Energetic Particle Transport Across the Mean Magnetic Field: Before Diffusion

Abstract

Current particle transport models describe the propagation of charged particles across the mean field direction in turbulent plasmas as diffusion. However, recent studies suggest that at short timescales, such as soon after solar energetic particle (SEP) injection, particles remain on turbulently meandering field lines, which results in nondiffusive initial propagation across the mean magnetic field. In this work, we use a new technique to investigate how the particles are displaced from their original field lines, and we quantify the parameters of the transition from field-aligned particle propagation along meandering field lines to particle diffusion across the mean magnetic field. We show that the initial decoupling of the particles from the field lines is slow, and particles remain within a Larmor radius from their initial meandering field lines for tens to hundreds of Larmor periods, for 0.1-10 MeV protons in turbulence conditions typical of the solar wind at 1 au. Subsequently, particles decouple from their initial field lines and after hundreds to thousands of Larmor periods reach time-asymptotic diffusive behavior consistent with particle diffusion across the mean field caused by the meandering of the field lines. We show that the typical duration of the prediffusive phase, hours to tens of hours for 10 MeV protons in 1 au solar wind turbulence conditions, is significant for SEP propagation to 1 au and must be taken into account when modeling SEP propagation in the interplanetary space.

Early propagation of energetic particles across the mean field in turbulent plasmas

“…Here, we exclude the early behaviour, t t1 discussed in Laitinen & Dalla (2017), as displacements of order Larmor radius are too small to be seen in our current analysis.…”

“…Figure 6 d) shows the parameter α, which describes the fast spreading of the particles until the time-asymptotic diffusive phase is reached. As interpreted by Laitinen & Dalla (2017), the fast spreading begins when the particles cease being well tied to their field lines. The onset time of the fast spreading phase, denoted by t1 in Laitinen & Dalla (2017), however, is masked by the early-time σ 2 ⊥0 (see Figure 5), and can only be quantified using the method described in Laitinen & Dalla (2017).…”

“…It should be noted that Equation (3) is of the same form as the fitting function used in Laitinen & Dalla (2017), at the limit of t t1 in their formulation. Here, we exclude the early behaviour, t t1 discussed in Laitinen & Dalla (2017), as displacements of order Larmor radius are too small to be seen in our current analysis.…”

“…While such a model is easy to implement and can be used as the first approach, as in, e.g., Laitinen et al (2016), we will consider here an improvement to the modelling of the transition, based on the work by Laitinen & Dalla (2017). In Appendix A, we derive a model with timedependent diffusion coefficient, which will justify fitting the variance with functional forms such as Equation (A6).…”

“…In this work, we will study the initial non-diffusive phase and the asymptotic diffusive phase in more detail, varying both the particle and turbulence parameters. We will study the nature of the transition from the initial to the asymptotic phase guided by the findings of Laitinen & Dalla (2017), who used a novel method to quantify how the particles are displaced from the meandering field lines and discovered that initially the particles are tied to their meandering field lines well, and decouple only at later stages. We explain the particle simulations and the analysis methods in Section 2 and Appendix A, present our results and discuss their relevance in Sections 3 and 4, and draw our conclusions in Section 5.…”