Experiments confirm that the maintenance of a Penning discharge in its normal mode is governed by a thin electron sheath, situated close to the anode. The observations indicate that electron transport to the anode occurs by a mechanism not involving molecular collisions. Electrons in the discharge undergo anomalous energy scattering, and the resulting excess energy electrons can readily cross the magnetic lines of force. This suggests cross-field diffusion through interaction with space charge oscillations, and the same mechanism may explain anomalous diffusion generally in magnetically confined discharges. The discharge structure is investigated, and mode changes are shown to be associated with the appearance of excess energy electrons in certain discharge regions.