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.