Stickiness in double-curl Beltrami magnetic fields

The double-curl Beltrami magnetic field in the presence of a uniform mean field is considered for investigating the nonlinear dynamical behavior of magnetic field lines. The solutions of the double-curl Beltrami equation being non-force-free in nature belong to a large class of physically interesting magnetic fields. A particular choice of solution for the double-curl equation in three dimensions leads to a wholly chaotic phase space. In the presence of a strong mean field, the phase space is a combination of closed magnetic surfaces and weakly chaotic regions that slowly tends to global randomness with a decreasing mean field. Stickiness is an important feature of the mixed phase space that describes the dynamical trapping of a chaotic trajectory at the border of regular regions. The global behavior of such trajectories is understood by computing the recurrence length statistics showing a long-tail distribution in contrast to a wholly chaotic phase space that supports a distribution which decays rapidly. Also, the transport characteristics of the field lines are analyzed in connection with their nonlinear dynamical properties.