skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: On virial analysis at low aspect ratio

Abstract

The validity of virial analysis to infer global MHD equilibrium poloidal beta β p and internal inductance ℓ i 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 R T. Alternate formulations for inferring β p and ℓ i that are independent of R T 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:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]
  1. Univ. of Wisconsin-Madison, Madison, WI (United States)
  2. 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, Madison, WI (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
OSTI Identifier:
1275599
Alternate Identifier(s):
OSTI ID: 1274826
Grant/Contract Number:  
FG02-96ER54375
Resource Type:
Journal Article: 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. doi: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. doi: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},
issn = {1070-664X},
number = 7,
volume = 23,
place = {United States},
year = {2016},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

    Works referencing / citing this record:

    Public Data Set: H-mode Plasmas at Very Low Aspect Ratio on the Pegasus Toroidal Experiment
    dataset, January 2016


    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
    • DOI: 10.18138/1257860

    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
    • DOI: 10.18138/1345037

    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)
    • DOI: 10.18138/1410490

    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)
    • DOI: 10.18138/1419641

    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)
    • DOI: 10.18138/1432455