Keyword: resonance
Paper Title Other Keywords Page
MOPSO31 Quasiperiodic Method of Averaging Applied to Planar Undulator Motion Excited by a Fixed Traveling Wave undulator, FEL, radiation, electron 762
 
  • K.A. Heinemann, J.A. Ellison
    UNM, Albuquerque, New Mexico, USA
  • M. Vogt
    DESY, Hamburg, Germany
 
  Funding: The work of JAE and KH was supported by DOE under DE-FG-99ER41104. The work of MV was supported by DESY.
We present a mathematical analysis of planar motion of energetic electrons moving through a planar dipole undulator, excited by a fixed planar polarized plane wave Maxwell field in the X-Ray FEL regime.* We study the associated 6D Lorentz system as the wavelength of the traveling wave varies. The 6D system is reduced, without approximation, to a 2D system (for a scaled energy deviation and generalized ponderomotive phase) in a form for a rigorous asymptotic analysis using the Method of Averaging (MoA), a long time perturbation theory. As the wavelength varies the system passes through resonant and nonresonant (NR) zones and we develop NR and near-to-resonant (NtoR) normal form approximations. For a special initial condition, on resonance, we obtain the well-known FEL pendulum system. We prove NR and NtoR first-order averaging theorems, in a novel way, which give optimal error bounds for the approximations. The NR case is an example of quasiperiodic averaging where the small divisor problem enters in the simplest possible way. To our knowledge the analysis has not been done with the generality here nor has the standard FEL pendulum system been derived with error bounds.
* J.A. Ellison, K. Heinemann, M. Vogt, M. Gooden: arXiv:1303.5797 [physics.acc-ph]
 
 
WEPSO78 Harmonic Lasing Self-seeded FEL undulator, FEL, simulation, electron 700
 
  • M.V. Yurkov, E. Schneidmiller
    DESY, Hamburg, Germany
 
  In this paper we perform analysis of capabilities of SASE FELs at the European XFEL for generation of narrow band radiation. An approach based on application of harmonic lasing self-seeding (HLSS) is under study[*]. Effective harmonic lasing occurs in the exponential gain regime in the first part of the undulator, making sure that the fundamental frequency is well below saturation. In the second part of the undulator the value of undulator parameter is reduced such that now the fundamental mode is resonant to the wavelength, previously amplified as the harmonic. The amplification process proceeds in the fundamental mode up to saturation. In this case the bandwidth is defined by the harmonic lasing (i.e. it is reduced by a significant factor depending on harmonic number) but the saturation power is still as high as in the reference case of lasing at the fundamental, i.e. brilliance increases. Application of the undulator tapering in the deep nonlinear regime would allow to generate higher peak powers approaching TW level.
* E.A. Schneidmiller and M.V. Yurkov, Phys. Rev. ST-AB 15, 080702 (2012)