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.
Highlights
It is established that widespread solar energetic particle (SEP) electron events can be explained by the presence of rather efficient perpendicular diffusion
Transport equation There is some criticism towards the addition of perpendicular diffusion to the focused transport equation, as it is usually derived without any cross-field transport terms [see e.g. 1]
We note that because a single SEP event will never show diffusive characteristics, while such characteristics are simulated by most SEP transport models, this could explain the dichotomy between so-called drop-out events and wide-spread events and numerical SEP transport models indicating that efficient lateral transport must be present: Drop-out events represents the SEP motion in a single magnetic field realization, while SEP transport models simulate the average behaviour and are unable to reproduce such small scale variations that result from a single magnetic field realization
Summary
It is established that widespread solar energetic particle (SEP) electron events can be explained by the presence of rather efficient perpendicular diffusion. We argue that if we consider a large ensemble of magnetic realizations, the average behaviour of the SEP will follow a field-line-random-walk-type [FLRW 21] description and in this limit a diffusive description for perpendicular transport will be appropriate. We note that because a single SEP event will never show diffusive characteristics, while such characteristics are simulated by most SEP transport models, this could explain the dichotomy between so-called drop-out events (assumed to indicate very little lateral transport) and wide-spread events and numerical SEP transport models indicating that efficient lateral transport must be present: Drop-out events represents the SEP motion in a single magnetic field realization, while SEP transport models simulate the average behaviour and are unable to reproduce such small scale variations that result from a single magnetic field realization These conclusions may change if particle decoupling (see the section) is considered. A useful way to describe the decoupling is to look at the guiding center drift in a turbulent magnetic field [see e.g. 23], streaming
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