Integral method to study transition radiation from surfaces with arbitraryprofile

Transition radiation is produced when an electron moving at constant speed crosses the boundary separating two media with different optical properties . We propose an alternative description of this phenomenon, based on an int egral representation of the electromagnetic held and show that the approach gives known results for a hat surface. Compared to previously published me thods, based either on the reciprocity theorem in electromagnetism or on a four-dimensional Fourier representation of the field generated by the movin g electron, this method has the advantage that it can be applied to general boundary geometries.