Numerical analysis of ion temperature effects to the plasma wall transition using a one-dimensional two-fluid model. I. Finite Debye to ionization length ratio

A one-dimensional, two-fluid, steady state model is used for the analysis of ion temperature effects to the plasma-wall transition. In this paper, the model is solved for a finite ratio e between the Debye and the ionization length, while in Part II [T. Gyergyek and J. Kovacic, Phys Plasmas 24, 063506 (2017)], the solutions for e = 0 are presented. Ion temperature is treated as a given, independent parameter and it is included in the model as a boundary condition. It is shown that when the ion temperature larger than zero is selected, the ion flow velocity and the electric field at the boundary must be consistent with the selected ion temperature. A numerical procedure, how to determine such “consistent boundary conditions,” is proposed, and a simple relation between the ion temperature and ion velocity at the boundary of the system is found. The effects of the ion temperature to the pre-sheath length, potential, ion temperature, and ion density drops in the pre-sheath and in the sheath are investigated. ...