Magnetic island deformation due to sheared flow and viscosity

Abstract

A partial differential equation for a two-dimensional magnetohydrodynamic ͑MHD͒ equilibrium with flow and viscosity is derived. The equation is used to describe the deformation of the magnetic island caused by the viscous drag of a sheared flow. The deformation is characterized by the phase gradient of the magnetic perturbation across a magnetic island. This phase gradient has been observed experimentally in electron cyclotron emission data from the DIII-D tokamak ͓J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 ͑1985͔͒.

Effect of externally applied resonant magnetic perturbations on resistive tearing modes

“…Distortion from flow shear has been expected and predicted theoretically and observed experimentally in [19,20]. Figures 9(c) and 9(d) indicate that the small locked island decouples from the plasma flow, and there is strong plasma vorticity in the island region.…”

“…The classical tearing mode stability in low β plasmas has been investigated in [18]. In recent years, the effect of plasma flow and its shear on the tearing mode stability were also studied [19][20][21][22]. As complicated mechanisms are involved in determining the mode amplitude, a better understanding of the island physics is necessary.…”

A data acquisition system for real-time magnetic equilibrium reconstruction on ASDEX Upgrade and its application to NTM stabilization experiments

“…This would suggest that a small offset may need to be introduced for pre-emptive stabilization experiments using the normalized radius of the rational flux surface calculated by the GradShafranov solver. Modeling has shown that the deformation of the magnetic island caused by the viscous drag of the sheared flow is consistent with electron temperature fluctuation measurements on DIII-D [57]. An additional point for understanding the need for a pre-programmed offset could be related to the uncertainty in the absolute value of the toroidal magnetic field.…”

Linear and nonlinear effect of sheared plasma flow on resistive tearing modes

“…As shown in Ref. 17, the velocity profile is crucial in determining the effect of flow shear on the tearing mode stability. However, most of the previous numerical results are obtained based on a narrow flow shear layer around the rational surface, which is substantially different from the actual rotation velocity profile of tokamak plasma.…”

“…[13][14][15] In the nonlinear phase, the flow shear is found to decrease the saturated island width 16 and leads to deformation of magnetic island. 17 Recently, the effect of velocity profiles on both TM and NTMs has been investigated in toroidal geometry, 18 and the differential rotation between rational surfaces is found to be stabilizing, while the toroidal velocity shear at the resonant surface is destabilizing. Besides, the effect of sheared plasma rotation on the stability of TM in an Ohmic regime is investigated.…”