Abstract
A multiple time scale derivative expansion scheme has been employed to reveal some aspects of Taylor’s relaxation theory, which states that a ‘‘slightly imperfect’’ plasma relaxes under the conservation of the overall magnetic helicity K toward a state of minimum magnetic energy. The purpose of this paper is to investigate the time evolution of K on the ideal magnetohydrodynamic (IMHD), the MHD-collision (CMHD), and resistive diffusion (RDMHD) time scales. On the ideal MHD time scale, it is found, just as expected, that K is an invariant of motion for each single flux tube. On the MHD-collision time scale Taylor’s conjecture is explicitly proven, namely that only the overall K is an invariant of motion. Finally for the resistive diffusion time scale, it is found that the time derivative is proportional to the resistivity, however, with additional terms arising from the MHD fluctuation spectrum.
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