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 M3DC1. 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:

 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 1070664X; PHPAEN
 Grant/Contract Number:
 AC0209CH11466; SC0004125
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: 10; Journal ID: ISSN 1070664X
 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 M3DC1. 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 = {1070664X},
number = 10,
volume = 23,
place = {United States},
year = {2016},
month = {10}
}
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