Physics – Plasma Physics
Scientific paper
Oct 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000aps..dppnp1072t&link_type=abstract
American Physical Society, 42nd Annual Meeting of the APS Division of Plasma Physics combined with the 10th International Congre
Physics
Plasma Physics
Scientific paper
The problem of the evolution of a passive magnetic field embedded in a chaotic flow---the kinematic dynamo problem---is of great relevance to planetary, solar, and astronomical physics. Progress can be made by transforming to Lagrangian coordinates, which move with the flow. The local growth rates of the magnetic field and of the induced current can then be estimated in terms of the finite-time Lyapunov exponents of the flow, which measure the instantaneous exponential rate of divergence of neighboring trajectories. A numerical method is presented to calculate the Lagrangian derivatives of the magnetic field, which allows comparison of the magnetic energy to the power needed to sustain its growth. It is found that the leading-order growth of the power is less than previously estimated [1], because of constraints on the asymptotic evolution of the flow arising from differential geometry [2]. [1] A.H. Boozer, Astrophys, J. 394, 357 (1992); X. Z. Tang and A. H. Boozer, Phys. Plasmas 7, 1113 (2000) [2] J.-L. Thiffeault and A. H. Boozer, submitted to Chaos (2000)
Boozer Allen
Thiffeault Jean-Luc
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