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Superponderomotive-energy electrons are observed experimentally from the interaction of an intense laser pulse with a relativistically transparent target. For a relativistically transparent target, kinetic modeling shows that the generation of energetic electrons is dominated by energy transfer within the main, classically overdense, plasma volume. The laser pulse produces a narrowing, funnel-like channel inside the plasma volume that generates a field structure responsible for the electron heating. The field structure combines a slowly evolving azimuthal magnetic field, generated by a strong laser-driven longitudinal electron current, and, unexpectedly, a strong propagating longitudinal electric field, generated by reflections off the walls of the funnel-like channel. The magnetic field assists electron heating by the transverse electric field of the laser pulse through deflections, whereas the longitudinal electric field directly accelerates the electrons in the forward direction. The longitudinal electric field produced by reflections is 30 times stronger than that in the incoming laser beam and the resulting direct laser acceleration contributes roughly one third of the energy transferred by the transverse electric field of the laser pulse to electrons of the super-ponderomotive tail.