Tokamak equilibrium reconstruction code LIUQE and its real time implementation

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 200 μs 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 1.5 D 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.

[1]  J-M Moret.  A software package to manipulate space dependencies and geometry in magnetic confinement fusion , 2005 .

[2]  F. Hofmann,et al.  Magnetic measurements on the TCV tokamak , 1998 .

[3]  F. Hofmann,et al.  FBT - a free-boundary tokamak equilibrium code for highly elongated and shaped plasmas , 1988 .

[4]  L. Segal.  John , 2013, The Messianic Secret.

[5]  R Akers,et al.  Optical boundary reconstruction of tokamak plasmas for feedback control of plasma position and shape. , 2010, The Review of scientific instruments.

[6]  L. Lao,et al.  Reconstruction of current profile parameters and plasma shapes in tokamaks , 1985 .

[7]  J. B. Lister,et al.  Breakdown in a continuous low resistivity vessel in TCV , 1996 .

[8]  L. Giannone,et al.  A Parallel Grad-Shafranov Solver for Real-Time Control of Tokamak Plasmas , 2012 .

[9]  Y. R. Martin,et al.  Extension of the TCV operating space towards higher elongation and higher normalized current , 2002 .

[10]  E. B. Rosa,et al.  Formulas and tables for the calculation of mutual and self-inductance (Revised) , 1912 .

[11]  李幼升,et al.  Ph , 1989 .

[12]  Stefano Coda,et al.  Distributed digital real-time control system for TCV tokamak , 2014 .

[13]  G. Tonetti,et al.  Tokamak equilibrium reconstruction using Faraday rotation measurements , 1988 .

[14]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[15]  F. Felici,et al.  Real-time physics-model-based simulation of the current density profile in tokamak plasmas , 2011 .

[16]  Faa Federico Felici,et al.  Snowflake divertor plasmas on TCV , 2009 .

[17]  Gene H. Golub,et al.  Cyclic Reduction - History and Applications , 1997 .

[18]  Eugenio Schuster,et al.  Equilibrium reconstruction improvement via Kalman-filter-based vessel current estimation at DIII-D , 2007 .

[19]  O. Sauter,et al.  Tokamak coordinate conventions: COCOS , 2013, Comput. Phys. Commun..

[20]  Per Strand,et al.  A generic data structure for integrated modelling of tokamak physics and subsystems , 2010, Comput. Phys. Commun..

[21]  K. Lackner,et al.  Computation of ideal MHD equilibria , 1976 .

[22]  P. McCarthy,et al.  The CLISTE Interpretive Equilibrium Code , 1999 .

[23]  J. B. Lister,et al.  On the possibility of creating doublet-shaped plasmas in TCV , 1996 .

[24]  L. L. Lao,et al.  Real time equilibrium reconstruction for tokamak discharge control , 1998 .

[25]  J-M Moret,et al.  Fast single loop diamagnetic measurements on the TCV tokamak , 2003 .

[26]  M. Cavinato,et al.  Dynamic identification of plasma magnetic contour in fusion machines , 2004 .

[28]  Yong Guo,et al.  Fast equilibrium reconstruction for tokamak discharge control based on GPU , 2013 .

[29]  Faa Federico Felici,et al.  Development of real-time plasma analysis and control algorithms for the TCV tokamak using SIMULINK , 2014 .