Abstract: The plasma sheath in the presence of virtual-cathode structure near a hot cathode was studied by combining the theory of thermionic emission and plasma fluid equations. Using Sagdeev potential method, the sheath solution and generalized Bohm criterion were discussed. It is shown that, different from usual Bohm sheath, the critical ion Mach number at the sheath-presheath edge is not an independent constant but depends on sheath potential drop as well as other parameters, owing to the fact that there exists large quantity of thermionic electrons near the hot cathode which has a significant influence on the whole sheath structure. The critical Mach number first increases and then decreases with the potential drop （from sheath-presheath edge to the virtual cathode）, and monotonically increases with the temperature of the hot cathode. In the plane geometry, there exists an appreciable quantity of residual thermionic electrons which traverse the virtual cathode and sheath and enter into bulk plasma.

Keywords: 
• sheath /
• thermionic emission /
• Bohm criterion