PARSIFEL

an FEL design and computational tool

M. Artioli, G. Dattoli and S. Pagnutti

Introduction

This on-line tool, developed on a Mathematica™ platform, provides a fast and reliable Free Electron lasers (FEL) are devices designed to generate coherent radiation through the mechanism of stimulated emission of radiation by relativistic electrons moving in magnetic undulators.

The electron beam is provided by an accelerating system which may be a Linac or a Storage Ring. They have provided us with a concrete tool for analysis when more serious and complete computations were not available or demanded long computational times. We decided to present this synopsis for various reasons, some of which are listed below.

The design of FELs is usually accomplished using massive computer codes, capable of modeling the various elements of the device. The use of these codes is rather expensive in terms of computer time. In alternative the wise use of scaling laws, benchmarked against theory and different numerical codes, may be an alternative to fix working points of a specific FEL configuration. In the following we will provide a serie of computational tools (in the form of "Mathematica Demonstrations") capable of including the most significant features of an actual FEL device and provide a quick preliminary design optimization.

Putting Things Together (Table of contents)

  1. Spontaneous Emission in a Free-Electron Laser
    [Snapshot] This Demonstration shows an electron bunch entering an undulator magnet. The electrons experience a Lorentz force (assuming the magnetic field is directed vertically) and execute transverse oscillations in the horizontal plane. The emission process is characterized by antenna lobe emission, which is more intense when the acceleration is greater. The process can be described either in the laboratory or in the electron rest frame. In the latter case, the electrons "see" the undulator field as an incoming electromagnetic wave with a wavelength that is linked to the undulator Lorentz contracted period.
  2. Design parameters
    FEL requires an electron beam of relativistic energy and an undulator magnet where electrons move and radiate. This tool specify how different variables (electron energy, magnetic field intensity and period) should be embedded to get quantities of FEL relevance.
  3. Gain
    FEL is a laser device, therefore the gain, defining the relevant intensity growth rate, is a quantity of pivotal importance. We define different regime of operation (low, high gain) and allow the evaluation of the gain function in the case of perfect beams (negligible energy spread and emittances).
  4. Gain and inhomogeneous broadening effects
    This Demonstration allows the evaluation of the FEL gain including the beam qualities. The gain reduction due to energy spread and emittances is specified in terms of appropriate parameters and scaling formulae are reported.
  5. Saturation
    The gain saturation mechanism plays for FEL the same role as in ordinary laser. We introduce the FEL saturation intensity, namely the intensity halving the small signal FEL gain and present parameterization of the gain saturation formulae in terms of such a reference quantity. The dependence of this crucial quantity on the different components of the device is carefully analyzed.
  6. High gain amplification
    The Demonstration provides a tool to evaluate the FEL power growth from an input seed, it is shown that the evolution till saturation can be reproduced by a logistic type function, different forms of logistic are shown to reproduce the evolution of the FEL intensity in different operating conditions.
  7. High gain amplification and inhomogeneous broadening effects
    The Demonstration provides a computational tool to introduce into the logistic intensity evolution equation the effect of the beam qualities and of the optical beam diffraction.
  8. Higher order harmonic generation
    One of the distinctive features of FEL is the possibility of lasing at the fundamental and higher order harmonics. This Demonstration offers an efficient tool for deriving the growth of the various harmonics via a modified set of logistic functions.