The present work revisits the subjects of mixing, saturation, and space-charge effects in free-electron lasers. Use is made of the compressibility factor, which proves to be a helpful tool in the related systems of charged beams confined by static magnetic fields. The compressibility allows to perform analytical estimates of the elapsed time until the onset of mixing, which in turn allows to estimate the saturated amplitude of the radiation field. In addition, the compressibility helps to pinpoint space-charge effects and the corresponding transition from Compton to Raman regimes. V C 2013 AIP Publishing LLC. [http://dx

In the present work, we extend results of a previous paper [Peter et al., Phys. Plasmas 20, 12 3104 (2013)] and develop a semi-analytical model to account for thermal effects on the nonlinear dynamics of the electron beam in free-electron lasers. We relax the condition of a cold electron beam but still use the concept of compressibility, now associated with a warm beam model, to evaluate the time scale for saturation and the peak laser intensity in high-gain regimes. Although vanishing compressibilites and the associated divergent densities are absent in warm models, a series of discontinuities in the electron density precede the saturation process. We show that full wave-particle simulations agree well with the predictions of the model. V C 2014 AIP Publishing LLC. [http://dx

In the present analysis, we study the dynamics of charged particles submitted to the action of slowly modulated electromagnetic carrier waves. While the velocity of the particles remains smaller than the carrier's phase-velocity, their dynamics is well described by a refined ponderomotive approach. The ponderomotive approach has its own validity limits well established, beyond which particles are resonantly trapped by the carrier waves. We show that under adequate conditions, the trapping mechanism places particles at an optimal relative phase with respect to the carrier for maximum acceleration. In addition to the analytical approach involved in the ponderomotive description, we use numerical simulations to validate the corresponding dynamics as well as to explore various features of the resonant trapping and acceleration. Published by AIP Publishing.

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In the present work, we describe the linear growth rate of the laser field for a one-dimensional theoretical single-pass free-electron laser, including space-charge and thermal effects, in the hydrodynamical regime. In a recent work (Peter, Endler & Rizzato, Phys. Plasmas, vol. 21, 2014, 113104), the thermal effects were already included for a water-bag initial distribution for the longitudinal velocities of the particles of the beam. Here, we extend the result for different and symmetrical initial distributions, considering that in the hydrodynamical regime, the beam can be thought of as a warm fluid composed of a sum of different fluids with different densities, where the initial distribution of each fluid is a water-bag distribution. The total pressure of the beam is related to the sum of the pressures of these fluids. This approach is much less complicated than the kinetic approach. We compare the results given by the linear set of equations and wave–particle simulations for water-bag and Gaussian initial distributions. The evolution of the particle distribution in the phase space is also shown in order to demonstrate that the assumption of the sum of different fluids reproduces the physics of the system in a reasonable fashion.

In the present analysis we study the dynamics of charged particles under the action of slowly modulated electromagnetic carrier waves. With the use of a high-frequency laser mode along with a modulated static magnetic wiggler, we show that the ensuing total field effectively acts as a slowly modulated high-frequency beat-wave field typical of inverse free-electron laser schemes. This effective resulting field is capable of accelerating particles in much the same way as space-charge wake fields do in plasma accelerators, with the advantage of being more stable than plasma related methods. Acceleration occurs as particles transition from ponderomotive to resonant regimes, so we develop the ponderomotive formalism needed to examine this problem. The ponderomotive formalism includes terms that, although not discussed in the usual applications of the approximation, are nevertheless of crucial importance in the vicinity of resonant capture. The role of these terms is also briefly discussed in the context of generic laser-plasma interactions.

In the present work, we make use of simplified nonlinear models based on the compressibility factor (Peter et al., Phys. Plasmas, vol. 20 (12), 2013, 123104) to predict the gain of one-dimensional (1-D) free-electron lasers (FELs), considering space-charge and thermal effects. These models proved to be reasonable to estimate some aspects of 1-D FEL theory, such as the position $z$ of the onset of mixing, in the case of a initially cold electron beam, and the position $z$ of the breakdown of the laminar regime, in the case of an initially warm beam (Peter et al., Phys. Plasmas, vol. 21 (11), 2014, 113104). The results given by the models are compared to wave–particle simulations showing a reasonable agreement.

Spatially modulated electrostatic fields can be designed to efficiently accelerate particles by exploring the relationships between the amplitude, the phase velocity, the shape of the potential, and the initial velocity of the particle. The acceleration process occurs when the value of the velocity excursions of the particle surpasses the phase velocity of the carrier, as a resonant mechanism. The ponderomotive approximation based on the Lagrangian average is usually applied in this kind of system in non-accelerating regimes. The mean dynamics of the particle is well described by this approximation far from resonance. However, the approximation fails to predict some interesting features of the model near resonance, such as the uphill acceleration phenomenon. A canonical perturbation theory is more accurate in these conditions. In this work, we compare the results from the Lagrangian average and from a canonical perturbation theory, focusing in regions where the results of these two approaches differ from each other.