Perpendicular diffusion of solar energetic particles: When is the diffusion approximation valid?

Abstract

Multi-spacecraft observations of widespread solar energetic particle (SEP) events indicate that perpendicular (to the mean field) diffusion is an important SEP transport mechanism. However, this is in direct contrast to so-called spike and drop-out events, which indicate very little lateral transport. To better understand these seemingly incongruous observations, we discuss the recent progress made towards understanding and implementing perpendicular diffusion in transport models of SEP electrons. This includes a re-derivation of the relevant focused transport equation, a discussion surrounding the correct form of the pitch-angle dependent perpendicular diffusion coefficient and what turbulence quantities are needed as input, and how models lead to degenerate solutions of the particle intensity. Lastly, we evaluate the validity of a diffusion approach to SEP transport and conclude that it is valid when examining a large number of (an ensemble of) events, but that individual SEP events may exhibit coherent structures related to the magnetic field turbulence at short timescales that cannot be accounted for in this modelling approach.

On the Seed Population of Solar Energetic Particles in the Inner Heliosphere

“…In the simulation, the reduction in interplanetary particle acceleration was especially notable near the MIR formation region, where cross-field diffusion efficiently removes particles from the collapsing magnetic bottle. We note that the presence and strength of interplanetary cross-field diffusion is still a matter of lively debate (see e.g., Strauss et al, 2020, for a recent discussion) and that crossfield diffusion likely varies depending on the underlying solar wind conditions and IMF structures. For example, SIs inside CIRs may act as efficient diffusion barriers due to the presence of non-axisymmetric turbulence (Strauss et al, 2016).…”

“…In this study, the Monte-Carlo model PARADISE is utilised to evolve a suprathermal particle seed population through the EUHFORIA solar wind domain. This is accomplished by solving the focused transport equation (see van den Berg et al, 2020, for a recent review)…”

A Self-consistent Simulation of Proton Acceleration and Transport Near a High-speed Solar Wind Stream

“…This is achieved by solving the 5-dimensional focused transport equation (FTE; e.g., Roelof 1969;Skilling 1971;le Roux & Webb 2012), which takes into account the effects of solar wind turbulence through a set of phase-space diffusion processes. The FTE utilised in PARADISE is expressed in guiding centre (GC) coordinates, and contains therefore the effects of GC drifts and cross-field diffusion (e.g., Zhang 2006;Wijsen 2020;Strauss et al 2020). The GC drifts have, however, a negligible effect on the transport of the low-energetic protons studied in this work (Wijsen et al 2020).…”