Generalized Formula for Calculating the Electric Field on the Electrode Surface in Plasma

The electric field on the surface of a metal electrode immersed in plasma with an electron temperature of T_e ∼ 10 eV and plasma density n_e from 10¹⁰ to 10¹³ cm⁻³ has been calculated under negative electric potential Ψ₀ of the electrode and large values of parameter |eΨ₀|/T_e  \( \gg \)  1. The obtained asymptotic formula for the field strength at |eΨ₀|/T_e  \( \gg \)   1 differs significantly from the classical formulas for calculating the electric field and the Debye length of field screening near the electrode surface in plasma, which are valid under condition |eΨ₀|/T_e  \( \ll \)  1. It has been shown that, at |eΨ₀|/T_e  \( \gg \)  1, near the electrode in a plasma, a modified Debye layer can exceed the classical Debye length by two orders of magnitude. To calculate the electric field on the electrode surface in plasma, a generalized formula has been proposed in the explicit form, which is valid in a wide range of parameter 0 < |eΨ₀|/T_e < 10⁴ at negative electrode potentials of up to 10 kV.