Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008apj...682.1416r&link_type=abstract
The Astrophysical Journal, Volume 682, Issue 2, pp. 1416-1435.
Astronomy and Astrophysics
Astronomy
4
Ism: Cosmic Rays, Magnetic Fields, Plasmas, Turbulence, Waves
Scientific paper
Turbulent magnetic field lines have long been thought to be diverging from each other (or converging toward each other) at exponential rates known as Lyapunov exponents. It is argued here that in a turbulent magnetized plasma, subexponential divergence (convergence) and diffusive twist better characterize the dispersal of magnetic field lines (MFLs) in the limit of the very small separations ρ than do the usual Lyapunov exponents or exponentiation rates. In that limit of the very small separations, the field-line equations give a variation rate for lnρ, not ρ, and the implied log-normality of the ρ distribution makes <(lnρ/ρ0)2> a much better probe of the exponential divergence of core MFLs. A fully nonlinear calculation shows that the separation logarithm, lnρ, and twist or rotation angle, Δθ, between pairs of MFLs diffuse with the distance Δz elapsed along the main field, as soon as Δz exceeds min(k-1II,ζII), the minimum of the parallel correlation length k-1II≡L∥∇ of the turbulent field gradients and of the associated nonlinear scale, ζII≡ζ∇, defined as the field-aligned length scale for which the mean cross-field displacement <(rζ-r0)2>1/2 reaches 21/2ξk-1II≡21/2L⊥∇, with kII the wavenumber where the turbulence spectrum becomes steeper than (k2∥+ξ2k2⊥)-1 and ξ the anisotropy parameter of the turbulence. The average growth of the core field-line separation ρ0e<(lnρ/ρ0)2>1/2=e~(Δz)1/2 along the direction of fastest growth, being subexponential, is not compatible with the definition of Lyapunov exponents. The largest exponentiation rate of the core MFLs actually decreases with the distance Δz. Application of the new nonlinear calculation to the solar wind shows a substantial MFL rotation in a plane transverse to the main field.
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