via parallelization and use of GPUs [29,30]. For the transport equations instead, efforts are made to reduce the complexity of the modeling while retaining the most relevant features [19,31,32], as well as using machine learning techniques to emulate the solutions of the most computational expensive part of the model [33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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.

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Fast parallel Grad–Shafranov solver for real-time equilibrium reconstruction in EAST tokamak using graphic processing unit

Cited by 13 publications

References 20 publications

Plasma shape optimization for EAST tokamak using orthogonal method

Plasma shape optimization for EAST tokamak using orthogonal method

ATEQ: Adaptive toroidal equilibrium code

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

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