As a result of experimental observations of localized heat flux on components magnetically connected to radiating waveguides in Tore Supra and in TdeV, the acceleration of electrons near lower hybrid (LH) antennas has been investigated. A simple analytical model has been developed to compute the dynamics of the particles in the near field approximation. Landau damping of the very high N|| (20 < N|| < 100) component of the launched spectrum on the thermal electrons of the scrape-off layer (SOL) is found to occur. Simulation of a typical LH pulse in Tore Supra indicates that the electrons can be accelerated up to 2-3 keV. Modelling of the interaction of this fast electron population with the edge plasma allows a calculation of the heat flux on plasma facing components that are magnetically connected to the antenna. Model results and the results of experiments in Tore Supra and TdeV are compared. The calculated heat fluxes are found to be fairly consistent when the variation of convective heat flux at the grill aperture is taken into account. From this analysis, it is concluded that, for an LH power density of 25 MW/m2, the resulting heat flux along the field lines (3.5 MW/m2) is manageable for the components connected to the antenna, provided that good coupling can be maintained at a low density in front of the grill.