A novel computation of the linear plasma response to a resonant error field in single-fluid rotating visco-resistive MHD

Abstract This paper reexamines the linear plasma response to a static resonant error field (EF) in the single-fluid rotating visco-resistive magneto-hydrodynamic (MHD). A tearing-mode stable, rotating plasma shields a resonant static EF by a current sheet at the resonant surface. This response is encapsulated within the delta prime ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi>′</mml:mi> </mml:msup> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> ), a quantity which measures the magnitude and phase of the current sheet. However, if EF exceeds an amplitude threshold this equilibrium breaks down and a wall-locked tearing mode is formed. Several basic aspects of the problem are addressed. First, we assess the validity of the radial Fourier transform method, commonly used to solve analytically the problem, by comparison with a completely different technique. Second, we derive a new analytical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>′</mml:mi> </mml:msup> </mml:mrow> </mml:math> global formula valid in a wide range of plasma parameters. This formula describes the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>′</mml:mi> </mml:msup> </mml:mrow> </mml:math> features much better than previous asymptotic regimes modeling. Third, we derive the EF amplitude threshold for producing a locked mode, pointing out the crucial role of the neoclassical poloidal flow damping effect. The result is almost identical to recent two-fluids outcomes, showing that the choice between single-fluid and two-fluids MHD is not crucial in this specific problem.