Synergetic effects of <i>E × B</i> shear flow and diamagnetic flow on boundary-perturbation-driven neoclassical tearing modes

Abstract Synergetic effects of diamagnetic flow and E <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>×</mml:mo> </mml:mrow> </mml:math> B shear flow on neoclassical tearing modes (NTMs) are numerically investigated by using a two-fluid four-field model. Such seed islands are driven by the boundary perturbation rather than through core seed islands. Firstly, in the single-helicity simulations, the initial equilibrium includes the 3/2 mode with negative Δ′. The boundary perturbation can induce a driven-reconnection on the 3/2 rational surface with island width as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>w</mml:mi> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mi mathvariant="normal">Ψ</mml:mi> <mml:mi>a</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">Ψ</mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> is the boundary perturbation amplitude. When the 3/2 island widths exceed a critical value (equivalently seed island), the 3/2 NTM is triggered with a much larger island width. It is found that when diamagnetic flow is greater than a threshold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>δ</mml:mi> <mml:mi>w</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , the 3/2 mode cannot enter the NTM phase, but still keeps in the driven-reconnection saturation state. A strong positive scaling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>δ</mml:mi> <mml:mi>w</mml:mi> </mml:msub> </mml:mrow> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mi mathvariant="normal">Ψ</mml:mi> <mml:mi>a</mml:mi> <mml:mrow> <mml:mn>1.15</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> is obtained. Further increasing diamagnetic flow accelerates the early island growth due to the excitation of drift tearing mode, but reduces the saturation of the driven-reconnection. The E <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>×</mml:mo> </mml:mrow> </mml:math> B shear flow can effectively enhance or offset the suppressing effect of the diamagnetic flow depending on their co- or counter-direction. Secondly, in the multiple-helicity simulations, an extra 2/1 mode with positive Δ′ is added in the system. The 3/2 mode enters quickly the nonlinear NTM saturation due to the boundary drive, but the early growth of 2/1 mode is slow. When the 2/1 mode reaches saturation, it can suppress the 3/2 NTM to a lower level saturation. It is found that the diamagnetic flow can keep the 3/2 mode in the driven-reconnection saturation, but raise the 2/1 mode saturation. The increase of 2/1 islands can trigger the 3/2 NTM with larger 3/2 islands on the 3/2 rational surfaces. The simultaneous growth of both 2/1 and 3/2 islands generates a wider flattened region of the pressure, significantly reducing the drive of bootstrap current for the 3/2 NTM. As a result, the 3/2 NTM returns to a very low driven-reconnection level or is completely stabilized. Moreover, the synergetic effects of diamagnetic flow and E <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>×</mml:mo> </mml:mrow> </mml:math> B shear flow with fixed and unfixed profiles are also studied, and the Poincaré plots of magnetic topology evolution are illustrated to clearly understand the interaction between multiple-helicity islands.