Nonlinear asymmetric tearing mode evolution in cylindrical geometry
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.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC02-09CH11466; SC0004125
- OSTI ID:
- 1335168
- Alternate ID(s):
- OSTI ID: 1330280
- Report Number(s):
- 5321; PHPAEN
- Journal Information:
- Physics of Plasmas, Vol. 23, Issue 10; ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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