A mathematical model of an inductively coupled radio-frequency discharge at low pressure as nonlinear partial eigenproblem

A new approach for modeling steady state inductively coupled radio frequency discharges at low pressure is described. A simple one-dimensional model is considered, which includes Maxwell’s equations and the electron balance equation with boundary conditions of the third kind. It is shown that the system of boundary value problems is a two-parameter partial eigenvalue problem. The smallest eigenvalue of the problem is the boundary value of the magnetic field strength. The second parameter of the problem is the concentration of electrons at the center of the plasma bunch. The developed approach makes it possible to calculate the inductor current required to maintain a steady state of the discharge. The results of calculations of the dependence of the inductor current, electron density, electric and magnetic fields on pressure are presented.