Anisotropies in Magnetic Field Evolution and Local Lyapunov Exponents
Authors: X.Z. Tang and A.H. Boozer
Date of PPPL Report: January 2000
Submitted to: Physics of Plasmas
The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic field embedded in a conducting flow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian ow trajectories. The local Lyapunov exponents and the characteristic direc- tions are functions of Lagrangian coordinates and time, which are completely determined once the flow field is specified. The characteristic directions that are associated with the spatial anisotropy of the problem, are prescribed in both Lagrangian and Eulerian frames. Coordinate transformation techniques are employed to relate the spatial distributions of the magnetic field, the induced current density, and the Lorentz force, which are usually followed in Eulerian frame, to those of the local Lyapunov exponents, which are naturally defined in Lagrangian coordinates.