Uncertainty Analysis in 3D Equilibrium Reconstruction
Abstract
Reconstruction is an inverse process where a parameter space is searched to locate a set of parameters with the highest probability of describing experimental observations. Due to systematic errors and uncertainty in experimental measurements, this optimal set of parameters will contain some associated uncertainty. This uncertainty in the optimal parameters leads to uncertainty in models derived using those parameters. V3FIT is a three-dimensional (3D) equilibrium reconstruction code that propagates uncertainty from the input signals, to the reconstructed parameters, and to the final model. Here in this paper, we describe the methods used to propagate uncertainty in V3FIT. Using the results of whole shot 3D equilibrium reconstruction of the Compact Toroidal Hybrid, this propagated uncertainty is validated against the random variation in the resulting parameters. Two different model parameterizations demonstrate how the uncertainty propagation can indicate the quality of a reconstruction. As a proxy for random sampling, the whole shot reconstruction results in a time interval that will be used to validate the propagated uncertainty from a single time slice.
- Authors:
-
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Auburn Univ., AL (United States). Allison Lab.
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- OSTI Identifier:
- 1423072
- Grant/Contract Number:
- AC05-00OR22725; FG02-03ER54692
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Fusion Science and Technology
- Additional Journal Information:
- Journal Volume: 73; Journal Issue: 3; Journal ID: ISSN 1536-1055
- Publisher:
- American Nuclear Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Bayesian inference; equilibrium reconstruction
Citation Formats
Cianciosa, Mark R., Hanson, James D., and Maurer, David A. Uncertainty Analysis in 3D Equilibrium Reconstruction. United States: N. p., 2018.
Web. doi:10.1080/15361055.2017.1392819.
Cianciosa, Mark R., Hanson, James D., & Maurer, David A. Uncertainty Analysis in 3D Equilibrium Reconstruction. United States. https://doi.org/10.1080/15361055.2017.1392819
Cianciosa, Mark R., Hanson, James D., and Maurer, David A. Wed .
"Uncertainty Analysis in 3D Equilibrium Reconstruction". United States. https://doi.org/10.1080/15361055.2017.1392819. https://www.osti.gov/servlets/purl/1423072.
@article{osti_1423072,
title = {Uncertainty Analysis in 3D Equilibrium Reconstruction},
author = {Cianciosa, Mark R. and Hanson, James D. and Maurer, David A.},
abstractNote = {Reconstruction is an inverse process where a parameter space is searched to locate a set of parameters with the highest probability of describing experimental observations. Due to systematic errors and uncertainty in experimental measurements, this optimal set of parameters will contain some associated uncertainty. This uncertainty in the optimal parameters leads to uncertainty in models derived using those parameters. V3FIT is a three-dimensional (3D) equilibrium reconstruction code that propagates uncertainty from the input signals, to the reconstructed parameters, and to the final model. Here in this paper, we describe the methods used to propagate uncertainty in V3FIT. Using the results of whole shot 3D equilibrium reconstruction of the Compact Toroidal Hybrid, this propagated uncertainty is validated against the random variation in the resulting parameters. Two different model parameterizations demonstrate how the uncertainty propagation can indicate the quality of a reconstruction. As a proxy for random sampling, the whole shot reconstruction results in a time interval that will be used to validate the propagated uncertainty from a single time slice.},
doi = {10.1080/15361055.2017.1392819},
journal = {Fusion Science and Technology},
number = 3,
volume = 73,
place = {United States},
year = {Wed Feb 21 00:00:00 EST 2018},
month = {Wed Feb 21 00:00:00 EST 2018}
}
Web of Science
Works referenced in this record:
Three dimensional equilibrium solutions for a current-carrying reversed-field pinch plasma with a close-fitting conducting shell
journal, March 2016
- Koliner, J. J.; Cianciosa, M. R.; Boguski, J.
- Physics of Plasmas, Vol. 23, Issue 3
Convective transport due to poloidal electric fields during electron cyclotron heating in IMS
journal, October 1989
- Talmadge, J. N.; Storlie, C. A.; Anderson, D. T.
- Nuclear Fusion, Vol. 29, Issue 10
Helical equilibrium reconstruction with V3FIT in the RFX-mod Reversed Field Pinch
journal, September 2013
- Terranova, D.; Marrelli, L.; Hanson, J. D.
- Nuclear Fusion, Vol. 53, Issue 11
Edge and internal transport barrier formations in CHS
journal, July 2005
- Okamura, S.; Minami, T.; Akiyama, T.
- Nuclear Fusion, Vol. 45, Issue 8
Reconstruction of current profile parameters and plasma shapes in tokamaks
journal, November 1985
- Lao, L. L.; St. John, H.; Stambaugh, R. D.
- Nuclear Fusion, Vol. 25, Issue 11
Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D
journal, July 2015
- King, J. D.; Strait, E. J.; Lazerson, S. A.
- Physics of Plasmas, Vol. 22, Issue 7
Three-dimensional equilibrium reconstruction on the DIII-D device
journal, January 2015
- Lazerson, S. A.
- Nuclear Fusion, Vol. 55, Issue 2
Experimental Demonstration of Improved Neoclassical Transport with Quasihelical Symmetry
journal, February 2007
- Canik, J. M.; Anderson, D. T.; Anderson, F. S. B.
- Physical Review Letters, Vol. 98, Issue 8
Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria
journal, January 1983
- Hirshman, S. P.
- Physics of Fluids, Vol. 26, Issue 12
Initial Vacuum Magnetic Field Mapping in the Compact Toroidal Hybrid
journal, December 2006
- Peterson, J. T.; Hartwell, G. J.; Knowlton, S. F.
- Journal of Fusion Energy, Vol. 26, Issue 1-2
MHD equilibrium reconstruction in the presence of correlated data
journal, January 2006
- Jones, Christopher S.; Finn, John M.
- Nuclear Fusion, Vol. 46, Issue 2
Transport in stellarators
journal, December 1993
- Maassberg, H.; Brakel, R.; Burhenn, R.
- Plasma Physics and Controlled Fusion, Vol. 35, Issue SB
Non-axisymmetric equilibrium reconstruction for stellarators, reversed field pinches and tokamaks
journal, July 2013
- Hanson, J. D.; Anderson, D. T.; Cianciosa, M.
- Nuclear Fusion, Vol. 53, Issue 8
Suppression of vertical instability in elongated current-carrying plasmas by applying stellarator rotational transform
journal, May 2014
- ArchMiller, M. C.; Cianciosa, M. R.; Ennis, D. A.
- Physics of Plasmas, Vol. 21, Issue 5
Plasma profile modifications using magnetic field perturbations in the ATF torsatron
journal, February 1993
- Colchin, R. J.; Aceto, S. C.; England, A. C.
- Nuclear Fusion, Vol. 33, Issue 2
Helical core reconstruction of a DIII-D hybrid scenario tokamak discharge
journal, May 2017
- Cianciosa, M.; Wingen, A.; Hirshman, S. P.
- Nuclear Fusion, Vol. 57, Issue 7
Equilibrium reconstruction in the Madison Symmetric Torus reversed field pinch
journal, December 2003
- Anderson, J. K.; Forest, C. B.; Biewer, T. M.
- Nuclear Fusion, Vol. 44, Issue 1
Use of reconstructed 3D VMEC equilibria to match effects of toroidally rotating discharges in DIII-D
journal, October 2016
- Wingen, A.; Wilcox, R. S.; Cianciosa, M. R.
- Nuclear Fusion, Vol. 57, Issue 1
V3FIT: a code for three-dimensional equilibrium reconstruction
journal, July 2009
- Hanson, James D.; Hirshman, Steven P.; Knowlton, Stephen F.
- Nuclear Fusion, Vol. 49, Issue 7
Three-dimensional free boundary calculations using a spectral Green's function method
journal, December 1986
- Hirshman, S. P.; van RIJ, W. I.; Merkel, P.
- Computer Physics Communications, Vol. 43, Issue 1