A stochastic solar wind magnetic field model and probing its meandering nature by Energetic Electrons

Energetic electrons in impulsive events can serve as an ideal probe of solar wind magnetic field. Using a recently developed Fractonal Velocity Dispersion Analysis (FVDA), the release time at the Sun and the path length of interplanetary magnetic field can be obtained with very small uncertainties in many impulsive events. Further knowing the source location, one can examine how much do the field lines deviate from the Parker spiral.  In this work, we present an analytic model for the angular dispersion of magnetic field lines that results from the turbulence in the solar wind and at the solar source surface. The heliospheric magnetic field lines in this  model is derived from a Hamiltonian $H_{\rm m}(\mu, \phi, r)$ in which the pair of canonically conjugated variables the cosine of the heliographic colatitude $\mu$ and the longitude $\phi$. This model naturally incorporates the effect of a random footpoint motion on the source surface since such a motion is due to the zero-frequency component of the solar wind turbulence. Assuming the footpoint motion is also diffusive, it is shown that the angular diffusivity of the stochastic Parker spirals is given by the angular diffusivity of the footpoints divided by the solar wind speed and is controlled by a unique parameter which is the Kubo number. We also present some model calculations of meandering field lines resulting from stochastic footpoint motion and statistical results of the field line path length from observations. Our model and statistical results can shed lights on observations made by Parker Solar Probe and Solar Orbiter.