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Title: Mapping the sawtooth

Abstract

The sawtooth oscillation involves a topological change of the magnetic field lines in the core of a tokamak discharge. In this work, we simulate a steady state sawtoothing discharge using the M3DC 1-code. During the sawtooth the topological structure of the magnetic field is analyzed by tracking the fixed points of the field line map: the mapping induced by the field lines going once around the tokamak. We numerically locate the fixed points of the field line map (of which the magnetic axis is one) and use them construct a Poincaré section that resolves the core region and the (1, 1) island. Finally, by following the evolution of the magnetic field through the motion and bifurcation of the fixed points of the field line map we get an intuitive picture of the processes that take place during a Kadomtsev style sawtooth crash.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]
+ Show Author Affiliations
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Leiden Univ. (Netherlands)
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
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:
1580273
Grant/Contract Number:  
AC02-09CH11466
Resource Type:
Accepted Manuscript
Journal Name:
Plasma Physics and Controlled Fusion
Additional Journal Information:
Journal Volume: 62; Journal Issue: 2; Journal ID: ISSN 0741-3335
Publisher:
IOP Science
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Smiet, C. B., Kramer, G. J., and Hudson, S. R.. Mapping the sawtooth. United States: N. p., 2019. Web. doi:10.1088/1361-6587/ab5073.
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Smiet, C. B., Kramer, G. J., & Hudson, S. R.. Mapping the sawtooth. United States. https://doi.org/10.1088/1361-6587/ab5073
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Smiet, C. B., Kramer, G. J., and Hudson, S. R.. Wed . "Mapping the sawtooth". United States. https://doi.org/10.1088/1361-6587/ab5073. https://www.osti.gov/servlets/purl/1580273.
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@article{osti_1580273,
title = {Mapping the sawtooth},
author = {Smiet, C. B. and Kramer, G. J. and Hudson, S. R.},
abstractNote = {The sawtooth oscillation involves a topological change of the magnetic field lines in the core of a tokamak discharge. In this work, we simulate a steady state sawtoothing discharge using the M3DC 1-code. During the sawtooth the topological structure of the magnetic field is analyzed by tracking the fixed points of the field line map: the mapping induced by the field lines going once around the tokamak. We numerically locate the fixed points of the field line map (of which the magnetic axis is one) and use them construct a Poincaré section that resolves the core region and the (1, 1) island. Finally, by following the evolution of the magnetic field through the motion and bifurcation of the fixed points of the field line map we get an intuitive picture of the processes that take place during a Kadomtsev style sawtooth crash.},
doi = {10.1088/1361-6587/ab5073},
journal = {Plasma Physics and Controlled Fusion},
number = 2,
volume = 62,
place = {United States},
year = {2019},
month = {10}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1088/1361-6587/ab5073
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Citation Metrics:
Cited by: 2 works
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Figures / Tables:

FIG. 1 FIG. 1: Construction of the field line map and calculation of the topological index. Top panel: The poloidal cross-section $D$ is given by the intersection of the blue plane and the torus. A point $x$ in $D$ is integrated once around the torus by following the magnetic field line (magentamore » line) to the point $f$($x$). The difference between these two locations is expressed in the vector field w($x$) = $f$($x$) − $x$. This vector field is zero at fixed points, such as the red, green and blue field lines. Bottom row: Illustration of the calculation of the topological index for an o-point (left two panels) and an x-point (right two panels). The topological index is calculated by traveling along a parametrized path $γ$($τ$) (colored circle, color corresponding to parameter $τ$) that encloses a zero of w. A few vectors of the field w are shown. The unit vectors |w| are shown to the right. The index of the fixed point is positive when gamma is followed clockwise (orange-blue-purple) the vectors |w| move around the circle in the clockwise direction. The linearized matrices M corresponding with these mappings are given. Level sets of the quadratic form $ψ$ are given by the black and grey lines.« less
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Works referenced in this record:

Geometrical properties of a “snowflake” divertor
journal, June 2007

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

Sawtooth oscillations
journal, January 1986

Two‐Dimensional Measure‐Preserving Mappings
journal, May 1968

  • Greene, John M.
  • Journal of Mathematical Physics, Vol. 9, Issue 5
  • DOI: 10.1063/1.1664639

Nonlinear studies of m =1 modes in high‐temperature plasmas
journal, November 1992

  • Aydemir, A. Y.
  • Physics of Fluids B: Plasma Physics, Vol. 4, Issue 11
  • DOI: 10.1063/1.860355

Model for the sawtooth period and amplitude
journal, December 1996

  • Porcelli, F.; Boucher, D.; Rosenbluth, M. N.
  • Plasma Physics and Controlled Fusion, Vol. 38, Issue 12
  • DOI: 10.1088/0741-3335/38/12/010

Model for Incomplete Reconnection in Sawtooth Crashes
journal, December 2011

Magnetic field lines, Hamiltonian dynamics, and nontwist systems
journal, June 2000

Magnetohydrodynamic modes driven by anomalous electron viscosity and their role in fast sawtooth crashes
journal, September 1990

  • Aydemir, A. Y.
  • Physics of Fluids B: Plasma Physics, Vol. 2, Issue 9
  • DOI: 10.1063/1.859433

Destruction of invariant surfaces and magnetic coordinates for perturbed magnetic fields
journal, February 2004

Calculation of the post-crash state and 1 1/2 D simulation of sawtooth cycles
journal, September 1994

Self-Organized Stationary States of Tokamaks
journal, November 2015

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

Multiple timescale calculations of sawteeth and other global macroscopic dynamics of tokamak plasmas
journal, January 2012

Studies of Internal Disruptions and m = 1 Oscillations in Tokamak Discharges with Soft—X-Ray Tecniques
journal, November 1974

A method for determining a stochastic transition
journal, June 1979

  • Greene, John M.
  • Journal of Mathematical Physics, Vol. 20, Issue 6
  • DOI: 10.1063/1.524170

The role of stochasticity in sawtooth oscillations
journal, March 1992

Area preserving nontwist maps: periodic orbits and transition to chaos
journal, March 1996

  • del-Castillo-Negrete, D.; Greene, J. M.; Morrison, P. J.
  • Physica D: Nonlinear Phenomena, Vol. 91, Issue 1-2
  • DOI: 10.1016/0167-2789(95)00257-X
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