Energy extraction efficiency of a free electron laser (FEL) can be increased when the undulator is tapered after the FEL saturation. By use of ray equation approximation to combine the one-dimensional FEL theory and optical guiding approach, an explicit physical model is built to provide insight to the mechanism of the electron-radiation coherent interaction with variable undulator parameters as well as electron beam radius. The contribution of variation in electron beam radius and related transverse effects are studied based on the presented model and numerical simulation. Taking a recent studied terawatt, 120 m long tapered FEL as an example, we demonstrate that a reasonably varied, instead of a constant, electron beam radius along the undulator helps to improve the optical guiding and thus the radiation output. Show Partial Abstract