On virial analysis at low aspect ratio
Abstract
The validity of virial analysis to infer global MHD equilibrium poloidal beta βp and internal inductance ℓi from external magnetics measurements is examined for low aspect ratio configurations with A < 2. Numerical equilibrium studies at varied aspect ratio are utilized to validate the technique at finite aspect ratio. The effect of applying high-A approximations to low-A experimental data is quantified and demonstrates significant over-estimation of stored energy (factors of 2–10) in spherical tokamak geometry. Experimental approximations to equilibrium-dependent volume integral terms in the analysis are evaluated at low-A. Highly paramagnetic configurations are found to be inadequately represented through the virial mean radius parameter RT. Alternate formulations for inferring βp and ℓi that are independent of RT to avoid this difficulty are presented for the static isotropic limit. Lastly, these formulations are suitable for fast estimation of tokamak stored energy components at low aspect ratio using virial analysis.
- Authors:
-
[1];
[1];
[1];
[1];
[2]
- Univ. of Wisconsin-Madison, Madison, WI (United States)
- Univ. of Wisconsin-Madison, Madison, WI (United States); Oak Ridge Associated Univ., Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Univ. of Wisconsin, Madison, WI (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- OSTI Identifier:
- 1275599
- Alternate Identifier(s):
- OSTI ID: 1274826
- Grant/Contract Number:
- FG02-96ER54375
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 7; Related Information: M.W. Bongard, J.L. Barr, R.J. Fonck, J.A. Reusch, and K.E. Thome, "Public Data Set: On Virial Analysis at Low Aspect Ratio," DOI: 10.18138/1240359; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; tokamaks; paramagnetism; integral equations; energy content; inductance
Citation Formats
Bongard, Michael W., Barr, Jayson L., Fonck, Raymond J., Reusch, Joshua A., and Thome, Kathreen E. On virial analysis at low aspect ratio. United States: N. p., 2016.
Web. doi:10.1063/1.4959808.
Bongard, Michael W., Barr, Jayson L., Fonck, Raymond J., Reusch, Joshua A., & Thome, Kathreen E. On virial analysis at low aspect ratio. United States. https://doi.org/10.1063/1.4959808
Bongard, Michael W., Barr, Jayson L., Fonck, Raymond J., Reusch, Joshua A., and Thome, Kathreen E. Thu .
"On virial analysis at low aspect ratio". United States. https://doi.org/10.1063/1.4959808. https://www.osti.gov/servlets/purl/1275599.
@article{osti_1275599,
title = {On virial analysis at low aspect ratio},
author = {Bongard, Michael W. and Barr, Jayson L. and Fonck, Raymond J. and Reusch, Joshua A. and Thome, Kathreen E.},
abstractNote = {The validity of virial analysis to infer global MHD equilibrium poloidal beta βp and internal inductance ℓi from external magnetics measurements is examined for low aspect ratio configurations with A < 2. Numerical equilibrium studies at varied aspect ratio are utilized to validate the technique at finite aspect ratio. The effect of applying high-A approximations to low-A experimental data is quantified and demonstrates significant over-estimation of stored energy (factors of 2–10) in spherical tokamak geometry. Experimental approximations to equilibrium-dependent volume integral terms in the analysis are evaluated at low-A. Highly paramagnetic configurations are found to be inadequately represented through the virial mean radius parameter RT. Alternate formulations for inferring βp and ℓi that are independent of RT to avoid this difficulty are presented for the static isotropic limit. Lastly, these formulations are suitable for fast estimation of tokamak stored energy components at low aspect ratio using virial analysis.},
doi = {10.1063/1.4959808},
journal = {Physics of Plasmas},
number = 7,
volume = 23,
place = {United States},
year = {Thu Jul 28 00:00:00 EDT 2016},
month = {Thu Jul 28 00:00:00 EDT 2016}
}
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Cited by: 4 works
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Figures / Tables:
FIG 1.: Boundary flux surfaces: A = 1.15 (a), 1.50 (b), 2.50 (c), and 6.00 (d).
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Public Data Set: H-mode Plasmas at Very Low Aspect Ratio on the Pegasus Toroidal Experiment
dataset, January 2016
- Thome, Kathreen; Bongard, Michael; Barr, Jayson
Public Data Set: A Novel, Cost-Effective, Multi-Point Thomson Scattering System on the Pegasus Toroidal Experiment
dataset, September 2016
- Schlossberg, D. J.; Bodner, G. M.; Reusch, J. A.
- AIP - Review of Scientific Instruments, Vol. 87, Issue 11, 49.6 MB
Public Data Set: Continuous, Edge Localized Ion Heating During Non-Solenoidal Plasma Startup and Sustainment in a Low Aspect Ratio Tokamak
dataset, January 2017
- Burke, Marcus; Barr, Jayson; Bongard, Michael
Public Data Set: A Power-Balance Model for Local Helicity Injection Startup in a Spherical Tokamak
dataset, May 2018
- Barr, J. L.; Bongard, M. W.; Burke, M. G.
- Pegasus Public Data Sets
Public Data Set: Non-inductively Driven Tokamak Plasmas at Near-Unity βt in the Pegasus Toroidal Experiment
dataset, March 2018
- Reusch, Joshua; Bodner, Grant; Bongard, Michael
- Pegasus-Supplementary information for journal article at DOI: 10.1063/1.5017966, 1 file (5.1 MB)
Public Data Set: Initiation and Sustainment of Tokamak Plasmas with Local Helicity Injection as the Majority Current Drive
dataset, July 2018
- Perry, Justin; Bodner, Grant; Bongard, Michael
- Pegasus-Supplementary information for journal article at DOI: https://doi.org/10.1088/1741-4326/aac72e, 1 file (17.1 MB)
Public Data Set: Radially Scanning Magnetic Probes to Study Local Helicity Injection Dynamics
dataset, July 2018
- Richner, Nathan; Bongard, Michael; Fonck, Raymond
- Pegasus-Supplementary information for journal article at DOI: 10.1063/1.5036527, 1 file (9.4 MB)
Public Data Set: Advancing Local Helicity Injection for Non-Solenoidal Tokamak Startup
dataset, January 2019
- Bongard, Michael; Bodner, Grant; Burke, Marcus
- University of Wisconsin-Madison
Public Data Set: Continuous, Edge Localized Ion Heating During Non-Solenoidal Plasma Startup and Sustainment in a Low Aspect Ratio Tokamak
dataset, January 2017
- Burke, Marcus; Barr, Jayson; Bongard, Michael
Public Data Set: H-mode Plasmas at Very Low Aspect Ratio on the Pegasus Toroidal Experiment
dataset, January 2016
- Thome, Kathreen; Bongard, Michael; Barr, Jayson
Public Data Set: A Novel, Cost-Effective, Multi-Point Thomson Scattering System on the Pegasus Toroidal Experiment
dataset, September 2016
- Schlossberg, D. J.; Bodner, G. M.; Reusch, J. A.
- AIP - Review of Scientific Instruments, Vol. 87, Issue 11, 49.6 MB
Public Data Set: A Power-Balance Model for Local Helicity Injection Startup in a Spherical Tokamak
dataset, May 2018
- Barr, J. L.; Bongard, M. W.; Burke, M. G.
- Pegasus Public Data Sets
Public Data Set: Non-inductively Driven Tokamak Plasmas at Near-Unity βt in the Pegasus Toroidal Experiment
dataset, March 2018
- Reusch, Joshua; Bodner, Grant; Bongard, Michael
- Pegasus-Supplementary information for journal article at DOI: 10.1063/1.5017966, 1 file (5.1 MB)
Public Data Set: Initiation and Sustainment of Tokamak Plasmas with Local Helicity Injection as the Majority Current Drive
dataset, July 2018
- Perry, Justin; Bodner, Grant; Bongard, Michael
- Pegasus-Supplementary information for journal article at DOI: https://doi.org/10.1088/1741-4326/aac72e, 1 file (17.1 MB)
Public Data Set: Radially Scanning Magnetic Probes to Study Local Helicity Injection Dynamics
dataset, July 2018
- Richner, Nathan; Bongard, Michael; Fonck, Raymond
- Pegasus-Supplementary information for journal article at DOI: 10.1063/1.5036527, 1 file (9.4 MB)
Public Data Set: Advancing Local Helicity Injection for Non-Solenoidal Tokamak Startup
dataset, January 2019
- Bongard, Michael; Bodner, Grant; Burke, Marcus
- University of Wisconsin-Madison
Works referencing / citing this record:
Simple and accurate method of diamagnetic flux measurement in Versatile Experimental Spherical Torus (VEST)
journal, October 2018
- Yang, J.; Kim, Y.; Jeong, W. I.
- Review of Scientific Instruments, Vol. 89, Issue 10
Public Data Set: H-mode Plasmas at Very Low Aspect Ratio on the Pegasus Toroidal Experiment
dataset, January 2016
- Thome, Kathreen; Bongard, Michael; Barr, Jayson
Public Data Set: On Virial Analysis at Low Aspect Ratio
dataset, July 2016
- Bongard, Michael; Barr, Jayson; Fonck, Raymond
- Pegasus-Supplementary information for journal article at DOI: 10.1063/1.4959808, 1 file (440 KB)
Public Data Set: A Novel, Cost-Effective, Multi-Point Thomson Scattering System on the Pegasus Toroidal Experiment
dataset, September 2016
- Schlossberg, D. J.; Bodner, G. M.; Reusch, J. A.
- AIP - Review of Scientific Instruments, Vol. 87, Issue 11, 49.6 MB
Public Data Set: Continuous, Edge Localized Ion Heating During Non-Solenoidal Plasma Startup and Sustainment in a Low Aspect Ratio Tokamak
dataset, January 2017
- Burke, Marcus; Barr, Jayson; Bongard, Michael
Public Data Set: A Power-Balance Model for Local Helicity Injection Startup in a Spherical Tokamak
dataset, May 2018
- Barr, J. L.; Bongard, M. W.; Burke, M. G.
- Pegasus Public Data Sets
Public Data Set: Non-inductively Driven Tokamak Plasmas at Near-Unity βt in the Pegasus Toroidal Experiment
dataset, March 2018
- Reusch, Joshua; Bodner, Grant; Bongard, Michael
- Pegasus-Supplementary information for journal article at DOI: 10.1063/1.5017966, 1 file (5.1 MB)
Public Data Set: Initiation and Sustainment of Tokamak Plasmas with Local Helicity Injection as the Majority Current Drive
dataset, July 2018
- Perry, Justin; Bodner, Grant; Bongard, Michael
- Pegasus-Supplementary information for journal article at DOI: https://doi.org/10.1088/1741-4326/aac72e, 1 file (17.1 MB)
Public Data Set: Radially Scanning Magnetic Probes to Study Local Helicity Injection Dynamics
dataset, July 2018
- Richner, Nathan; Bongard, Michael; Fonck, Raymond
- Pegasus-Supplementary information for journal article at DOI: 10.1063/1.5036527, 1 file (9.4 MB)
Public Data Set: Spatial Heterodyne Spectroscopy for High Speed Measurements of Stark Split Neutral Beam Emission in a High Temperature Plasma
dataset, January 2018
- Burke, Marcus; Fonck, Raymond; McKee, George
- University of Wisconsin-Madison
Public Data Set: Advancing Local Helicity Injection for Non-Solenoidal Tokamak Startup
dataset, January 2019
- Bongard, Michael; Bodner, Grant; Burke, Marcus
- University of Wisconsin-Madison
Figures / Tables found in this record:
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.