Nonlinear saturation of ideal interchange modes in a sheared magnetic field

Pressure-driven ideal modes cannot completely interchange flux tubes of a sheared magnetic field; instead, they saturate, forming new helical equilibria. These equilibria are studied both analytically and numerically with reduced MHD equations in a flux conserving Lagrangian representation. For unstable localized modes, the structure of the nonlinear layer generated around the resonant flux surface depends on the value of Mercier parameter D sub M. Its width is found to be proportional to the position of the inflection point on the linear eigenfunction. Perturbed surfaces in equilibrium always have folds, i.e., areas where the direction of the original reduced magnetic field is reserved. But only far from the instability threshold does the internal structure of the nonlinear layer resemble bubble formation. The appearance of sheet currents and island-like structures along the resonant flux surface may be of interest for the description of forced reconnection in models with finite resistivity. Analytic results are found to be in agreement with 2-D numerical simulations. The case of ballooning instability is included by representing nonlocal driving terms through the matching parameter (Delta prime), which defines the outer boundary conditions for the interchange layer.