The sheath criterion for a collisional plasma sheath at the presence of external magnetic field

The Bohm sheath criterion is modified for collisional plasma containing Boltzmann electrons and cold fluid ions at the presence of external magnetic field. Based on fluid model, the effects of the strength and the orientation of an external magnetic field on the upper and lower limits of Bohm sheath criterion have been studied by considering the collision frequency between ions and neutrals. The results show that the sheath criterion depends on the orientation and magnitude of magnetic field and the ion flow velocity at the sheath boundary.