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

We investigate properties of large-scale solar wind Alfv & eacute;nic fluctuations and their evolution during radial expansion. We assume a strictly radial background magnetic field B parallel to R, and we use two-dimensional hybrid (fluid electrons, kinetic ions) simulations of balanced Alfv & eacute;nic 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 similar to const. spatially in the plasma. We show that within the constraint of spherical polarization, variations in the radial component of the magnetic field, B-R lead to a simple relation between delta B-R and delta B = |delta B| as delta B-R similar to delta B-2/(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, delta B similar to B, this causes local magnetic field reversals, consistent with solar wind switchbacks.