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Both electron-repelling and electron-attracting anode sheaths in a Hall thruster were characterized by measuring the plasma potential with biased and emissive probes [L. Dorf, Y. Raitses, V. Semenov, and N. J. Fisch, Appl. Phys. Lett. 84, 1070 (2004)]. In the present work, two-dimensional structures of the plasma potential, electron temperature, and plasma density in the near-anode region of a Hall thruster with clean and dielectrically coated anodes are identified. Possible mechanisms of anode sheath formation in a Hall thruster are analyzed. The path for current closure to the anode appears to be the determining factor in the anode sheath formation process. The main conclusion of this work is that the anode sheath formation in Hall thrusters differs essentially from that in the other gas discharge devices, such as a glow discharge or a hollow anode, because the Hall thruster utilizes long electron residence times to ionize rather than high neutral pressures.