Self-consistent in internal and external parameters model of indactively coupled RF discharge at low-pressure.

The low-pressure RFI model is considered as a nonlinear eigenvalue problem with a parameter for a system that includes the electron balance equations and the Maxwell equations with mixed boundary conditions. The free parameter of the problem is the value of the electron density at the center of the plasma bunch $n_{e0}$. A condition for the existence of a non-trivial solution of the system under consideration is obtained in the form of a nonlinear relation that relates the value of the electric field strength at the discharge boundary with the smallest eigenvalue of the auxiliary linear Sturm-Liouville problem. This approach allows one to find not only the self-consistent distribution of the electron concentration, the strength of the electric and magnetic fields in the discharge, but also to match the value of $n_{e0}$ (internal parameter) with the inductor current $I_{ind}$ (external parameter). The results of calculation of dependences of $n_{e0}$, electric and magnetic field strengths on $I_{ind}$ for an RFID discharge in a discharge chamber with a diameter of $2{,}4$ cm at a pressure of $60$ Pa and an oscillator frequency of $13.56$ are presented. MHz.

Keywords: RF discharge, reduced pressure, numerical simulation, self-consistent model, eigenvalue problem, electron balance equation, Maxwell equations, electron concentration, electric field strength, magnetic field strength, inductor current