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

Title: Use of reconstructed 3D equilibria to determine onset conditions of helical cores in tokamaks for extrapolation to ITER

Abstract

The threshold for spontaneous symmetry breaking, which results in growth of m/n = 1/1 helical cores, in tokamaks is determined using VMEC. This model is based on a DIII-D hybrid discharge with helical core, and it predicts ITER (15MA scenario) to operate far in the helical core formation regime. Helical cores can only exist in tokamak discharges with monotonic but low, or reversed q-shear and qmin 1 in the core. The helical core is a saturated internal kink mode; its onset threshold is proportional to (dp/d)/B 2 t around q = 1. Below the threshold, applied 3-D fields can drive a helical core to finite size, as in DIIID. Above it, a random 3-D kick causes a bifurcation from axisymmetry and excites a spontaneous helical core. Helical cores occur frequently in C-Mod due to impurities; modeling shows the axisymmetric equilibrium becomes unstable at the end of the current ramp up due to the slow current penetration and a resultant reversed shear q-profile, which lowers the threshold. Lastly, a comparison of the helical core onset threshold for discharges from DIII-D, C-Mod and ITER confirms that while DIII-D is marginally stable, C-Mod and especially ITER are highly susceptible to helical core formation.

Authors:
ORCiD logo; ; ; ORCiD logo; ORCiD logo; ; ;
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); General Atomics, San Diego, CA (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
OSTI Identifier:
1422609
Alternate Identifier(s):
OSTI ID: 1375431
Grant/Contract Number:  
FC02-04ER54698; AC05-00OR22725; AC02-09CH11466
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Nuclear Fusion
Additional Journal Information:
Journal Volume: 58; Journal Issue: 3; Journal ID: ISSN 0029-5515
Publisher:
IOP Science
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Wingen, A., Wilcox, R. S., Seal, S. K., Unterberg, E. A., Cianciosa, M. R., Delgado-Aparicio, L. F., Hirshman, S. P., and Lao, L. L. Use of reconstructed 3D equilibria to determine onset conditions of helical cores in tokamaks for extrapolation to ITER. United States: N. p., 2018. Web. doi:10.1088/1741-4326/aaa33d.
Wingen, A., Wilcox, R. S., Seal, S. K., Unterberg, E. A., Cianciosa, M. R., Delgado-Aparicio, L. F., Hirshman, S. P., & Lao, L. L. Use of reconstructed 3D equilibria to determine onset conditions of helical cores in tokamaks for extrapolation to ITER. United States. doi:10.1088/1741-4326/aaa33d.
Wingen, A., Wilcox, R. S., Seal, S. K., Unterberg, E. A., Cianciosa, M. R., Delgado-Aparicio, L. F., Hirshman, S. P., and Lao, L. L. Mon . "Use of reconstructed 3D equilibria to determine onset conditions of helical cores in tokamaks for extrapolation to ITER". United States. doi:10.1088/1741-4326/aaa33d. https://www.osti.gov/servlets/purl/1422609.
@article{osti_1422609,
title = {Use of reconstructed 3D equilibria to determine onset conditions of helical cores in tokamaks for extrapolation to ITER},
author = {Wingen, A. and Wilcox, R. S. and Seal, S. K. and Unterberg, E. A. and Cianciosa, M. R. and Delgado-Aparicio, L. F. and Hirshman, S. P. and Lao, L. L.},
abstractNote = {The threshold for spontaneous symmetry breaking, which results in growth of m/n = 1/1 helical cores, in tokamaks is determined using VMEC. This model is based on a DIII-D hybrid discharge with helical core, and it predicts ITER (15MA scenario) to operate far in the helical core formation regime. Helical cores can only exist in tokamak discharges with monotonic but low, or reversed q-shear and qmin 1 in the core. The helical core is a saturated internal kink mode; its onset threshold is proportional to (dp/d)/B2t around q = 1. Below the threshold, applied 3-D fields can drive a helical core to finite size, as in DIIID. Above it, a random 3-D kick causes a bifurcation from axisymmetry and excites a spontaneous helical core. Helical cores occur frequently in C-Mod due to impurities; modeling shows the axisymmetric equilibrium becomes unstable at the end of the current ramp up due to the slow current penetration and a resultant reversed shear q-profile, which lowers the threshold. Lastly, a comparison of the helical core onset threshold for discharges from DIII-D, C-Mod and ITER confirms that while DIII-D is marginally stable, C-Mod and especially ITER are highly susceptible to helical core formation.},
doi = {10.1088/1741-4326/aaa33d},
journal = {Nuclear Fusion},
issn = {0029-5515},
number = 3,
volume = 58,
place = {United States},
year = {2018},
month = {1}
}

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

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Figures / Tables:

Figure 1 Figure 1: Time evolution of the local soft X-ray emission along the major radius at Z = 0 in shot 164661, obtained by tomographic inversion of measured, line-integrated soft-X-ray data.

Save / Share:

Works referenced in this record:

Self-Organized Stationary States of Tokamaks
journal, November 2015


Molybdenum emission from impurity-induced m = 1 snake-modes on the Alcator C-Mod tokamak
journal, October 2012

  • Delgado-Aparicio, L.; Bitter, M.; Granetz, R.
  • Review of Scientific Instruments, Vol. 83, Issue 10
  • DOI: 10.1063/1.4733731

Persistent density perturbations at rational- q surfaces following pellet injection in the Joint European Torus
journal, November 1987


Formation and Stability of Impurity “Snakes” in Tokamak Plasmas
journal, February 2013


Nonlinear evolution of ideal internal kink modes in tokamaks with nonmonotonic q profiles
journal, October 1990

  • Avinash, K.
  • Physics of Fluids B: Plasma Physics, Vol. 2, Issue 10
  • DOI: 10.1063/1.859503

Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria
journal, January 1983


Stability of ideal and resistive internal kink modes in toroidal geometry
journal, January 1987

  • Hastie, R. J.; Hender, T. C.; Carreras, B. A.
  • Physics of Fluids, Vol. 30, Issue 6
  • DOI: 10.1063/1.866242

Internal Kink Modes in Toroidal Plasmas with Circular Cross Sections
journal, December 1975


Nonlinear growth of the quasi‐interchange instability
journal, March 1989

  • Waelbroeck, F. L.
  • Physics of Fluids B: Plasma Physics, Vol. 1, Issue 3
  • DOI: 10.1063/1.859165

Tungsten as target material in fusion devices
journal, June 1996


Impact of ideal MHD stability limits on high-beta hybrid operation
journal, November 2016


NBI fast ion confinement in the helical core of MAST hybrid-like plasmas
journal, May 2014


Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas
journal, May 2017


Sawtooth oscillations
journal, January 1986


JET snake magnetohydrodynamic equilibria
journal, June 2011


Snake-like phenomena in Tore Supra following pellet injection
journal, April 1997


Reconstruction of current profile parameters and plasma shapes in tokamaks
journal, November 1985


V3FIT: a code for three-dimensional equilibrium reconstruction
journal, July 2009


Bifurcated helical core equilibrium states in tokamaks
journal, June 2013


Helical core reconstruction of a DIII-D hybrid scenario tokamak discharge
journal, May 2017


Connection between plasma response and resonant magnetic perturbation (RMP) edge localized mode (ELM) suppression in DIII-D
journal, September 2015


Use of reconstructed 3D VMEC equilibria to match effects of toroidally rotating discharges in DIII-D
journal, October 2016


Free boundary equilibrium in 3D tokamaks with toroidal rotation
journal, May 2015


Ideal saturated MHD helical structures in axisymmetric hybrid plasmas
journal, May 2014


Chapter 1: Overview and summary
journal, December 1999

  • Editors, ITER Physics Basis; Co-Chairs, ITER Physics Expert Group Chairs an; Unit, ITER Joint Central Team and Physics
  • Nuclear Fusion, Vol. 39, Issue 12
  • DOI: 10.1088/0029-5515/39/12/301

3D vacuum magnetic field modelling of the ITER ELM control coil during standard operating scenarios
journal, August 2013