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Title: Numerical analysis of two-fluid tearing mode instability in a finite aspect ratio cylinder

ORCiD logo [1];  [2]
  1. National Institute for Fusion Science, National Institutes of Natural Sciences, 322-6 Oroshi-cho, Toki 509-5292, Japan
  2. Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
DEFC02-08ER54969; DEFG02-91-ER54109
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 1; Related Information: CHORUS Timestamp: 2018-01-22 11:48:32; Journal ID: ISSN 1070-664X
American Institute of Physics
Country of Publication:
United States

Citation Formats

Ito, Atsushi, and Ramos, Jesús J. Numerical analysis of two-fluid tearing mode instability in a finite aspect ratio cylinder. United States: N. p., 2018. Web. doi:10.1063/1.5009389.
Ito, Atsushi, & Ramos, Jesús J. Numerical analysis of two-fluid tearing mode instability in a finite aspect ratio cylinder. United States. doi:10.1063/1.5009389.
Ito, Atsushi, and Ramos, Jesús J. 2018. "Numerical analysis of two-fluid tearing mode instability in a finite aspect ratio cylinder". United States. doi:10.1063/1.5009389.
title = {Numerical analysis of two-fluid tearing mode instability in a finite aspect ratio cylinder},
author = {Ito, Atsushi and Ramos, Jesús J.},
abstractNote = {},
doi = {10.1063/1.5009389},
journal = {Physics of Plasmas},
number = 1,
volume = 25,
place = {United States},
year = 2018,
month = 1

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on January 22, 2019
Publisher's Accepted Manuscript

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  • A code has been developed for calculating magnetohydrodynamic equilibria with poloidal-sonic flow and finite Larmor radius effects in high-beta tokamaks using an inverse aspect-ratio expansion and a reduced two-fluid model. The Grad-Shafranov equations governing the first- and second-order poloidal fluxes can be expressed in terms of five free profiles of the first-order poloidal flux. Sample equilibria, illustrating behaviors such as the deviation of pressure contours from the flux surfaces, and the criteria for the presence of the 'poloidal-sonic singularity' are presented.
  • A numerical simulation is performed to investigate the nonlinear phase of the collisionless tearing mode instability. The results are found consistent with the expectation from the theory by Galeev, Coroniti, and Ashour-Abdalla, who predicted the existence of an explosive phase of the instability caused by the magnetization of particles by the perturbed component of the magnetic field normal to the neutral sheet. Since electrostatic effects on the evolution of the instability are neglected a priori in the present numerical simulation, we do not obtain the final answer. But there seems to be a good possibility of the explosive evolution ofmore » the tearing mode instability in its nonlinear stage. It is argued that for a sufficiently long-wavelength perturbation the nonlinear explosive evolution can become faster than the nonlinear coalescence mode. It is further noted that the particles are heated adiabatically within the magnetic islands by the one-dimensional compression process.« less
  • The generalized Green's function method proposed by Miller and Dewar (J. Comput. Phys. 66, 356 (1986)) and Pletzer and Dewar in Computational Techniques Applications: CTAC-89, Proceedings, Int. Conf, Brisbane, 1989, edited by WL. Hogarth and B. J. Noye, in press, for solving the singular differential equation occurring in the finite [beta] tearing mode problem has been tested numerically on a model differential equation. This method is compatible with a variational formulation of the problem and gives accurate numerical answers with high powers of convergence with respect to the number of grid points used. When the method is extended to themore » more physically relevant two-sided problem at moderate pressure gradients, a less stringent condition on the Frobenius expansion is required because the principal value of the otherwise divergent integrals associated with the method is shown to exist.« less
  • The nonlinear interaction of tearing modes centered on different resonant surfaces in a low-{beta} tokamak is studied. Center manifold theory is applied to the reduced equations of resistive magnetohydrodynamics, including the electron energy equation. For the equilibrium current profile a polynomial parametrized by the values of shear and safety factor at several given radii is chosen. Amplitude equations describing the asymptotic time behavior of interacting modes are obtained. The coefficients of these equations depend on the mode numbers of the modes involved and on the parameters of the problem. They were calculated for the interaction of the (2,1)- and themore » (3,2)-tearing mode. The dependence of the corresponding solutions on equilibrium parameters and transport coefficients is investigated. {copyright} {ital 1996 American Institute of Physics.}« less