Magnetized plasma sheath with two positive ions where collision frequencies have a power law dependency on ions velocities

We study the dynamics of collisional magnetized plasma sheath with two species of positive ions by using the plasma fluid model. the basic equations of the fluid model are solved numerically where the sheath is in the external magnetic field and the elastic collision between ions and neutrals has been taken into account. in our model, we assume that the collisional momentum transferring cross section has a power law dependency on ion flow velocity. our analysis demonstrates that the sheath dynamics are sensitive to the power law dependency, especially for the ion with greater density.