Antonelli et al. - 2014 - On the XFEL Schrodinger Equation Highly Oscillatory Magnetic Potentials and Time Averaging.pdf (342.2 kB)
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On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

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journal contribution
posted on 11.01.2016, 11:41 by Agisilaos Athanassoulis, P. Antonelli, P. A. Markowich, H. Hajaiej
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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Citation

Archive for Rational Mechanics and Analysis, 2014, 211 (3), pp. 711-732

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Archive for Rational Mechanics and Analysis

Publisher

Springer Berlin Heidelberg

issn

0003-9527

eissn

1432-0673

Acceptance date

14/01/2014

Copyright date

2014

Available date

11/01/2016

Publisher version

http://link.springer.com/article/10.1007/s00205-013-0715-8

Language

en

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