DISPERSAL OF MAGNETIC FIELD LINES: NONLINEAR STATISTICAL THEORY AND APPLICATION TO THE SLOW SOLAR WIND

The recent result that pairs of nearby magnetic field lines diverge (converge) subexponentially rather than exponentially in a turbulent magnetized plasma is extended to a broad range of initial field-line separations. The substantial twist, Delta theta, or rotation of the magnetic field lines relative to each other, simultaneous with the field-line divergence, is also demonstrated in a more general framework. Two main regimes of field-line dispersal emerge from the more general calculation of this paper. For the longer field-line separation distances rho, for which the turbulence spectral index exceeds -1 near 3 rho(-1), the field-line spreading <(Delta rho)(2)> and mean-square cross-field displacement <(Delta r)(2)> have very similar behaviors, and both rho and Delta r have Gaussian statistics. For shorter rho, the statistics of rho become log-normal. In that regime of more moderate rho, magnetic field lines perform random walks relative to each other in the (theta, ln rho) space that become diffusive on the field-aligned distance Delta z of a few zeta(B) max {min(zeta(II), k(II)(-1) ), min[zeta(rho), (3 xi)(-1) rho], k(II) being the wavenumber where the three-dimensional turbulence spectrum becomes steeper than (k(parallel to)(2) +xi(2)k(perpendicular to)(2))(-1), xi the anisotropy parameter of the turbulence, and zeta(II) and zeta(rho) the nonlinear scales associated with k(II)(-1) and rho, respectively. In the nonlinear regime of field-line dispersal where zeta(II) or zeta(rho) determines zeta(B), the decorrelation of the field-lines' relative random walk is driven by Delta r. Application to the slow solar wind at 1AU shows that the mixing of field-line bundles starts beyond Delta z similar to 0.01-0.1 AU and occurs from the smallest transversal scales up. Another major conclusion is that the closer the magnetic field lines, the faster they rotate relative to each other.