Antonelli, Paolo and Athanassoulis, Agissilaos and Hajaiej, Hichem and Markowich, Peter
(2014)
*On the XFEL Schroedinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging.*
Archive for Rational Mechanics and Analysis, Springer, 211 (3).
pp. 711-732.
ISSN 0003-9527

Text (XFEL)
acmac-0277.pdf - Submitted Version Download (354Kb) |

## 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.

Item Type: | Article |
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Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics > Department of Applied Mathematics |

Depositing User: | Dr Agisilaos Athanasoulis |

Date Deposited: | 07 Feb 2014 11:01 |

Last Modified: | 24 Feb 2018 10:09 |

URI: | http://preprints.acmac.uoc.gr/id/eprint/277 |

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