Topological Formation of Small Scales in Magnetohydrodynamics: A Fast Dissipation Mechanism

Abstract

The dissipation of Alfve n wave packets propagating in an inhomogeneous three-dimensional magnetic eld is numerically studied in the Wentzel-Kramers-Brillouin (WKB) approximation. The dissipation rate is found to scale proportionally to the logarithm of viscosity and/or resistivity, i.e., much faster than the scaling found for two-dimensional congurations (phase mixing, resonance absorption). This phenomenon is related to the exponential separation of neighboring rays ; estimations of the corresponding rate are consistent with the behavior of the Kolmogorov entropy in this kind of structure. The scaling law is the e-folding dissipation time and S is the Reynolds number) holds not only in an irregular t d P ln S (t d magnetic eld (which was studied by Similon & Sudan), but is also veried in quasi-uniform magnetic structures, which contain very small chaotic regions. This study can apply to the heating of low-collision plasmas, e.g., in astrophysical contexts such as the solar corona.