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 Psi when the parameter vertical bar e Psi vertical bar/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 [e Psi/2T(e)](3/4), as L = r(D)[e Psi/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 10(10)-10(13) cm(-3) and electron temperature from 1 to 10 eV, at high potential for the parameter e Psi/T-e >> 1, the electric field calculated by the obtained formula E = Psi/L near the surface of the electrode up to 200 times lower than the fields calculated by the classical formula E = Psi/r(D), which was obtained at low potential and for the parameter e Psi/T-e << 1.