Forced Magnetic Reconnection in Helical Plasmas

Abstract

Magnetic islands excited by resonant magnetic perturbations (RMPs) in helical plasmas are investigated. A Rutherford-type equation is coupled with the time evolution equation of the radial electric field associated with the neoclassical particle diffusion due to helically rippled magnetic fields. Using the model, bifurcation between the excitation and the annihilation of non-rotating magnetic islands are newly observed, depending on the magnitude of RMPs and the anomalous plasma viscosity. It is found that the transition between these states is triggered by the change in the radial electric field profile in the vicinity of magnetic island. Keywords: magnetic island, radial electric field, plasma rotation, neoclassical particle diffusion DOI: 10.1585/pfr.5.040Forced magnetic reconnection due to resonant magnetic perturbations (RMPs) is of great interest in magnetic fusion plasmas. Bifurcation of equilibria between with and without magnetic islands is observed in helical devices such as the LHD [1, 2] and the TJ-II [3], where the tearing mode is linearly stable. In particular, spontaneous annihilation of magnetic islands called 'self-healing' triggers the improvement of plasma confinements. Magnetic islands and stochastic layers in helical plasmas have been investigated in the context of the three-dimensional resistive magnetohydrodynamics (MHD) equilibrium [4], and mechanism of the self-healing is under investigation. Such bifurcation is also observed in tokamaks, and theoretical works reveal that poloidal and toroidal rotations of plasmas play key roles, screening the penetration of RMPs [5]. In helical plasmas, the poloidal rotation is driven by E × B and diamagnetic drifts, where radial electric fields are produced by the neoclassical particle diffusion associated with helically rippled magnetic fields [6]. Therefore, the poloidal rotation might be associated with the self-healing mechanism. In order to test this hypothesis, theoretical models including finite Lamor radius (FLR) effects, such as the neoclassical particle diffusion, are necessary.In this paper, we introduce a simple theoretical model describing the forced magnetic reconnection in helical plasmas, and the bifurcation mechanism associated with the poloidal rotation is examined.The derivation of the model equations is outlined below. We start from two-fluids equations including FLR effects based on the drift ordering [7]. Perpendicular electric current is composed of the polarization current, the diamagnetic current and currents due to anisotropic presauthor's e-mail: nishimura.seiya@lhd.nifs.ac.jp sure tensors. Neoclassical particle fluxes are perturbatively included by substituting gyrophase-averaged distribution functions given by linearized drift-kinetic equations into moment formulae of anisotropic pressure tensors. We adopt a simplified version of the radial neoclassical particle fluxes given in Ref. [8]. For parallel electric currents, we focus on the regime where the bootstrap current is less important than the inductive current. In fact, ...

Stability of Externally Driven Magnetic Islands in a Helical Plasma

“…However, influence of neoclassical transport has not been discussed so far. In our previous study, using a theoretical model, it is shown that the self-healing of islands is clearly reproduced, when the neoclassical transport-driven poloidal flows is taken into account [5]. In this paper, we report that such mechanism is actually observed in reduced fluid simulations.…”

“…In addition, the curvature driven current might be affected by non ideal effects. Based on the analytical theory [5], the shrink threshold of islands in the absence of the curvature effect is estimated as ν nc = 1.8 × 10 −4 , where the balance between the neoclassical force and the Lorentz force is essential in our parameters. This estimation is consistent with the simulations without the curvature effect.…”

Nonlinear stability of magnetic islands in a rotating helical plasma

“…[7][8][9] A different point is that the neoclassical viscosity due to the helical trapped particles is taken into account. [24][25][26][27][28] In tokamaks, the non-axisymmetric magnetic field perturbation by RMP drives the so-called neoclassical toroidal viscosity. 51 While, in stellarators, the ambient magnetic field has the considerable non-axisymmetric component (jB h j=B 0 $ 10 À1 ), which dominates the influence of RMP.…”

“…For this reason, by analogy with tokamaks, it has been attempted to explain the self-healing mechanism by the screening effect of helical trapped particle-induced neoclassical flows. [24][25][26][27][28][29] However, a problematic point is that, historically, the magnetic reconnection in stellarators (helical systems) has been investigated in the context of the curvature-driven tearing mode. The curvature-driven current perturbation, such as the resonant Pfirsch-Schl€ uter current, is excited by normal magnetic field line curvature, and magnetic islands are generated to sustain three-dimensional magnetohydrodynamics (MHD) equilibria.…”

Plasma flow healing of magnetic islands in stellarators

“…While T V0 is used to denote the "viscous" torque, it should be noted that both cross-field viscosity and neoclassical damping physics are used to calculate this contribution to the steady-state torque balance relation. 42 In the limit z ¼ 0; k f ¼ 1. In this small island limit, the viscous torque can be interpreted as the being proportional to the jump in dX a =dq across the rational surface 13 as in the standard cylindrical case.…”