A linear model for the tearing mode of a tokamak plasma with flow and a resistive wall boundary condition

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Abstract
The tearing mode of a tokamak plasma without flow may be stabilized by the presence of a conducting wall surrounding the plasma. When the wall has a finite resistivity, its presence does not affect stability, only growth rates. If, however the plasma has a flow relative to the resistive wall, both stability and growth rates may be affected. For the cylindrical, circular cross-section tokamak the problem is formulated as a complex eigenvalue problem, with a complex eigenvalue Δ', which in the limit of vanishing flow becomes identical to the usual ‘delta prime’. The real part of Δ' describes as usual the power absorbed at the singular surface while the imaginary part describes absorption of momentum. It is found that for a plasma with shearless flow, a resistive wall has a stabilizing effect which even for relatively small flow velocities approaches that of a wall of infinite conductivity. Shear flow is found inherently destabilizing, but important only for very large flow velocities.