Abstract: The FEL theoretical analysis discuss on two different dynamical domains; the low gain regime and the high gain regime. Numerical simulation codes are basic tools for designing Free Electron Lasers (FEL). Several simulation code such as GINGER, GENESIS, and PERSEO, MEDUS, ... with the variety of techniques are used in simulations of the FELs and model their radiation. MEDUSA, based on non averaged approximation, is used to simulate the high and low gain FEL classes in one and three dimensions.
We discuss about about our recent code, corresponding to the MEDUSA 1D. It focuses to simulate single-pass free-electron lasers, both the FEL amplifier and the SASE FEL, as well Oscillator FEL through the planer wiggler. The code includes the slippage, inhomogeneous and thermal effects.