On the XFEL Schroedinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging
Abstract
We analyse a nonlinear Schr\"odinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree-Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray Free Electron Laser (XFEL). We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schr\"odinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.
Keywords
Cite
@article{arxiv.1209.6089,
title = {On the XFEL Schroedinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging},
author = {Paolo Antonelli and Agisillaos Athanassoulis and Hichem Hajaiej and Peter Markowich},
journal= {arXiv preprint arXiv:1209.6089},
year = {2012}
}
Comments
17 pages, submitted