Electric Field on the Surface of a Metal Electrode Immersed in Plasma at a High Negative Potential

An analytical solution of the Poisson’s equation is found for the electric field on the surface of the electrode immersed in a homogeneous non-isothermal collisionless plasma consisting of electrons and single-charged ions with charge e, with electron temperature T_e and high values of negative electric potential Ψ when the parameter |eΨ|/T_e ≫ 1. It is found that the plasma layer L with violated quasi neutrality near the high-potential electrode increases compared to the Debye length r_D proportionally to the parameter [eΨ/2T_e]^3/4, as L = r_D[eΨ/2T_e]^3/4. The electric field was calculated on the surface of the negative electrode in plasma. It is shown that in a laboratory plasma with density in the range 10¹⁰–10¹³ cm^–3 and electron temperature from 1 to 10 eV, at high potential for the parameter eΨ/T_e ≫ 1, the electric field calculated by the obtained formula E = Ψ/L near the surface of the electrode up to 200 times lower than the fields calculated by the classical formula E = Ψ/r_D, which was obtained at low potential and for the parameter eΨ/T_e ≪ 1.