One-dimensional free-electron laser equations without the slowly varying envelope approximation

Abstract

A set of one-dimensional equations has been deduced in the time domain from the Maxwell-Lorentz system with the aim of describing the free-electron laser radiation without using the slowly varying envelope approximation (SVEA). These equations are valid even in the case of arbitrarily short electron bunches and of current distributions with ripples on the scale of or shorter than the wavelength. Numerical examples are presented, showing that for long homogeneous bunches the new set of equations gives results in agreement with the SVEA free-electron laser theory and that the use of short or prebunched electron beams leads to a decrease of the emission lethargy. Furthermore, we demonstrate that in all cases in which the backward low frequency wave has negligible effects, these equations can be reduced to a form similar to the usual 1D SVEA equations but with a different definition of the bunching term.

Demonstration Scheme for a Laser-Plasma-Driven Free-Electron Laser

“…As expected, the power is only weakly dependent on K for smaller energy spreads. The figure also illustrates that the concepts discussed in this paper are not crucially dependent on reaching ultimate undulator performance, as the normalized power curves flatten for higher K. As described in [28], with the bunch length z on the same order as the FEL wavelength , the slowly varying amplitude approximation [16], usually implied to describe the FEL process, is not strictly fulfilled. However, as indicated in [28], this leads to an underestimation of the FEL gain, and therefore we consider the present simulations as a conservative estimation of the FEL process for extremely short electron bunches.…”

Velocity dispersion of correlated energy spread electron beams in the free electron laser

“…In addition, the slowly varying envelope approximation (SVEA) [22] means that they cannot model a broadband range of frequencies produced by large energy differences due to the chirp and/or a large taper. So-called 'unaveraged' FEL codes [23][24][25][26][27] are free of these limitations. For this reason, the unaveraged 3D FEL code Puffin [23] is used in the following analysis.…”

Two-colour free electron laser with wide frequency separation using a single monoenergetic electron beam

“…Puffin (along with other unaveraged codes e.g. [20][21][22]23]) is then ideally suited to simulating and investigating the physics of multi-colour FELs.…”