Structure of plasmas generated by the interaction between metallic ions and neutral gas particles in a low-pressure arc

A numerical solution for the metallic-plasma-neutral-gas structure generated in a low-pressure arc is presented. The equations correspond to a spherically symmetric fluid-like steady model, valid for the outer region of the arc, and describe the ion slowing down by elastic scattering with the neutral particles. Technically, the obtention of the profiles of different magnitudes is complicated due to the existence of a critical point in the steady-state system of equations. The proposed approach to overcome this difficulty is to solve instead a pseudotransient system of equations which rapidly and efficiently relax to the stationary state. By employing this numerical method of second-order accuracy in space, the plasma and neutral gas density, the electron and ion drift velocities, the electron and neutral temperatures, and the electrostatic potential profiles are obtained from the border of the arc channel up to the discharge chamber wall. It is found that the value of the neutral gas filling pressure strongly influences the plasma density and plasma potential distributions. An important result is that metallic ions emitted from the arc channel deliver their kinetic energy to the filling gas in a gradual manner, up to a pressure-dependent point beyond which they move to the walls sustained against collisions with the gas by a self-consistent electric field. Near the mentioned point, the metallic ion density presents a peculiar behavior, showing an increase that is more pronounced at high pressures; a pattern also evident in the electrostatic potential.