An Analytical Model of Turbulence in Parker Spiral Geometry and Associated Magnetic Field Line Lengths

Abstract

Understanding the magnetic connections from the Sun to interplanetary space is crucial for linking in situ particle observations with the solar source regions of the particles. A simple connection along the large-scale Parker spiral magnetic field is made complex by the turbulent random walk of field lines. In this paper, we present the first analytical model of heliospheric magnetic fields where the dominant 2D component of the turbulence is transverse to the Parker spiral. The 2D wave field is supplemented with a minor wave field component that has asymptotic slab geometry at small and large heliocentric distances. We show that turbulence spreads field lines from a small source region at the Sun to a 60° heliolongitudinal and heliolatitudinal range at 1 au, with a standard deviation of the angular spread of the field lines of 14°. Small source regions map to an intermittent range of longitudes and latitudes at 1 au, consistent with dropouts in solar energetic particle intensities. The lengths of the field lines are significantly extended from the nominal Parker spiral length of 1.17 au up to 1.6 au, with field lines from sources at and behind the west limb considerably longer than those closer to the solar disk center. We discuss the implications of our findings for understanding charged particle propagation and the importance of understanding the turbulence properties close to the Sun.

Solar Energetic Particle event onsets at different heliolongitudes: The effect of turbulence in Parker Spiral Geometry

“…which describes the evolution of the variance of the diffusing particle population, with diffusion coefficient of κ φ and initial distribution being a Gaussian with standard deviation of σ FL . A fit done by eye gives σ FL = 13 • , which corresponds to the standard deviation of the meandering magnetic field line distribution obtained for our turbulence parameters in Laitinen et al (2023), and particle longitudinal diffusion coefficient κ φ = (3.6 • ) 2 /hr (orange curve). The close match between the two curves shows that the longitudinal evolution of the particle distribution can be described as diffusion of particles from an initial distribution that is determined by the random-walk of field lines as they traverse the distance between the Sun and 1 au.…”

“…In a more recent work, we introduced a novel Parker spiral geometry turbulence model, where for the first time the dominant 2D turbulence component wave modes are 2-dimensional with respect to the Parker spiral background magnetic field (Laitinen et al 2023). Analysis of field-line lengths using this model agreed with the asymmetric distribution of field line lengths found by the random-walk model of Laitinen & Dalla (2019).…”

“…We investigate the onset time of the simulated SEP event at 1 au further in Figure 3, where we define the onset time as the first time the SEP intensity exceeds a threshold of 1% of the global peak intensity of the simulated event, n = 1.5 particles/ (s • ) at φ = −52 • at 1 au. We further convert the onset time to an apparent path length (solid blue curve in Figure 3), for comparison with the field line lengths obtained in Laitinen et al (2023) for the same turbulence parameters as in this study (contour lines, with the dashed black line showing the mean field line length), and the nominal Parker spiral length (the horizontal red solid line).…”

“…We modified our Parker Spiral full-orbit 3D test particle code (Dalla & Browning 2005;Marsh et al 2013) to include, in addition to the Parker spiral field, a turbulent magnetic field component. The turbulence model, fully described in Laitinen et al (2023), is dominated by a transverse 2D component where the wavenumber vector and the magnetic field vector are normal to each other, and normal to the background Parker spiral field. In addition to the 2D component, also a slab-like component is included.…”

“…In this paper, we use the same parametrisation of the solar wind and turbulence as in Laitinen et al (2023). The Parker spiral magnetic field is parametrised by the magnetic field at 1 r of 1.78 gauss, the solar wind velocity v sw = 400 km/s and solar angular rotation rate Ω = 2.86533 × 10 −6 rad s −1 .…”