Stochastic properties of the magnetic field lines in the presence of current sheets

The process of separatrix broadening under the action of periodic perturbations is investigated in the case when the equilibrium magnetic configuration contains current sheets. The change of the magnetic field topology due to the presence of current sheets is discussed, and compared to the case of the standard figure-eight separatrix. In this case, the Hamiltonian structure of the the magnetic field separatrix modifies due to the presence of Y-points instead of X-points. Contrary to the case of X-points, the period of the motion is always finite, and experiences a finite jump when the trajectory in the phase plane crosses the separatrix. This fact leads to the appearance of a stochastic layer. This phenomenon is of relevance in the analysis of the processes arising in the nonlinear stage of the m=1 mode instability in a tokamak magnetic field.