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Title: Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaksa)

Abstract

Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at LHD. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy and tomographic inversion, XICS can provide pro file measurements of the local emissivity, temperature and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modifi ed Levenberg-Marquardt optimizationmore » scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.« less

Authors:
 [1];  [1];  [1];  [1];  [1];  [1];  [2]
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  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  2. National Inst. for Fusion Science, Gifu (Japan)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES)
OSTI Identifier:
1172892
Report Number(s):
PPPL-5048
Journal ID: ISSN 0034-6748; RSINAK; TRN: US1600661
Grant/Contract Number:  
AC02-09CH11466
Resource Type:
Accepted Manuscript
Journal Name:
Review of Scientific Instruments
Additional Journal Information:
Journal Volume: 85; Journal Issue: 11; Conference: 20th Topical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, June, 2014.; Related Information: Contributed paper, published as part of the Proceedings of the 20th Topical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014.; Journal ID: ISSN 0034-6748
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Pablant, N. A., Bell, R. E., Bitter, M., Delgado-Aparicio, L., Hill, K. W., Lazerson, S., and Morita, S. Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaksa). United States: N. p., 2014. Web. doi:10.1063/1.4891977.
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Pablant, N. A., Bell, R. E., Bitter, M., Delgado-Aparicio, L., Hill, K. W., Lazerson, S., & Morita, S. Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaksa). United States. https://doi.org/10.1063/1.4891977
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Pablant, N. A., Bell, R. E., Bitter, M., Delgado-Aparicio, L., Hill, K. W., Lazerson, S., and Morita, S. Fri . "Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaksa)". United States. https://doi.org/10.1063/1.4891977. https://www.osti.gov/servlets/purl/1172892.
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@article{osti_1172892,
title = {Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaksa)},
author = {Pablant, N. A. and Bell, R. E. and Bitter, M. and Delgado-Aparicio, L. and Hill, K. W. and Lazerson, S. and Morita, S.},
abstractNote = {Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at LHD. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy and tomographic inversion, XICS can provide pro file measurements of the local emissivity, temperature and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modifi ed Levenberg-Marquardt optimization scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.},
doi = {10.1063/1.4891977},
journal = {Review of Scientific Instruments},
number = 11,
volume = 85,
place = {United States},
year = {Fri Aug 08 00:00:00 EDT 2014},
month = {Fri Aug 08 00:00:00 EDT 2014}
}
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https://doi.org/10.1063/1.4891977
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Works referenced in this record:

An inversion technique to obtain full poloidal velocity profiles in a tokamak plasma
journal, February 1997

  • Bell, Ronald E.
  • Review of Scientific Instruments, Vol. 68, Issue 2
  • DOI: 10.1063/1.1147885

X-ray imaging crystal spectroscopy for use in plasma transport research
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  • Reinke, M. L.; Podpaly, Y. A.; Bitter, M.
  • Review of Scientific Instruments, Vol. 83, Issue 11
  • DOI: 10.1063/1.4758281

STELLOPT modeling of the 3D diagnostic response in ITER
journal, June 2013

Objectives and layout of a high-resolution x-ray imaging crystal spectrometer for the large helical device
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  • Bitter, M.; Hill, K.; Gates, D.
  • Review of Scientific Instruments, Vol. 81, Issue 10
  • DOI: 10.1063/1.3490016

Layout and results from the initial operation of the high-resolution x-ray imaging crystal spectrometer on the Large Helical Device
journal, August 2012

  • Pablant, N. A.; Bitter, M.; Delgado-Aparicio, L.
  • Review of Scientific Instruments, Vol. 83, Issue 8
  • DOI: 10.1063/1.4744935
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