Publication
By explicitly writing the equations of motion for highly relativistic electrons in an electromagnetic field we show the equivalence between the magnetostatic and optical (laser) undulator-based free electron lasers (FELs). In order to gain insight into the physics behind both FEL mechanisms we use a simplified approach developed in Ref. 1 to describe the optical amplification process. By using elementary physics we explain the phenomenon of microbunching, caused by the interaction of electrons with the emitted wave, which leads to coherent emission of radiation and is the essential ingredient in the lasing effect of a FEL. With our simplified model we derive the two main FEL parameters the gain and saturation lengths. Finally, we discuss the potential advantages of using an optical instead of a magnetostatic undulator in a FEL. With our approach the physics behind FELs becomes evident and accessible to researchers outside the specialized field.