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This paper presents a conducting channel model aimed at elucidating the generation of high-energy particles within a plasma chamber. Initially, the chamber is charged with neutral hydrogen gas at a density of approximately ~3.3×1022/m3, equivalent to 1 torr at 300K under ideal gas conditions. A Townsend discharge (dark discharge), driven by an externally imposed electric potential (500-1000V) across the cathode and anode, is utilized to induce partial ionization of the hydrogen gas. Once a stable conducting channel with a high conductivity is established, a low electric potential (e.g., 100V-500V) is introduced to sustain the current in the conducting channel. Our investigation then delves into the impact of a high electron emissivity cathode, such as lanthanum hexaboride (LaB6) during an arc discharge. We develop a theoretical model of the conducting channel that may emerge under these conditions. As the cathode surface undergoes heating, emitted thermionic electrons form a localized layer of negative charge density, leading to an electric potential dip. Our multi-fluid simulations unveil the emergence of electron-ion two-stream instability owing to the high-density electron layer, leading to the appearance of multiple potential peaks and dips, each measuring several to tens of kV. We delineate a set of conditions conducive to the formation of these potential peaks and dips within the conducting channel. Our proposed scenario furnishes a framework for elucidating electron and ion acceleration within a weakly ionized plasma chamber.