Lengths of wandering magnetic field lines in the turbulent solar wind

Charged energetic and suprathermal particles propagating in the solar wind ( SW), as in most astrophysical environments, follow magnetic field-line irregularities down to very short scales of turbulence. Their minimal path length, or path length in the absence of scattering, is determined by the length of the traced magnetic field line resolved to those scales. The lengths of turbulent field lines are investigated here as functions of resolution scale and turbulence condition in the SW. In situ measurements on board Helios 2, turbulent field-line simulations, and theory all give excellent agreement for the dependence of the turbulent length on the resolution scale, as well as for the average field-line lengthening. Close to 1 AU, the length of a turbulent field segment is increased on average by close to 50%, with even longer field lines in some slow SW streams. While in fast SW most of the field-line lengthening is due to short-scale irregularities, wandering on a 0.1 AU scale can produce in slow SW as much lengthening as irregularities on shorter scales, explaining a strong stream-to-stream variability. In solar impulsive particle events, noticeable travel delays of the first arriving particles should result from the turbulent lengthening of the magnetic field lines, with significant variations of these travel delays from one event to another.