Growth rate for free-electron lasers through a warm beam layered model

Abstract

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.

Application of nonlinear models to estimate the gain of one-dimensional free-electron lasers

“…It is usually measured in a decibel scale and the typical range of it is approximately tens of dB. The purpose of this work is to use the nonlinear models recently developed (Peter et al 2013;Peter, Endler & Rizzato 2014, 2016 to estimate the theoretical gain of one-dimensional (1-D) FELs in a single pass and time-independent (steady-state regime) configuration, both for Compton and Raman regimes. In the Compton regime, the system dynamics is mainly driven by the ponderomotive potential, while in the Raman regime, the space-charge effects are comparable to the ponderomotive potential.…”

Triplet and beam interaction in a plasma

“…The combined action of the wiggler and laser fields forms the ponderomotive potential, which is responsible for the energy conversion. [10][11][12][13]19 In the FEL case, the evolution of the laser field occurs as the evolution of J, a rearrangement time, then an exponential growth, the first peak and oscillations with frequency in the order of the plasma frequency. The turning point from linear growth to saturation is also related to the onset of the mixing process.…”

“…The turning point from linear growth to saturation is also related to the onset of the mixing process. Moreover, the initial velocity that maximizes the growth rate of the amplified mode is slightly greater than the resonance velocity (the difference of velocities is related to the detuning [11][12][13]19 ) and if the beam has an initial distribution of velocities, just as in FEL, the growth rate becomes smaller. 12,13 While in the FEL dynamics, the laser field 10 -a transversal plane wave-is amplified, in this case, the longitudinal mode is amplified J.…”

“…Moreover, the initial velocity that maximizes the growth rate of the amplified mode is slightly greater than the resonance velocity (the difference of velocities is related to the detuning [11][12][13]19 ) and if the beam has an initial distribution of velocities, just as in FEL, the growth rate becomes smaller. 12,13 While in the FEL dynamics, the laser field 10 -a transversal plane wave-is amplified, in this case, the longitudinal mode is amplified J. One of the reasons for that is because in the present model, the beam velocity is limited to non-relativistic velocities.…”

“…An analogy is made in the present work between this behavior and the dynamics of a one-dimensional freeelectron laser. [10][11][12][13] In the present work, we allow the waves to interact with themselves based on the concept of the wave triplet and to interact with a non-relativistic particle beam in a plasma. The interaction between waves affects dramatically the system dynamics described in Ref.…”