On the XFEL Schroedinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

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

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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
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: 18 Nov 2017 00:01
URI: http://preprints.acmac.uoc.gr/id/eprint/277

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