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A considerable fraction of the energy in a solar flare is released assuprathermal electrons; such electrons play a major role in energy depositionin the ambient atmosphere and hence the atmospheric response to flare heating.Historically the transport of these particles has been approximated through adeterministic approach in which first-order secular energy loss to electrons inthe ambient target is treated as the dominant effect, with second-orderdiffusive terms (in both energy and angle) being generally either treated as asmall correction or neglected. However, it has recently been pointed out thatwhile neglect of diffusion in energy may indeed be negligible, diffusion inangle is of the same order as deterministic scattering and hence must beincluded. Here we therefore investigate the effect of angular scattering on theenergy deposition profile in the flaring atmosphere. A relatively simplecompact expression for the spatial distribution of energy deposition into theambient plasma is presented and compared with the corresponding deterministicresult. For unidirectional injection there is a significant shift in heatingfrom the lower corona to the upper corona; this shift is much smaller forisotropic injection. We also compare the heating profiles due to return currentOhmic heating in the diffusional and deterministic models.

Energy Deposition by Energetic Electrons in a Diffusive Collisional Transport Model