Modelling the perpendicular transport of energetic electrons in the inner heliosphere

Abstract

The transport of charged particles across a background magnetic field can occur through either particle drifts or perpendicular diffusion caused by magnetic turbulence. The former process, which was proposed by some as an explanation for the efficient perpendicular transport of solar energetic particles (SEPs), competes with the latter process, which can also disrupt the drift patterns and reduce the efficiency of drift effects. The phenomenon of turbulent drift reduction is well known in cosmic ray studies, but not yet considered in SEP models. Although cross-field diffusion has also been well studied in cosmic ray modelling, the exact pitch-angle and energy dependence of this process are currently uncertain. A review is therefore given in this thesis on the current knowledge and shortcomings of the perpendicular transport of SEPs and the focused transport equation is derived to show how perpendicular transport can be retained and how different physical processes give rise to the various terms therein. A first theoretical step for a theory of drift suppression in SEP transport is presented by deriving the drift reduction factor with a pitch-angle dependence. A ‘physics first’ approach is also taken to the diffusion coefficients by using theoretical scattering theories with realistic inputs from observations and turbulence transport models for the turbulence conditions in the inner heliosphere. It is investigated to what extent drifts will be reduced in the inner heliosphere for these realistic turbulence conditions and different pitch-angle dependencies of the perpendicular diffusion coefficient. It is found that cross-field diffusion will have the largest influence on the perpendicular transport of energetic electrons, not particle drifts. Stochastic differential equations are then used to solve both the Parker and focused transport equations for isotropic and anisotropic distributions, respectively. Given the difficulty to disentangle transport effects from the uncertainty about the spatial, temporal, and spectral dependence of the SEP source, Jovian electrons are modelled to constrain the amount of pitch-angle scattering and perpendicular diffusion that energetic electrons experience. It is found that the results from the Parker transport equation in the isotropic limit fitting observations, might be unreliable due to the particle distribution being anisotropic. Such an anisotropic distribution can result from transport effects, large mean free paths, and theories of pitch-angle scattering predicting pitch-angle diffusion coefficients that are not symmetric.