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Title: Two-fluid tearing mode instability in cylindrical geometry

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:
DEFG02-91-ER54109, DEFC02-08ER54969
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 7; Related Information: CHORUS Timestamp: 2018-02-15 00:20:17; Journal ID: ISSN 1070-664X
American Institute of Physics
Country of Publication:
United States

Citation Formats

Ito, Atsushi, and Ramos, Jesús J. Two-fluid tearing mode instability in cylindrical geometry. United States: N. p., 2017. Web. doi:10.1063/1.4986116.
Ito, Atsushi, & Ramos, Jesús J. Two-fluid tearing mode instability in cylindrical geometry. United States. doi:10.1063/1.4986116.
Ito, Atsushi, and Ramos, Jesús J. 2017. "Two-fluid tearing mode instability in cylindrical geometry". United States. doi:10.1063/1.4986116.
title = {Two-fluid tearing mode instability in cylindrical geometry},
author = {Ito, Atsushi and Ramos, Jesús J.},
abstractNote = {},
doi = {10.1063/1.4986116},
journal = {Physics of Plasmas},
number = 7,
volume = 24,
place = {United States},
year = 2017,
month = 7

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on June 27, 2018
Publisher's Accepted Manuscript

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  • 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.more » 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.« less
  • The saturation of the tearing mode instability is described within the standard framework of reduced magnetohydrodynamics in the case of an r-dependent or uniform resistivity profile. Using the technique of matched asymptotic expansions, where the perturbation parameter is the island width w, the problem can be solved in two ways: with the so-called flux coordinate method, which is based on the fact that the current profile is a flux function, and with a new perturbative method that does not use this property. The latter is applicable to more general situations where an external forcing or a sheared velocity profile aremore » involved. The calculation provides a new relationship between the saturated island width and the {delta}{sup '} stability parameter that involves a ln w/w{sub 0} term, where w{sub 0} is a nonlinear scaling length that was missing in previous work. It also yields the modification of the equilibrium magnetic-flux function.« less
  • The effect of sheared equilibrium plasma rotation on the stability of tearing modes in an Ohmic (low plasma {beta}) regime is investigated. It is found, by means of numerical MHD simulations in a cylindrical geometry, that plasma rotation in the equivalent toroidal direction can result either in the increase or in the decrease of the instability growth rate. Perpendicular plasma viscosity and plasma rotation shear at the modes' rational surface play a key role on assessing the effect of shear flow. While destabilizing for low viscosity plasmas (ratio of the resistive to viscous diffusion time scales {tau}{sub R}/{tau}{sub V}<<1), formore » viscous plasmas ({tau}{sub R}/{tau}{sub V}>1) shear flow reduces the growth rate. Above a given threshold in the rotation shear (that depends on the ratio {tau}{sub R}/{tau}{sub V}) a tearing mode, unstable in the absence of rotation, can be stabilized. The effect of sheared toroidal flow on mode stability, in both viscosity regimes that are considered in the paper, is qualitatively independent of the aspect ratio.« less
  • The effect of cylindrical neutral sheet geometry on the tearing-mode (disruptive) instability is studied in detail. The instability growth rates are found for all the pertinent cases. Cylindrical effects come into play when the distance from the neutral sheet to the axis is small in comparison with the characteristic thickness of the sheet. The ultimate result is that the electron instability mode is replaced by an ion mode. These results are of interest in connection with the study of the plasma stability in devices of the Astron type and in magnetospheres like that of Uranus.