EFIT Equilibrium Reconstruction Including Polarimetry Measurements on Tore Supra

Li, Y. G.; Lotte, P.; Zwingmann, W.; Gil, C.; Imbeaux, F.

doi:10.13182/fst11-a11654

Cited by 12 publications

(11 citation statements)

References 15 publications

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“…HIT [14], START [15,16], MAST [17], KSTAR [18,19], JT-60U [20], NSTX [21], TORE SUPRA [8,22], HT-7 [23], HL-2A [24], and EAST [25,26] devices. Equilibrium reconstruction is a critical part of the development of the fusion.…”

Section: Introductionmentioning

confidence: 99%

Single Gaussian Process Method for Arbitrary Tokamak Regimes with a Statistical Analysis

Leddy¹,

Madireddy²,

Howell³

et al. 2022

Preprint

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Gaussian Process Regression (GPR) is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including intrinsic uncertainty quantification and robustness to over-fitting. This work investigates the use of a new method, the change-point method, for handling the varying length scales found in different tokamak regimes. The use of the Student's t-distribution for the Bayesian likelihood probability is also investigated and shown to be advantageous in providing good fits in profiles with many outliers. To compare different methods, synthetic data generated from analytic profiles is used to create a database enabling a quantitative statistical comparison of which methods perform the best. Using a full Bayesian approach with the change-point method, Matérn kernel for the prior probability, and Student's t-distribution for the likelihood is shown to give the best results.

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Section: Introductionmentioning

confidence: 99%

Single Gaussian Process Method for Arbitrary Tokamak Regimes with a Statistical Analysis

Leddy¹,

Madireddy²,

Howell³

et al. 2022

Preprint

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“…A basic approach to perform a KER is constraining p and j-related profiles from direct measurements of internal plasma quantities (T e , n e , T i , Z ef f , magnetic field pitch angle) [7,[13][14][15]. However the diagnostics for internal measurements, compared to the external magnetic measurements, have typically larger error-bars, might not cover the full radial profile and/or have operational limits [16] that prevent their routine use in all the experiments and during the full plasma discharge.…”

Section: Introductionmentioning

confidence: 99%

“…A Bayesian framework called integrated data analysis (IDA) [11] is used to combine internal kinetic measurements from several diagnostics, while propagating measurements uncertainties. The integrated modeling with 'One Modeling Framework for Integrated Tasks' (OMFIT) [10] performs KER with transport codes (TRANSP [21], ONETWO [22]) including self-consistent equilibrium (EFIT [15]) and CDE solution and it is routinely used in several tokamaks. In TCV [23] the free boundary equilibrium reconstruction code LIUQE [3] has been coupled with the transport code ASTRA [24] and used to test the coupling technique [25] presented in this paper .…”

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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“…In particular, within the most used code, EFIT, the polarimetry (Li et al. 2011) and/or the motional Stark effect (Lao et al. 2005) have both been used to further constrain the problem and to improve the reconstructed poloidal flux mapping.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of the Grad Shafranov equation in an elliptical prolate geometry

Crisanti

2019

J. Plasma Phys.

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The analytical solution in toroidal coordinates of the Grad Shafranov equation has been at the origin of the tokamak breakthrough in the fusion development. Unfortunately, the standard toroidal coordinates have a circular poloidal section, which does not fit the elongated cross-section of the present tokamak experiments. In axisymmetry, the vacuum Grad Shafranov equation coincides with the Laplace equation for the toroidal component of the vector potential. In the present paper the solutions for the Laplace equation and that for the vacuum Grad Shafranov equation are tackled in the elliptical prolate toroidal cap-cyclide coordinates framework. The following report of the geometrical properties and of the metric of these coordinates allows us to work out the analytical solution of both equations in terms of the Wangerin functions.

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EFIT Equilibrium Reconstruction Including Polarimetry Measurements on Tore Supra

Cited by 12 publications

References 15 publications

Single Gaussian Process Method for Arbitrary Tokamak Regimes with a Statistical Analysis

Single Gaussian Process Method for Arbitrary Tokamak Regimes with a Statistical Analysis

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

Analytical solution of the Grad Shafranov equation in an elliptical prolate geometry

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