Magnetic flux ropes immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Each collision results in magnetic field line reconnection and the generation of a quasi-separatrix layer. Three-dimensional magnetic field lines are computed by conditionally averaging the data using correlation techniques. Conditional averaging is possible for only a number of rotation cycles as the field line motion becomes chaotic. The permutation entropy can be calculated from the time series of the magnetic field data (this is also done with flows) and is used to calculate the positions of the data on a Jensen–Shannon complexity map. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The Lyapunov and Hurst exponents are calculated and the complexity and permutation entropy of the flows and field components are shown throughout the volume.
Three-dimensional Cauchy-condition surface method to identify the shape of the last closed magnetic surface in the Large Helical Device