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The linear theory of current-driven resistive modes is presented in terms of the ballooning formalism. which employs the extended poloidal angle as the independent variable. This variable is proportional to the radial wave number. In the vicinity of the singular boundary layer. this formalism is applied to modes with high as well as with low poloidal mode numbers.The M H D solutions in the external region impose singular boundary conditions on the inner solutions. which must be satisfied near the origin of the extended variable. This is in contrast with coordinate space where they are expressed in integral form. These conditions are characterized by a single parameter which is assumed to be known.The collisional tearing and Alfven modes and them = 1 internal kink mode are obtained from a common dispersion relation. This is also the case for the semi-collisional tearing and .Alfven modes. The structure of the modes in k,-space as well as in coordinate space is discussed.
The m=1 kink mode is investigated in the high temperature regime where the width of the singular layer is determined by the mean ion gyroradius. This regime is reached in a number of present-day fusion experiments with strong auxiliary heating. A dispersion relation that contains the full kinetic response of the ions is derived and analyzed. The growth rates are larger than the corresponding ones obtained from fluid theory. Diamagnetic stabilization is weaker than in the fluid case. Ion temperature gradients are shown to be stabilizing at low values of the diamagnetic frequency and destabilizing at large values.
The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. Regions where the magnetic field is stochastic exist next to regions where the field is more regular. In regions between stochastic layers and between a stochastic layer and an island structure, the field of the finite time Lyapunov exponent (FTLE) shows a structure with ridges. These ridges, which are special gradient lines that are transverse to the direction of minimum curvature of this field, are approximate Lagrangian coherent structures (LCS) that act as barriers for the transport of field lines.
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