Publication Date:
2016-10-28
Description:
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 ′ q l ( w ) , Δ A ′ ( w ) [White et al ., Phys. Fluids 20 , 800 (1977); Phys. Plasmas 22 , 022514 (2015)]. In this work, we present a simple method to calculate the quasilinear stability index Δ q l ′ rigorously, for poloidal mode number m ≥ 2 . Δ q l ′ is derived by solving the outer equation through the Frobenius method. Δ ′ q l is composed of four terms proportional to: constant Δ ′ 0 , w , w ln w , and w 2 . Δ A ′ is proportional to the asymmetry of island that is roughly proportional to w . The sum of Δ q l ′ and Δ A ′ is consistent with the more accurate expression calculated perturbatively [Arcis et al ., Phys. Plasmas 13 , 052305 (2006)]. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1 [Jardin et al ., Comput. Sci. Discovery 5 , 014002 (2012)]. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. It is also confirmed by the simulation that the Δ A ′ has to be considered in calculating island saturation.
Print ISSN:
1070-664X
Electronic ISSN:
1089-7674
Topics:
Physics
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