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On the XFEL Schrödinger Equation

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

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Original languageEnglish
Pages (from-to)711-732
Number of pages22
JournalArchive for Rational Mechanics and Analysis
Volume211
Issue number3
DOIs
StatePublished - Mar 2014

Abstract

We analyse a nonlinear Schrödinger 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. We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schrödinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.

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