Radial evolution of the wave-vector anisotropy of solar wind turbulence between 0.3 and 1 AU

We present observations of the power spectral anisotropy in wave-vector space of solar wind turbulence, and study how it evolves in interplanetary space with increasing heliocentric distance. For this purpose we use magnetic field measurements made by the Helios-2 spacecraft at three positions between 0.29 and 0.9 AU. To derive the power spectral density (PSD) in $(k_\parallel, k_\bot)$-space based on single-satellite measurements is a challenging task not yet accomplished previously. Here we derive the spectrum $\rm{PSD}_{\rm{2D}}$($\rm{k}_\parallel$, $\rm{k}_\bot$) from the spatial correlation function $\rm{CF}_{\rm{2D}}(r_\parallel, r_\bot)$ by a transformation according to the projection-slice theorem. We find the so constructed PSDs to be distributed in k-space mainly along a ridge that is more inclined toward the $\rm{k}_\bot$ than $\rm{k}_\parallel$ axis, a new result which probably indicates preferential cascading of turbulent energy along the $\rm{k}_\bot$ direction. Furthermore, this ridge of the distribution is found to gradually get closer to the $\rm{k}_\bot$ axis, as the outer scale length of the turbulence becomes larger while the solar wind flows further away from the Sun. In the vicinity of the $\rm{k}_\parallel$ axis, there appears a minor spectral component that probably corresponds to quasi-parallel Alfv\'enic fluctuations. Their relative contribution to the total spectral density tends to decrease with radial distance. These findings suggest that solar wind turbulence undergoes an anisotropic cascade transporting most of its magnetic energy towards larger $\rm{k}_\bot$, and that the anisotropy in the inertial range is radially developing further at scales that are relatively far from the ever increasing outer scale

Proton Heating in Solar Wind Compressible Turbulence with Collisions between Counter-propagating Waves

Magnetohydronamic turbulence is believed to play a crucial role in heating the laboratorial, space, and astrophysical plasmas. However, the precise connection between the turbulent fluctuations and the particle kinetics has not yet been established. Here we present clear evidence of plasma turbulence heating based on diagnosed wave features and proton velocity distributions from solar wind measurements by the Wind spacecraft. For the first time, we can report the simultaneous observation of counter-propagating magnetohydrodynamic waves in the solar wind turbulence. Different from the traditional paradigm with counter-propagating Alfv\'en waves, anti-sunward Alfv\'en waves (AWs) are encountered by sunward slow magnetosonic waves (SMWs) in this new type of solar wind compressible turbulence. The counter-propagating AWs and SWs correspond respectively to the dominant and sub-dominant populations of the imbalanced Els\"asser variables. Nonlinear interactions between the AWs and SMWs are inferred from the non-orthogonality between the possible oscillation direction of one wave and the possible propagation direction of the other. The associated protons are revealed to exhibit bi-directional asymmetric beams in their velocity distributions: sunward beams appearing in short and narrow patterns and anti-sunward broad extended tails. It is suggested that multiple types of wave-particle interactions, i.e., cyclotron and Landau resonances with AWs and SMWs at kinetic scales, are taking place to jointly heat the protons perpendicularly and parallel