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arXiv · 1209.6089

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

Paolo Antonelli·Agisillaos Athanassoulis·Hichem Hajaiej·Peter Markowich
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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 (XFEL). 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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Paolo Antonelli, Agisillaos Athanassoulis, Hichem Hajaiej, Peter Markowich. 2012-09-26. On the XFEL Schroedinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging. https://arxiv.org/abs/1209.6089

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