Self-consistent nonlinear transmission line model of standing wave effects in a capacitive discharge

Two different global discharge models was coupled to a transmission line model to obtain the self consistent characteristics of the standing wave effect. A hamiltonian description was used to obtain an analytical expression for the wavelength and to determine the dependence of wavelength upon the main control parameters. The value of wavelength divided by wavelength in vacuum gives a direct measure of the amplitude of nonuniformities induced by the standing wave effect. The models limitation and possible area of improvement were also discussed.