Nonlinear dynamics of the m=1 kink-tearing instability in a modified magnetohydrodynamic model

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Abstract
A theory is given for the nonlinear dynamical evolution of the collisionless m=1 kink‐tearing instability, including the effects of electron inertia and electron pressure gradient in a generalized Ohm’s law. It is demonstrated that electron pressure gradients can cause near‐explosive growth in the nonlinear regime of a thin m=1 island. This near‐explosive phase is followed by a rapid decay phase as the island width becomes comparable to the radius of the sawtooth region. An island equation is derived for the entire nonlinear evolution of the instability, extending recent work on the subject [X. Wang and A. Bhattacharjee, Phys. Rev. Lett. 70, 1627 (1993)] to include the effects of both electron inertia and electron pressure gradient. Comparisons are made with experimental data from present‐day tokamaks. It is suggested that the present model not only accounts for fast sawtooth crashes, but also provides possible explanations for the problems of sudden onset and incomplete reconnection that have been, heretofore, unexplained features of observations.