Distributions of magnetic field orientations in the turbulent solar wind

The Parker spiral model for interplanetary magnetic fields gives a first-order approximation to the magnetic field geometry in the solar wind (SW). How much real magnetic fields deviate from a Parker spiral in the turbulent SW, however, remains a broadly open question from the theory-modeling viewpoint. By generalizing to three-dimensional space a method, recently introduced, that allows for the simulation of realistic turbulent field lines with as many as 1015 turbulent modes, the distributions of the magnetic field orientations relative to the Parker spiral fields or mean fields are computed in quiet slow and fast SW at 0.3 and 1 AU. A comparison of these distributions with distributions determined from Helios 2 in situ data shows excellent agreement, further confirming the validity of the method. The angle distributions in three-dimensional space are relatively broad and peak away from 0 degrees. The locations of these peaks, anywhere between 5 degrees and 65 degrees on timescales of 1.5 minutes to 10 hr in quiet wind within 1 AU from the Sun, are studied as a function of the SW conditions, length of the field segments, and realization of the turbulent field. Analytical predictions for the statistical distributions of field-line orientations are also made and compared to the numerical results.