Phase Coherence of Solar Wind Turbulence from the Sun to Earth

The transport of energetic particles in response to solar wind turbulence is important for space weather. To understand charged particle transport, it is usually assumed that the phase of the turbulence is randomly distributed (the random phase approximation) in quasi-linear theory and simulations. In this paper, we calculate the coherence index, $C_\phi$, of solar wind turbulence observed by the Helios 2 and Parker Solar Probe spacecraft using the surrogate data technique to check if the assumption is valid. Here, values of $C_\phi=0$ and $1$ indicate that the phase coherence is random and correlated, respectively. We estimate that the coherence index at the resonant scale of energetic ions ($10$ MeV protons) is $0.1$ at $0.87$ and $0.65$ au, $0.18$ at $0.29$ au, and $0.3$ ($0.35$) at $0.09$ au for super (sub)-Alfv\'enic intervals, respectively. Since the random phase approximation corresponds to $C_\phi=0$, this may indicate that the random phase approximation is not valid for the transport of energetic particles in the inner heliosphere, especially very close to the Sun ($\sim0.09$ au).