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Title: Evaluation of Magnetic Diagnostics for MHD Equilibrium Reconstruction of LHD Discharges

Abstract

Equilibrium reconstruction is the process of determining the set of parameters of an MHD equilibrium that minimize the difference between expected and experimentally observed signals. This is routinely performed in axisymmetric devices, such as tokamaks, and the reconstructed equilibrium solution is then the basis for analysis of stability and transport properties. The V3FIT code [1] has been developed to perform equilibrium reconstruction in cases where axisymmetry cannot be assumed, such as in stellarators. The present work is focused on using V3FIT to analyze plasmas in the Large Helical Device (LHD) [2], a superconducting, heliotron type device with over 25 MW of heating power that is capable of achieving both high-beta ({approx}5%) and high density (>1 x 10{sup 21}/m{sup 3}). This high performance as well as the ability to drive tens of kiloamperes of toroidal plasma current leads to deviations in the equilibrium state from the vacuum flux surfaces. This initial study examines the effectiveness of using magnetic diagnostics as the observed signals in reconstructing experimental plasma parameters for LHD discharges. V3FIT uses the VMEC [3] 3D equilibrium solver to calculate an initial equilibrium solution with closed, nested flux surfaces based on user specified plasma parameters. This equilibrium solution is thenmore » used to calculate the expected signals for specified diagnostics. The differences between these expected signal values and the observed values provides a starting {chi}{sup 2} value. V3FIT then varies all of the fit parameters independently, calculating a new equilibrium and corresponding {chi}{sup 2} for each variation. A quasi-Newton algorithm [1] is used to find the path in parameter space that leads to a minimum in {chi}{sup 2}. Effective diagnostic signals must vary in a predictable manner with the variations of the plasma parameters and this signal variation must be of sufficient amplitude to be resolved from the signal noise. Signal effectiveness can be defined for a specific signal and specific reconstruction parameter as the dimensionless fractional reduction in the posterior parameter variance with respect to the signal variance. Here, {sigma}{sub i}{sup sig} is the variance of the ith signal and {sigma}{sub j}{sup param} param is the posterior variance of the jth fit parameter. The sum of all signal effectiveness values for a given reconstruction parameter is normalized to one. This quantity will be used to determine signal effectiveness for various reconstruction cases. The next section will examine the variation of the expected signals with changes in plasma pressure and the following section will show results for reconstructing model plasmas using these signals.« less

Authors:
 [1];  [2];  [3];  [1];  [4];  [4]
  1. ORNL
  2. Auburn University, Auburn, Alabama
  3. Princeton Plasma Physics Laboratory (PPPL)
  4. National Institute for Fusion Science, Toki, Japan
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1024698
DOE Contract Number:  
DE-AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Conference: European Physical Society 38th Conference on Plasma Physics, Strasbourg, France, 20110627, 20110701
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 30 DIRECT ENERGY CONVERSION; ALGORITHMS; AMPLITUDES; ELECTRIC CURRENTS; EVALUATION; HEATING; HELIOTRON; MAGNETIC SURFACES; MHD EQUILIBRIUM; PERFORMANCE; PHYSICS; PLASMA; PLASMA PRESSURE; STABILITY; STELLARATORS; TRANSPORT

Citation Formats

Sontag, Aaron C, Hanson, James D., Lazerson, Sam, Harris, Jeffrey H, Sakakibara, S., and Suzuki, Y. Evaluation of Magnetic Diagnostics for MHD Equilibrium Reconstruction of LHD Discharges. United States: N. p., 2011. Web.
Sontag, Aaron C, Hanson, James D., Lazerson, Sam, Harris, Jeffrey H, Sakakibara, S., & Suzuki, Y. Evaluation of Magnetic Diagnostics for MHD Equilibrium Reconstruction of LHD Discharges. United States.
Sontag, Aaron C, Hanson, James D., Lazerson, Sam, Harris, Jeffrey H, Sakakibara, S., and Suzuki, Y. Sat . "Evaluation of Magnetic Diagnostics for MHD Equilibrium Reconstruction of LHD Discharges". United States.
@article{osti_1024698,
title = {Evaluation of Magnetic Diagnostics for MHD Equilibrium Reconstruction of LHD Discharges},
author = {Sontag, Aaron C and Hanson, James D. and Lazerson, Sam and Harris, Jeffrey H and Sakakibara, S. and Suzuki, Y.},
abstractNote = {Equilibrium reconstruction is the process of determining the set of parameters of an MHD equilibrium that minimize the difference between expected and experimentally observed signals. This is routinely performed in axisymmetric devices, such as tokamaks, and the reconstructed equilibrium solution is then the basis for analysis of stability and transport properties. The V3FIT code [1] has been developed to perform equilibrium reconstruction in cases where axisymmetry cannot be assumed, such as in stellarators. The present work is focused on using V3FIT to analyze plasmas in the Large Helical Device (LHD) [2], a superconducting, heliotron type device with over 25 MW of heating power that is capable of achieving both high-beta ({approx}5%) and high density (>1 x 10{sup 21}/m{sup 3}). This high performance as well as the ability to drive tens of kiloamperes of toroidal plasma current leads to deviations in the equilibrium state from the vacuum flux surfaces. This initial study examines the effectiveness of using magnetic diagnostics as the observed signals in reconstructing experimental plasma parameters for LHD discharges. V3FIT uses the VMEC [3] 3D equilibrium solver to calculate an initial equilibrium solution with closed, nested flux surfaces based on user specified plasma parameters. This equilibrium solution is then used to calculate the expected signals for specified diagnostics. The differences between these expected signal values and the observed values provides a starting {chi}{sup 2} value. V3FIT then varies all of the fit parameters independently, calculating a new equilibrium and corresponding {chi}{sup 2} for each variation. A quasi-Newton algorithm [1] is used to find the path in parameter space that leads to a minimum in {chi}{sup 2}. Effective diagnostic signals must vary in a predictable manner with the variations of the plasma parameters and this signal variation must be of sufficient amplitude to be resolved from the signal noise. Signal effectiveness can be defined for a specific signal and specific reconstruction parameter as the dimensionless fractional reduction in the posterior parameter variance with respect to the signal variance. Here, {sigma}{sub i}{sup sig} is the variance of the ith signal and {sigma}{sub j}{sup param} param is the posterior variance of the jth fit parameter. The sum of all signal effectiveness values for a given reconstruction parameter is normalized to one. This quantity will be used to determine signal effectiveness for various reconstruction cases. The next section will examine the variation of the expected signals with changes in plasma pressure and the following section will show results for reconstructing model plasmas using these signals.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2011},
month = {1}
}

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