Simulation codes for high brightness electron beam free-electron laser experiments

Abstract

The high brightness electron beam required by a short wavelength self-amplified spontaneous emission free-electron laser (FEL) may be reached only with an accurate design of the beam dynamics from the generation in the rf injector up to the undulator. The beam dynamics is affected by strong selfconsistent effects at injection, in the compression stage, and during the FEL process. The support of numerical simulations is extensively used in the predictions of the beam behavior in these nonlinear dynamical conditions. I present a review of available simulation techniques, currently exploited in the design of short wavelength free-electron lasers.

Beyond the limits of 1D coherent synchrotron radiation

“…As the compression ratio increases, the differences between the simulation methods become more clear. As expected, the 1D simulation results diverge more significantly both from the experimental data, and from simulations results with codes which take the transverse extent of the bunch into account in situations where the condition equation (19) is strongly violated, and the 1D CSR approximation breaks down. The breakdown of this condition has been studied experimentally; the theory suggested that the condition is valid only in the parameter regime σ v =1, whereas it has been demonstrated that up to σ v 2, the 1D CSR approximation remains valid, and so this condition can be relaxed.…”

“…A number of other codes exist which are capable of simulating the effects of CSR [18,19], some of which utilise a 1D approximation, based on [6,8], and others which extend the model to incorporate 2D and 3D effects [20][21][22]. While previous studies have shown good agreement between results from some of these simulation codes and experimental data [3,4], there is a point at which the 1D approximation is no longer valid, as shown in [23], which suggests that projecting the bunch distribution onto a line may overestimate the level of coherent emission, particularly when the bunch has a large transverse-to-longitudinal aspect ratio.…”

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

“…Under this hypothesis, (i) the second order wave equation can be simplified in a first order one, (ii) the regressive wave, resonant on a low frequency, is disregarded, and (iii) the shorter interval of length that can be resolved is just the wavelength . The SVEA equations, in the 1D version [3,4,6] and in their 3D extension [5], are at the basis of the development of several numerical codes [7][8][9][10][11][12][13] extensively and successfully used in the projects and in the interpretation of almost all free-electron laser (FEL) experiments. Few works [14][15][16][17] reintroduced the backward wave in the model, associating to the particle equations not one, but a couple of radiation equations, written for two wave packets centered, respectively, on two different single resonances and correlated only via the electron dynamics.…”

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

“…Under this hypothesis, (i) the second order wave equation can be simplified in a first order one, (ii) the regressive wave, resonant on a low frequency, is disregarded, and (iii) the shorter interval of length that can be resolved is just the wavelength . The SVEA equations, in the 1D version [3,4,6] and in their 3D extension [5], are at the basis of the development of several numerical codes [7][8][9][10][11][12][13] extensively and successfully used in the projects and in the interpretation of almost all free-electron laser (FEL) experiments. Few works [14][15][16][17] reintroduced the backward wave in the model, associating to the particle equations not one, but a couple of radiation equations, written for two wave packets centered, respectively, on two different single resonances and correlated only via the electron dynamics.…”