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

Title: Nonlinear asymmetric tearing mode evolution in cylindrical geometry

Abstract

The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ'(w). For a low beta plasma without external heating, Δ'(w) can be approximately described by two terms, Δ' ql(w), Δ'A(w). In this work, we present a simple method to calculate the quasilinear stability index Δ'ql rigorously, for poloidal mode number m ≥ 2. Δ' ql is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ' 0, w, wlnw, and w2. Δ' A is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δ' ql and Δ' A is consistent with the more accurate expression calculated perturbatively. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. Lastly, it is also confirmed by the simulation that the Δ' A has to be considered in calculating island saturation.

Authors:
ORCiD logo [1];  [1]; ORCiD logo [1]; ORCiD logo [1];  [1]
  1. 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
OSTI Identifier:
1335168
Alternate Identifier(s):
OSTI ID: 1330280
Report Number(s):
5321
Journal ID: ISSN 1070-664X; PHPAEN
Grant/Contract Number:  
AC02-09CH11466; SC0004125
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 10; 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

Citation Formats

Teng, Qian, Ferraro, N., Gates, David A., Jardin, Stephen C., and White, R. B. Nonlinear asymmetric tearing mode evolution in cylindrical geometry. United States: N. p., 2016. Web. doi:10.1063/1.4966243.
Teng, Qian, Ferraro, N., Gates, David A., Jardin, Stephen C., & White, R. B. Nonlinear asymmetric tearing mode evolution in cylindrical geometry. United States. doi:10.1063/1.4966243.
Teng, Qian, Ferraro, N., Gates, David A., Jardin, Stephen C., and White, R. B. Thu . "Nonlinear asymmetric tearing mode evolution in cylindrical geometry". United States. doi:10.1063/1.4966243. https://www.osti.gov/servlets/purl/1335168.
@article{osti_1335168,
title = {Nonlinear asymmetric tearing mode evolution in cylindrical geometry},
author = {Teng, Qian and Ferraro, N. and Gates, David A. and Jardin, Stephen C. and White, R. B.},
abstractNote = {The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ'(w). For a low beta plasma without external heating, Δ'(w) can be approximately described by two terms, Δ'ql(w), Δ'A(w). In this work, we present a simple method to calculate the quasilinear stability index Δ'ql rigorously, for poloidal mode number m ≥ 2. Δ'ql is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ'0, w, wlnw, and w2. Δ'A is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δ'ql and Δ'A is consistent with the more accurate expression calculated perturbatively. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. Lastly, it is also confirmed by the simulation that the Δ'A has to be considered in calculating island saturation.},
doi = {10.1063/1.4966243},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 10,
volume = 23,
place = {United States},
year = {2016},
month = {10}
}

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

Save / Share:

Works referenced in this record:

A predictive model for the tokamak density limit
journal, July 2016


Saturation of the tearing mode
journal, January 1977

  • White, Roscoe B.; Monticello, D. A.; Rosenbluth, Marshall N.
  • Physics of Fluids, Vol. 20, Issue 5
  • DOI: 10.1063/1.861939

Finite-Resistivity Instabilities of a Sheet Pinch
journal, January 1963

  • Furth, Harold P.; Killeen, John; Rosenbluth, Marshall N.
  • Physics of Fluids, Vol. 6, Issue 4
  • DOI: 10.1063/1.1706761

Nonlinear growth of the tearing mode
journal, January 1973


Simulation of Large Magnetic Islands: A Possible Mechanism for a Major Tokamak Disruption
journal, December 1977


Origin of Tokamak Density Limit Scalings
journal, April 2012


Tearing mode in the cylindrical tokamak
journal, January 1973


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


Helical temperature perturbations associated with tearing modes in tokamak plasmas
journal, March 1995

  • Fitzpatrick, Richard
  • Physics of Plasmas, Vol. 2, Issue 3
  • DOI: 10.1063/1.871434

Thermal island destabilization and the Greenwald limit
journal, February 2015

  • White, R. B.; Gates, D. A.; Brennan, D. P.
  • Physics of Plasmas, Vol. 22, Issue 2
  • DOI: 10.1063/1.4913433

The tokamak density limit: A thermo-resistive disruption mechanism
journal, June 2015

  • Gates, D. A.; Brennan, D. P.; Delgado-Aparicio, L.
  • Physics of Plasmas, Vol. 22, Issue 6
  • DOI: 10.1063/1.4922472

Rigorous approach to the nonlinear saturation of the tearing mode in cylindrical and slab geometry
journal, May 2006

  • Arcis, N.; Escande, D. F.; Ottaviani, M.
  • Physics of Plasmas, Vol. 13, Issue 5
  • DOI: 10.1063/1.2199208