A magnetized plasma sheath where the ion collision frequency depends on ion flow velocity

Recently some correlative works have been done to investigate the effects of collisions between ion and neutral gas atoms on the characteristics of plasma sheath in an external magnetic field. In general, the momentum transferring cross section (and thus the ion collision frequency) has a power law dependence on the ion flow velocity in the depth direction. Usually in the literature, constant collision frequency and constant mean free path are treated. Here, by using a collisional fluid model, we investigate the characteristics of a magnetized plasma sheath where the ion cross section depends on the ion flow velocity. The numerical calculations show that the effects of collisions on ion characteristics are more powerful when the momentum transferring cross section is constant. However, some parameters such as the electron density distribution are independent of this dependence