Simulation of positive streamer evolution is important for understanding the microscopic physical process in discharges. Simulations described in this paper are done using a 3D Particle-In-Cell, Monte-Carlo-Collision code with photoionization. Three phases of a positive streamer evolution, identified as initiation, propagation, and branching are studied during simulations. A homogeneous electric field is applied between parallel-flat electrodes forming a millimeter air gap to make simulations and analysis more simple and general. Free electrons created by the photoionization process determine initiation, propagation, and branching of the streamers. Electron avalanches form a positive streamer tip, when the space charge of ions at the positive tip dominates the local electric field. The propagation of the positive tip toward a cathode is the result of combinations of the positive tip and secondary avalanches ahead of it. A curved feather-like channel is formed without obvious branches when the electric field between electrodes is 50 kV/cm. However, a channel is formed with obvious branches when the electric field increases up to 60 kV/cm. In contrast to the branches around a sharp needle electrode, branches near the flat anode are formed at a certain distance away from it. Simulated parameters of the streamer such as diameter, maximum electric field, propagation velocity, and electron density at the streamer tip are in a good agreement with those published earlier.
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