Nonlinear coupling of tearing modes with self-consistent resistivity evolution in tokamaks

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Abstract
The nonlinear interaction of tearing modes of different helicity in tokamaks is studied for realistic values of resistivity and parallel heat conduction. The self‐consistent evolution of the resistivity is taken into account through the electron heat conduction equation. For equilibrium q profiles inferred from electron temperature profiles measured before a tokamak disruption, the essential result is that the (m=2;n=1) mode nonlinearly destabilizes other modes on a rapid time scale. Because of the development of magnetic islands of different helicity, the toroidal current density is severely deformed. These islands overlap and field lines become stochastic in a sizable plasma volume, flattening the temperature profile in this region through parallel heat transport. The deformation of the toroidal current produces a rapid decrease in the self‐inductance of the plasma, and the voltage at the limiter decreases, becoming increasingly negative. An extensive survey of equilibria and initial conditions has been conducted and a simple prescription for their nonlinear stability properties is given.