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dc.contributor.authorAntonelli, Paolo
dc.contributor.authorAthanassoulis, Agissilaos
dc.contributor.authorHuang, Zhongyi
dc.contributor.authorMarkowich, Peter A.
dc.date.accessioned2015-05-25T08:34:33Z
dc.date.available2015-05-25T08:34:33Z
dc.date.issued2014-11-04
dc.identifier.citationNumerical Simulations of X-Ray Free Electron Lasers (XFEL) 2014, 12 (4):1607 Multiscale Modeling & Simulation
dc.identifier.issn1540-3459
dc.identifier.issn1540-3467
dc.identifier.doi10.1137/130927838
dc.identifier.urihttp://hdl.handle.net/10754/555671
dc.description.abstractWe study a nonlinear Schrödinger equation which arises as an effective single particle model in X-ray free electron lasers (XFEL). This equation appears as a first principles model for the beam-matter interactions that would take place in an XFEL molecular imaging experiment in [A. Fratalocchi and G. Ruocco, Phys. Rev. Lett., 106 (2011), 105504]. Since XFEL are more powerful by several orders of magnitude than more conventional lasers, the systematic investigation of many of the standard assumptions and approximations has attracted increased attention. In this model the electrons move under a rapidly oscillating electromagnetic field, and the convergence of the problem to an effective time-averaged one is examined. We use an operator splitting pseudospectral method to investigate numerically the behavior of the model versus that of its time-averaged version in complex situations, namely the energy subcritical/mass supercritical case and in the presence of a periodic lattice. We find the time-averaged model to be an effective approximation, even close to blowup, for fast enough oscillations of the external field. This work extends previous analytical results for simpler cases [P. Antonelli, A. Athanassoulis, H. Hajaiej, and P. Markowich, Arch. Ration. Mech. Anal., 211 (2014), pp. 711--732].
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/130927838
dc.rightsArchived with thanks to Multiscale Modeling & Simulation
dc.subjectX-ray free electron laser
dc.subjectnonlinear Schrodinger equation
dc.subjecttime-splitting spectral method
dc.subjectBloch decomposition
dc.titleNumerical Simulations of X-Ray Free Electron Lasers (XFEL)
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalMultiscale Modeling & Simulation
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionCentro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Piazza dei Cavalieri, 3, 56100 Pisa, Italy
dc.contributor.institutionDepartment of Mathematics, University of Leicester, 1 University Road, LE1 7RH Leicester, UK
dc.contributor.institutionDepartment of Mathematical Sciences, Tsinghua University, Beijing 100084, China
kaust.personMarkowich, Peter A.
refterms.dateFOA2018-06-13T20:12:03Z


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