(TH/P3-11) Dynamical origin of shear flow induced modifications of nonlinear magnetic islands

Abstract.  The nonlinear evolution of magnetic islands due to unstable classical or neoclassical tearing modes is a topic of much current interest particularly in the context of confinement limits for long pulse experiments in superconducting tokamaks. The stability characteristics of these resistive modes can be strongly affected by the presence of equilibrium plasma flows and recent numerical investigations employing a fully toroidal code based on generalized reduced MHD equations have revealed a number of interesting results. It has been found that differential flow provides a strong stabilizing influence leading to lower saturated island widths for the classical tearing mode and reduced growth rates for the neoclassical tearing mode. The effect of velocity shear is found to depend on the sign of the shear at the mode resonant surface with negative shear providing a stabilizing effect and positive shear acting in a destabilizing fashion. In this paper we present a detailed analytic understanding of these results through model calculations that trace the dynamical origin of the various flow induced effects. To assess the changes in the outer layer dynamics we calculate the modifications in the parameter delta prime from a general set of ideal MHD equations that include inertial contributions of flow as well as flow induced pressure profile changes. Next a generalized Rutherford model equation incorporating such a modified delta prime and shear flow contributions in the inner layer dynamics is derived and used to estimate the nonlinear saturated island widths as well as threshold conditions. Our analytic results are found to compare very favourably with the numerical findings of the toroidal reduced MHD code and should prove useful for interpreting similar numerical investigations carried out on more complex codes like NIMROD.

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