Abstract
The linear and nonlinear stability of a nonmonotonic q profile is examined using a reduced set of magnetohydrodynamic (MHD) equations with an equilibrium, sheared toroidal flow. The reversed shear profile is shown to be unstable to a rich variety of resistive MHD modes including pressure-driven instabilities and tearing instabilities possessing a tearing/interchange character at low Lundquist number, S, and taking on a double/triple tearing structure at high S. Linear calculations show that the destabilizing effect of toroidal velocity shear on tearing modes is enhanced at finite pressure. In addition, this velocity shear decreases the stabilizing effect of finite pressure seen previously for tearing modes at high S. Nonlinear calculations show the generation of a large, m=1, n=0, Reynolds-stress-driven poloidal flow in the absence of significant flow damping. Calculations in which the poloidal flow was heavily damped show that sub-Alfvénic, sheared toroidal flows have a minimal effect on weakly coupled, localized instabilities.
Highlights
The enhanced core confinement and high neutron rate of reversed shear plasmas present a promising operating regime for future tokamaks'
This paper examines the influence of toroidal flow shear on resistive tearing mode growth rates in a finite-/3, reversed-shear plasma using a reduced set of MHD equations with a sub-Alfvhic, equilibrium toroidal flow
Because the effects of the tearing mode were hidden by the pressure-driven instability and the poloidal flow,O was reduced and the equilibrium ( n = 0) components of U and g5 were not evolved in further calculations
Summary
The enhanced core confinement and high neutron rate of reversed shear plasmas present a promising operating regime for future tokamaks'. The advective term from the vorticity equation, may be positive or negative definite This demands that the magnitude of the equilibrium flow be small enough to prevent it from entering as an energy source in nonlinear calculations, but large enough to have an effect on mode coupling. For this reason, the toroidal flow is ordered as, V'/VH* 5 .01, where V H =~ B,/(pop)1'2is the poloidal Alfv6n velocity. This ordering is sufficient to prevent toroidal flow, which was not included self-consistentlyin the equilibrium, from competing with the pressure gradient in the equilibrium momentum equation This effect appeared in the distortion of linear eigenmodes whenever the magnitude of the toroidal flow was too large. Judicious choice of the convergence parameter (timestep) permits rapid convergence to different linearly unstable eigenmodes with different growth rates
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