Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields
In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enha...
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MDPI AG
2021-01-01
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| Online Access: | https://www.mdpi.com/2073-8994/13/1/135 |
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| author | Konstantin Zhukovsky Igor Fedorov |
| author_facet | Konstantin Zhukovsky Igor Fedorov |
| author_sort | Konstantin Zhukovsky |
| collection | DOAJ |
| description | In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of the high harmonics of undulator radiation (UR). The effect on the spontaneous and stimulated UR was explored. The exact integral forms for the Bessel coefficients were obtained for undulators with general symmetric and asymmetric field harmonics. Spectral properties of the radiation from several configurations of the undulator fields with harmonics were compared with each other. The resulting spontaneous UR spectrum and harmonic intensities were obtained analytically in the form of integrals and compared with the respective results that were obtained numerically with SPECTRA program. The dimensionless scaling parameter of a free electron laser (FEL)—the Pierce parameter (<i>ρ</i>)—was computed and compared for the different considered undulators. We studied the differences in the behavior of the high-gain single pass FEL harmonics and the spontaneous UR harmonics in the same undulators. The undulators with variable deflection parameter (<i>k</i>) were considered. The effect of the <i>k</i> parameter (deflection parameter for a common planar undulator) on the spontaneous UR and on the high-gain FEL radiation was explored. In this context, an experiment with variable strength undulators at FLASH 2 FEL was analyzed; the shorter saturated length in high harmonic self-seeding (HHSS) regime vs. self-amplified spontaneous emission (SASE) is explained. |
| first_indexed | 2024-03-09T04:40:45Z |
| format | Article |
| id | doaj.art-2c3a1eb77add442c85ad60964fe7ee6a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T04:40:45Z |
| publishDate | 2021-01-01 |
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| series | Symmetry |
| spelling | doaj.art-2c3a1eb77add442c85ad60964fe7ee6a2023-12-03T13:20:11ZengMDPI AGSymmetry2073-89942021-01-0113113510.3390/sym13010135Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic FieldsKonstantin Zhukovsky0Igor Fedorov1Department of Theoretical Physics, Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, RussiaDepartment of Theoretical Physics, Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, RussiaIn this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of the high harmonics of undulator radiation (UR). The effect on the spontaneous and stimulated UR was explored. The exact integral forms for the Bessel coefficients were obtained for undulators with general symmetric and asymmetric field harmonics. Spectral properties of the radiation from several configurations of the undulator fields with harmonics were compared with each other. The resulting spontaneous UR spectrum and harmonic intensities were obtained analytically in the form of integrals and compared with the respective results that were obtained numerically with SPECTRA program. The dimensionless scaling parameter of a free electron laser (FEL)—the Pierce parameter (<i>ρ</i>)—was computed and compared for the different considered undulators. We studied the differences in the behavior of the high-gain single pass FEL harmonics and the spontaneous UR harmonics in the same undulators. The undulators with variable deflection parameter (<i>k</i>) were considered. The effect of the <i>k</i> parameter (deflection parameter for a common planar undulator) on the spontaneous UR and on the high-gain FEL radiation was explored. In this context, an experiment with variable strength undulators at FLASH 2 FEL was analyzed; the shorter saturated length in high harmonic self-seeding (HHSS) regime vs. self-amplified spontaneous emission (SASE) is explained.https://www.mdpi.com/2073-8994/13/1/135undulatorradiationharmonicsfree electron laser |
| spellingShingle | Konstantin Zhukovsky Igor Fedorov Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields Symmetry undulator radiation harmonics free electron laser |
| title | Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields |
| title_full | Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields |
| title_fullStr | Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields |
| title_full_unstemmed | Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields |
| title_short | Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields |
| title_sort | spontaneous and stimulated undulator radiation in symmetric and asymmetric multi periodic magnetic fields |
| topic | undulator radiation harmonics free electron laser |
| url | https://www.mdpi.com/2073-8994/13/1/135 |
| work_keys_str_mv | AT konstantinzhukovsky spontaneousandstimulatedundulatorradiationinsymmetricandasymmetricmultiperiodicmagneticfields AT igorfedorov spontaneousandstimulatedundulatorradiationinsymmetricandasymmetricmultiperiodicmagneticfields |