  The transport of the energy contained in suprathermal electrons in solar
flares plays a key role in our understanding of many aspects of flare physics,
from the spatial distributions of hard X-ray emission and energy deposition in
the ambient atmosphere to global energetics. Historically the transport of
these particles has been largely treated through a deterministic approach, in
which first-order secular energy loss to electrons in the ambient target is
treated as the dominant effect, with second-order diffusive terms (in both
energy and angle) being generally either treated as a small correction or even
neglected. We here critically analyze this approach, and we show that spatial
diffusion through pitch-angle scattering necessarily plays a very significant
role in the transport of electrons. We further show that a satisfactory
treatment of the diffusion process requires consideration of non-local effects,
so that the electron flux depends not just on the local gradient of the
electron distribution function but on the value of this gradient within an
extended region encompassing a significant fraction of a mean free path. Our
analysis applies generally to pitch-angle scattering by a variety of
mechanisms, from Coulomb collisions to turbulent scattering. We further show
that the spatial transport of electrons along the magnetic field of a flaring
loop can be modeled rather effectively as a Continuous Time Random Walk with
velocity-dependent probability distribution functions of jump sizes and
occurrences, both of which can be expressed in terms of the scattering mean
free path.
