Numerical Simulations of X-Ray Free Electron Lasers (XFEL)

Handle URI:
http://hdl.handle.net/10754/555671
Title:
Numerical Simulations of X-Ray Free Electron Lasers (XFEL)
Authors:
Antonelli, Paolo; Athanassoulis, Agissilaos; Huang, Zhongyi; Markowich, Peter A. ( 0000-0002-3704-1821 )
Abstract:
We 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].
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Numerical Simulations of X-Ray Free Electron Lasers (XFEL) 2014, 12 (4):1607 Multiscale Modeling & Simulation
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
Multiscale Modeling & Simulation
Issue Date:
4-Nov-2014
DOI:
10.1137/130927838
Type:
Article
ISSN:
1540-3459; 1540-3467
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/130927838
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAntonelli, Paoloen
dc.contributor.authorAthanassoulis, Agissilaosen
dc.contributor.authorHuang, Zhongyien
dc.contributor.authorMarkowich, Peter A.en
dc.date.accessioned2015-05-25T08:34:33Zen
dc.date.available2015-05-25T08:34:33Zen
dc.date.issued2014-11-04en
dc.identifier.citationNumerical Simulations of X-Ray Free Electron Lasers (XFEL) 2014, 12 (4):1607 Multiscale Modeling & Simulationen
dc.identifier.issn1540-3459en
dc.identifier.issn1540-3467en
dc.identifier.doi10.1137/130927838en
dc.identifier.urihttp://hdl.handle.net/10754/555671en
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].en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/130927838en
dc.rightsArchived with thanks to Multiscale Modeling & Simulationen
dc.subjectX-ray free electron laseren
dc.subjectnonlinear Schrodinger equationen
dc.subjecttime-splitting spectral methoden
dc.subjectBloch decompositionen
dc.titleNumerical Simulations of X-Ray Free Electron Lasers (XFEL)en
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalMultiscale Modeling & Simulationen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionCentro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Piazza dei Cavalieri, 3, 56100 Pisa, Italyen
dc.contributor.institutionDepartment of Mathematics, University of Leicester, 1 University Road, LE1 7RH Leicester, UKen
dc.contributor.institutionDepartment of Mathematical Sciences, Tsinghua University, Beijing 100084, Chinaen
kaust.authorMarkowich, Peter A.en
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