volume | PIER Journals

Abstract

In this paper, we discuss the spectral property of radiation of an electron moving in a bi-period harmonic undulator field with a phase between the primary undulator field and the harmonic field component. We derive the expression for the photons per second per mrad² per 0.1% BW of the radiation. A small signal gain analysis is also discussed highlighting this feature of the radiation. A bi-period index parameter, i.e., Λ is introduced in the calculation. According to the value of the index parameter, the scheme can operate as one period or bi-period undulator. It is shown that when Λ = π, the device operates at the fundamental and the third harmonic. However, when Λ = π/2, it is possible to eliminate the third harmonic.

1. Seddon, E. A., J. A. Clarke, D. J. Dunning, C. Masciorecchio, C. J. Miline, F. Parmigiani, R. Dugg, J. C. H. Spence, N. R. Thompson, K. Udea, S. M Vinko, J. S. Wark, and W. Wurth, "Short wavelength free electron laser sources and science: A review," Reports on Progress in Physics, Vol. 80, No. 11, 115901, 2017.
doi:10.1088/1361-6633/aa7cca Google Scholar

2. Huang, C. S., J. C. Jan, C. S. Chang, S. D. Chen, C. H. Chang, and T. M. Ven, "Development trends for insertion devices for future light sources," Phy. Rev. Spl. Topics — Accl. & Beams, Vol. 14, 044801, 2017. Google Scholar

3. Pellegrini, C., "X-ray free electron lasers: From dreams to reality," Physica Scripta, Vol. T169, 014004, 2017. Google Scholar

4. Rossbach, J., J. R. Schneider, and W. Wurth, "10 years of Pioneering x-ray science at the free electron laser FLASH at DESY," Physics Reports, Vol. 808, 1-74, 2019.
doi:10.1016/j.physrep.2019.02.002 Google Scholar

5. Dattoli, G., E. Di Palma, S. Pagnutti, and E. Sabia, "Free electron coherent sources: From microwave to X rays," Physics Reports, Vol. 739, 1-52, 2018.
doi:10.1016/j.physrep.2018.02.005 Google Scholar

6. Tanaka, T., "Current status and future prospective of accelerator based x-ray light source," Journal of Optics, Vol. 19, No. 9, 2017.
doi:10.1088/2040-8986/aa7bf7 Google Scholar

7. Gaith, A., D. Oumbarek, and M. E. Couprie, "Tunable high spatio spectral purity undulator radiation from a transported laser plasma accelerated electron beam," Scientific Reports, Vol. 9, 19020, 2019.
doi:10.1038/s41598-019-55209-4 Google Scholar

8. Couprie, M. E., "Undulator technologies for future free electron laser facilities and storage rings," Proceedings of IPAC, 29-30, MOZB102, Shanghai, China, 2013. Google Scholar

9. Yamamoto, S., "Development of very short period undulators," 9th International Particle Accelerator Conference, IPAC 2018, 1845-1847, Jacow Publishing, Vancouver, B.C, Canada, 2018. Google Scholar

10. Ji, F., R. Chang, Q. Zhou, W. Zhang, M. Ye, S. Sasaki, and S. Qiao, "Design and performance of the APPLE knot undulator," Journal of Synchrotron Radiation, Vol. 22, Part 4, 901, 2015. Google Scholar

11. Kitamura, H., "Recent trends of insertion device technology for X-ray sources," Journal of Synchrotron Radiation, Vol. 7, Part 3, 121, June 2000. Google Scholar

12. Huang, J. C., H. Kitamura, C. K. Yang, and C. H. Chang, "Challenges of in vacuum and cryogenic permanent magnet undulator technologies," Phys. Rev. Accl. Beams. — Accl. & Beams, Vol. 20, 064801, 2017.
doi:10.1103/PhysRevAccelBeams.20.064801 Google Scholar

13. Heung, S., K. Kang, and H. Loos, "X ray free electron laser tuning for variable gap undulator," Phys. Rev. Accl. Beams, Vol. 22, No. 6, 060703, 2019.
doi:10.1103/PhysRevAccelBeams.22.060703 Google Scholar

14. Jaroszynski, D. A., R. Prazers, F. Glotin, and J. M. Ortega, "Two colour operation of the free electron laser using a step tapered undulator," Nuclear Instruments and Methods in Physics Research, A, Vol. 358, No. 1–3, 224-227, 1995.
doi:10.1016/0168-9002(94)01595-3 Google Scholar

15. Blau, J., V. Bouras, W. B. Colson, K. Polykandriotis, A. Kalfoutzos, S. V. Bcnson, and G. R. Neil, "Simulation of the 100KW TJNAF FEL using step tapered undulator," Nuclear Instruments and Methods in Physics Research A, Vol. 483, 138-141, 2002.
doi:10.1016/S0168-9002(02)00299-1 Google Scholar

16. Peng, L., Z. Yang, and S. Liu, "Dual undulator free electron laser," Optics Communication, Vol. 98, No. 4–6, 285, 1993.
doi:10.1016/0030-4018(93)90197-D Google Scholar

17. Mahadizadeh, N., "Efficiency enhancement in a two stream free electron laser with a helical wiggler," Optik, Vol. 182, 1170, 2019.
doi:10.1016/j.ijleo.2019.01.112 Google Scholar

18. Kulish, V. V., A. Lysenko, and V. I. Savchenko, "Two stream free electron laser: General properties," International Journal of Infrared and Millimeter Waves, Vol. 24, No. 2, 129, 2003.
doi:10.1023/A:1021838618554 Google Scholar

19. Marinelli, A., D. Ratner, A. Lutman, J. Turner, J. welch, F. J. Decker, H. Loos, C. Behrens, S. Gilevich, A. A. Miahnahri, S. Vetter, T. J. Maxwell, Y. Ding, R. Coffe, S. Wakatsuki, and Z. Huang, "High intensity double pulse x ray free electron laser," Nature Communications, Vol. 6, 6369, 2015.
doi:10.1038/ncomms7369 Google Scholar

20. Bekefi, G., "Double stream cyclotron maser," Nuclear Instruments and Methods in Physics Research A, Vol. 318, 243, 1992.
doi:10.1016/0168-9002(92)91060-M Google Scholar

21. Saviz, S., Z. Rezaei, and F. M. Aghamir, "Gain enhancement in two-stream free electron laser with a planar wiggler and an axial guide magnetic field," Chin. Phys. B, Vol. 21, No. 9, 094103, 2012.
doi:10.1088/1674-1056/21/9/094103 Google Scholar

22. Davidyuk, I. V., O. A. Shevchenko, V. G. Tcheskidov, N. A. Vinokurov, and Ya. V. Getnamov, "Developing an undulator with a variable period for the first stage of Novosibirsk free electron laser," Bulletin of the Russian Academy of Science: Physics, Vol. 83, No. 2, 155-158, 2019.
doi:10.3103/S1062873819020114 Google Scholar

23. Davidyuk, I. V., "Modelling and designing of variable period and variable Pole number undulator," Phy. Rev. Accl. Beams, Vol. 19, 020701, 2016.
doi:10.1103/PhysRevAccelBeams.19.020701 Google Scholar

24. Vinokurov, N. A., O. A. Shevchenko, and V. G. Tcheskidov, "Variable period permanent magnet undulators," Phys. Rev. Spl. Topics — Accl. & Beams, Vol. 14, 040701, 2011.
doi:10.1103/PhysRevSTAB.14.040701 Google Scholar

25. Meseck, A., J. Bahrdt, W. Frentrup, M. Huck, C. Kuhn, R. Rethfeldt, M. Scheer, and E. Rial, "Tripple period undulator," 10th International Particle Accelerator Conference, IPAC 2019, TUPRB022, Australia, 2019. Google Scholar

26. Su, C. H., Designing and multi staggered array undulator, "Designing and multi staggered array undulator," IEEE Trans. Applied Superconductivity, Vol. 14, No. 2, 576-579, 2004.
doi:10.1109/TASC.2004.829978 Google Scholar

27. Shenoy, G. K., J. W. Lewellen, D. Suha, and N. A. Vinukurov, "Variable period undulators as synchrotron radiation sources," J. Synchrotron Radiation Sources, Vol. 10, 205, 2003.
doi:10.1107/S0909049502023257 Google Scholar

28. Mun, J., Y. U. Jeong, N. A. Vinokurov, K. Lee, K. H. Jang, S. H. Park, M. Y. Jeon, and S. I. Shin, "Variable period permanent magnet helical undulator," Phys. Rev. Spl. Topics — Accl. & Beams, Vol. 17, 080701, 2014.
doi:10.1103/PhysRevSTAB.17.080701 Google Scholar

29. Ramm, T. and M. Tischer, "Development of a revolver type undulator," Proceedings of the 10th Mechanical Engineering Design of Synchrotron Radiation Equipment and Instrumentation, TUPH3, Paris, France, 2018. Google Scholar

30. Tanaka, T. and H. Kitamura, "Composite period undulator to improve the wavelength tunability of free electron lasers," Phys. Rev. Spl. Topics — Accl. & Beams, Vol. 15, 050701, 2011.
doi:10.1103/PhysRevSTAB.14.050701 Google Scholar

31. Jia, Q., "Effects of undulator harmonics field on free electron laser harmonic generation," Phy. Rev. Spl. Topics — Accl. & Beams, Vol. 14, 060702, 2011.
doi:10.1103/PhysRevSTAB.14.060702 Google Scholar

32. Zhuovsky, K. V. and A. M. Kalitenko, "Harmonics generation on Planar undulators in single pass free electron lasers," Russian Physics Journal, Vol. 62, No. 2, 354-362, 2019.
doi:10.1007/s11182-019-01719-7 Google Scholar

33. Zhukovsky, K. V., I. A. Potapov, and A. M. Kaliterko, "Two-frequency undulators for generation of x-ray radiation in free electron lasers," Quantum Electronics, Vol. 61, No. 3, 216-231, 2018. Google Scholar

34. Zhukovsky, K., "Two frequency undulator in a short SASE FEL for angstrom wavelengths," Journal of Optics, Vol. 20, No. 9, 2018.
doi:10.1088/2040-8986/aad6af Google Scholar

35. Dattoli, G. V., V. Mikhalin, P. L. Ottaviani, and K. V. Zhukovsky, "Two frequency undulator and harmonic generation by an ultra relativistic electron," Journal of Applied Physics, Vol. 100, No. 8, 084507-084507-12, 2006.
doi:10.1063/1.2357841 Google Scholar

36. Zhukovsky, K. and I. Potapov, "Two frequency undulator usage in compact self amplified spontaneous emission free electron laser in Ranentgen range," Laser and Particle Beams, Vol. 35, No. 2, 325-336, 2017.
doi:10.1017/S0263034617000180 Google Scholar

37. Jeevakhan, H. and G. Mishra, "Spectral properties of two frequency harmonic undulator radiation and effect of energy spread," Nuclear Instruments and Methods in Physics Research, Vol. 656, No. 1, 101, 2011.
doi:10.1016/j.nima.2011.07.011 Google Scholar

38. Mishra, G., M. Gehlot, and H. Jeevakhan, "Spectral properties of bi harmonic undulator radiation," Nuclear Instruments and Methods in Physics Research, Vol. 603, No. 3, 495, 2009.
doi:10.1016/j.nima.2009.02.009 Google Scholar

Dr. Ganeswar Mishra

Dr. Avani Sharma

Dr. Saif Md Khan