Alfvénic fluctuations in the expanding solar wind: Formation and radial evolution of spherical polarization

We investigate properties of large-scale solar wind Alfvénic fluctuations and their evolution during radial expansion. We assume a strictly radial background magnetic field B∥R, and we use two-dimensional hybrid (fluid electrons, kinetic ions) simulations of balanced Alfvénic turbulence in the plane orthogonal to B; the simulated plasma evolves in a system comoving with the solar wind (i.e., in the expanding box approximation). Despite some model limitations, simulations exhibit important properties observed in the solar wind plasma: Magnetic field fluctuations evolve toward a state with low-amplitude variations in the amplitude B=|B| and tend to a spherical polarization. This is achieved in the plasma by spontaneously generating field aligned, radial fluctuations that suppress local variations of B, maintaining B∼ const. spatially in the plasma. We show that within the constraint of spherical polarization, variations in the radial component of the magnetic field, BR lead to a simple relation between δBR and δB=|δB| as δBR∼δB2/(2B), which correctly describes the observed evolution of the rms of radial fluctuations in the solar wind. During expansion, the background magnetic field amplitude decreases faster than that of fluctuations so that their the relative amplitude increases. In the regime of strong fluctuations, δB∼B, this causes local magnetic field reversals, consistent with solar wind switchbacks.