Propagation of magnetic island due to self-induced zonal flow

Abstract

We have investigated the propagation of magnetic island caused by the drift-tearing mode by numerically solving a reduced set of two-fluid equations 1) . It is found that the island propagates into the ion diamagnetic direction when the island growth is saturated, and the propagation velocity becomes small as the viscosity increases. We have found that the island phase velocity is approximately same as the E × B flow averaged inside the island at the saturation state. In Figure 1 the total E × B flow velocity and each Fourier component �v (m) E � = �∂ x φ m e i2πmy � from m = 0 to m = 2 at saturation state are shown as a function of the viscosity. When the viscosity is around 5 × 10 −5 , excitation of m = 1 mode is comparable to that of the m = 0 mode, and both modes affect the direction of the averaged E × B flow. Since the signs of zonal flow and other modes are opposite, the propagation directinon of the island is determined by the competition between them. The zonal flow component is slightly larger than other modes, and thus the total E × B flow directs toward the ion diamagnetic direction. It is observed that the averaged E × B flow velocity monotonically decreases as the viscosity reduces. The contribution of the zonal flow to the averaged E × B flow becomes dominant to those of other modes when the viscosity is smaller than 10 −5 . This indicates that the self-induced zonal flow plays an important role in determining the propagation direction when the viscosity is small. We have examined the generation mechanism of the zonal flow and found that the contribution of each stress depends on the viscosity. Figure 2 plots contributions of each stress to zonal flow generation at saturation state as a function of the viscosity. The sum of contributions from the Reynolds stress �v (R) 0 �, the Maxwell stress �v (M ) 0 � and the viscous stress �v (V ) 0 � is also plotted as a reference. Note that all contributions are averaged inside the island. The Reynolds stress is positive so that it forces the zonal flow into the equilibrium electron diamagnetic direction in all viscoisty regimes. On the contrary, the direction of the flow due to the Maxwell stress shows monotonically decreasing function with respect to the viscosity. When the viscosity is small, the Reynolds stress generates the zonal flow in the electron diamagnetic direction and the Maxwell stress almost cancels out the flow generation by the Reynolds stress. The small difference between them drives the flow in the electron diamagnetic direction. The flow velocity driven by the ion diamagnetic stress is negative so that it directs in ion diamagnetic direction. The direction of the flow due to the Maxwell stress is negative for small viscosity cases and is positive for large viscosity cases. The flow velocity driven by viscous stress is negative and is very small when the viscosity is small. The balance of these stresses depends on the viscosity. When the viscosity is small, the Reynolds stress and the Maxwell stress almost cancel out each other, and ...

Magnetic island evolution in hot ion plasmas

“…This last case differs from the simulations of Ref. 34 and from the simulations of Ref. 30 having negligible electron viscosity in two ways.…”

“…For large islands (W $ 40q s ), this is in agreement with experimental observations 33 and with numerical results. 30,34 For intermediate-size islands (W=q s $ 5 À 10) comparable to the observed "seed" islands for NTM, however, the propagation frequency and the polarization current are still poorly understood. Analytically, such islands fall between the hypersonic and sonic regimes of Ref.…”

Modelling of (2,1) NTM dynamics with flow in JET advanced scenarios

“…This equilibrium flow generation also exists in simulations with anisotropic viscosity, and is therefore associated with the low perpendicular Prm. The origin of this flow is different from the zonal flow generated by drift-island which was found to a structure with respect to the resonant surface [34]. It has more similarity with the radial structure of toroidal velocity generated by turbulence, as described in [35] for example, although the precise mechanism of flow generation may be different in our case.…”

Gyrofluid simulations of collisionless reconnection in the presence of diamagnetic effects

“…We also note that, in spite of the fact that, in the linear phase, the islands exhibited very little rotation for these parameters, in the nonlinear regime, upward shifts of the O-points are present, in particular in the case v * = −0.4. Island propagation in the ion diamagnetic drift direction, caused either by viscosity [33,16] or by nonlinear zonal flows, [34,35] has been reported in FLR simulations of visco-resistive reconnection. An effective way to look at the nonlinear dynamics of our system is to express the model in terms of its "normal fields", suggested by the Hamiltonian structure.…”