Carbon fiber production is an energy intensive process requiring new approaches for energy efficient heating. One possible option might be the dielectric heating. A basic requirement to design an efficient applicator is the knowledge of the variation of dielectric properties during processing. The experience shows strongly increasing dielectric loss of a Polyacrylonitrile (PAN) fiber with increasing temperatures while it decreases during the chemical transformation in the stabilization stage. For the applicator design an electrical field that counteracts the variation of the dielectric loss is a suitable choice. In this presentation the focus is on the combination of the generalized scattering matrix (GSM) code with a process model. It shall allow for the optimization of the geometry of a cylindrical resonator usable during the stabilization stage of the PAN fiber. The scattering matrix code is utilized to calculate the field profile of a cylindrical resonator with step-wise changing diameter that acts as applicator. The number of steps can be varied, depending on the ability of production and spacial requirements.