TY - JOUR
T1 - On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging
AU - Antonelli, Paolo
AU - Athanassoulis, Agisillaos
AU - Hajaiej, Hichem
AU - Markowich, Peter A.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: P. Antonelli and A. Athanassoulis would like to thank the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge for its hospitality and support during the preparation of this work. This research was supported by the Investigator Award Nr. KUK-I1-007-43 funded by the King Abdullah University of Science and Technology. H. Hajaiej extends his appreciation to the deanship of scientific research at King Saud University through the research group project RGP-VPP124.
PY - 2014/1/14
Y1 - 2014/1/14
N2 - 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. © 2014 Springer-Verlag Berlin Heidelberg.
AB - 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. © 2014 Springer-Verlag Berlin Heidelberg.
UR - http://hdl.handle.net/10754/563339
UR - http://arxiv.org/abs/arXiv:1209.6089v1
UR - http://www.scopus.com/inward/record.url?scp=84895903084&partnerID=8YFLogxK
U2 - 10.1007/s00205-013-0715-8
DO - 10.1007/s00205-013-0715-8
M3 - Article
SN - 0003-9527
VL - 211
SP - 711
EP - 732
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 3
ER -