Field-Line Dispersal and the Death of Lyapunov Exponents

Statistics

Scientific paper

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2114 Energetic Particles (7514), 2134 Interplanetary Magnetic Fields, 7803 Active Perturbation Experiments, 7859 Transport Processes, 7863 Turbulence (4490)

Scientific paper

Turbulent magnetic field lines have long been thought to be diverging from each other (or converging towards each other) at exponential rates known as Lyapunov exponents. It is now shown that in a turbulent magnetized plasma, subexponential divergence (convergence) and diffusive twist better characterize the dispersal of magnetic field lines than do the usual Lyapunov exponents or exponentiation rates. Pairs of nearby magnetic field lines diverge (converge) sub-exponentially rather than exponentially, and as soon as they diverge (converge) by a significant amount, they also experience substantial twist or rotation relative to each other. More distant magnetic field lines follow the same dynamics of twist and sub-exponential divergence (convergence), though at a slower rate. It is also found that on a very broad range of separation length scales, the statistics of the field-line separations are log-normal rather than Gaussian. Most importantly, the field-line dispersal can now be evaluated quantitatively and accurately. These results will be presented and some implications for the dispersal and mixing of solar wind magnetic field lines and particles will be discussed.

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