The present generation of particle accelerators requires gradients of  levels which are at least one order of magnitude higher than gradients available today. The need for a high gradient on one hand and power levels below the breakdown threshold on the other hand, pushes the operating frequency upwards. Therefore acceleration of electrons by radiation at optical wavelengths is one of the promising alternatives for future electron accelerators. The essence of the idea is to inject a charged particle in an active medium, and in this way the energy stored in the medium could be transferred to a charged particle without prior generation of radiation.

In this text a theoretical model based on the set of equations which describe the dynamics of electrons in the presence of electromagnetic wave propagating in an active medium is examined. This formalism, is based on the assumption that there is a single electromagnetic mode that propagates in the interaction region. It is shown that due to a double selection process, a single space mode exists, which is amplified by the medium and interacts with the electron beam.

Furthermore, the interaction model is extended to account for the effects of spontaneously emitted radiation, and the signal to noise ratio of the system is analyzed. Two possible systems have been examined in the computer simulations: a system utilizing as an active medium and a system utilizing  as an active medium.

Gradient levels above are obtained in simulations of   system and acceleration of   beams of  particles to  is predicted in system in which population inversion density resulting in linear gain of up to can be obtained for a certain set of system parameters. In the system, the relatively low linear gain of up to , limits the effect of the active medium to gradient levels below .

 show, that by varying the beam modulation in the range of , the at the system output can be increased from  to in medium with  linear gain. Other parameters, such as structure geometry and beam average energy are shown to have a small effect on the