Magnetic flux surfaces in anisotropic three dimensional complex fields

In a turbulent state (or even in a slightly turbulent system), in contrast to a highly symmetric and well-behaved field configurations, magnetic field lines may become "ergodic", and eventually wander to infinity. Smooth and linear configurations may be very unrealistic in nature, since turbulence affects most of the astrophysical plasmas, and so simple pictures of the structure of the magnetic field may become inaccurate. The actual topology of the magnetic field can be described in terms of magnetic surfaces. We present a study of the topological aspects of magnetic surfaces in a simplified model of magnetohydrodynamics (MHD), studying fields coming from both synthetic (Gaussian) construction and from direct numerical simulations of Reduced MHD (RMHD). Here, an accurate algorithm for identification of these surfaces is presented, and their statistical properties are investigated. In particular, preliminary results find that, in turbulence, magnetic surfaces suddenly produce small scale structures, while they are advected by the field along the mean magnetic axis "z". The associated spectrum of the flux surface label acquires structure at high perpendicular wavenumbers, in a kind of topological cascade in space. Following suggestions from passive tracers and 2D MHD simulations, we computed the average thickness of the magnetic flux function "delta", as a function of z. The functional behavior of delta(z) is consistent with exponential-like behavior, which presents conceptual difficulties which we discuss, including consequences for field-line diffusion theory, turbulence, reconnection and particle energization. For example we may ask whether reconnection is a well-defined process in 3D turbulence.