Statistical Research of the Intermittency and Cascade of Solar Wind Turbulence Based on Analysis of PSP Measurements

By analyzing the turbulent magnetic field data from PSP, we find that: the solar wind turbulence in the inner heliosphere close to the Sun has formed the transition from multifractal intermittency at MHD scales to monofractal intermittency at kinetic scales. The order-dependent scaling exponent of the multi-order structure function shows a concave profile indicating the multifractal property at MHD scales, while its counterpart at kinetic scales shows a linear trend suggesting the monofractal property. We also find that, the closer to the sun, the more obvious the concave profile of the scaling exponent in the inertial range, which indicates that the multifractal characteristic of the magnetic field turbulence intermittency is also more evident when getting closer to the Sun.

Based on the Castaing description of the probability distribution function(PDF) of the disturbance difference, the key parameters(μ & λ^2) of the Castaing function are estimated as a function of scale. We find that: (1) when close to the sun (R~0.17 AU), the break point of μ is about 0.2 second, and the peak point of λ^2 is about 0.6 second, the two of which are about three times different in scale; (2) when far from the sun (R~0.8 AU), the break point of μ is about 1 second and the peak point of λ^2 is about 3 seconds, the two of which are also about three times different in scale. We also point out that the profiles (including the break/peak position) of both the parameters (μ & λ^2) along with the scale together determine the profile (including the spectral breaks) of the power spectrum.

Following the PP98 model function of incompressible MHD turbulent cascade rate (εZ), we first compared the cascade rate εZ with εB=<δB^3>/τ at the distance close to the sun, we find that the two trends over scales are in good agreement with one another. We therefore suggest that, to some extent (e.g. in the inertial region), εB=<δB^3>/τ can be used as a proxy of the cascade rate εZ. For the first time, by statistical analysis, we obtained that εB satisfies the following relation with the scale and the heliocentric distance: εB=((τ/τ0)^α)((r/r0)^β). In the inertial range, α changes from about -0.5 to about 0.5 as r increases from 0.17 AU to 0.81 AU, and β is about 6.4; in the kenetic range, when r increases from 0.17 AU to 0.25 AU, α keeps at about 2, and β is about 12.8. The εB(τ,r) expression given in this work, is believed to help understanding the transport and cascade processes of solar wind turbulence in the inner heliosphere. 

Corresponding author:
Jiansen HE, jshept@pku.edu.cn

Acknowledgements:
We would like to thank the PSP team for providing the data of PSP to the public.