Optimization of the lattice function in the planar undulator applied for terahertz FEL oscillators

  • Since the beta function of the electron beam within the undulator has a great influence on the power gain of the free electron laser (FEL), optimization of the undulator lattice becomes important. In this paper, the transfer matrix of the planar undulator is obtained from differential equations of the electron motion. Based on this, the lattice function of the planar undulator in a terahertz FEL oscillator proposed by Huazhong University of Science and Technology (HUST-FEL) is optimized and the expressions of the average beta function are derived. The accuracy of the optimization result was confirmed well by the numerical method. The application range of this analytical method is given as well. At last, the emittance growth in the horizontal direction due to the attenuation of the magnetic field is discussed.
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  • [1] Krinsky S. The Physics and Properties of Free-Electron Lasers. AIP Conference Proceedings. 2002, 648: 23[2] HUANG Z, Kim K J. Physical Review Special Topics-Accelerators and Beams, 2007, 10(2): 034801[3] Feldhaus J, Arthur J, Hastings J B. Journal of Physics B: Atomic, Molecular and Optical Physics, 2005, 38(9): S799[4] Pellegrini C, Sthr J. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2003, 500(1): 33-40[5] Saldin E L, Schneidmiller E E A, Yurkov M V. The Physics of Free Electron Lasers. Springer Verlag, 2000[6] XIE M. Design Optimization for an X-ray Free Electron Laser Driven by SLAC Linac Particle Accelerator Conference, 1995, Proceedings of the 1995. IEEE, 1995, 1: 183-185[7] Nuhn H D. Linac Coherent Light Source (LCLS) Conceptual Design Report. Stanford Linear Accelerator Center, Menlo Park, CA (US), 2002[8] Schmüser P, Dohlus M, Rossbach J. Ultraviolet and Soft X-ray Free-Electron Lasers: Introduction to Physical Principles, Experimental Results, Technological Challenges. Springer Verlag, 2008[9] Qi-ka J, Shancai Z, Shengkuan L et al. Design of Undulator for the Shanghai DUV-FEL Proceedings of the 2004 FEL Conference. 2004, 494-497[10] QIN B, TAN P, YANG L, LIU X L. Nuclear Instruments and Methods in Physics Research A, 2013, 727: 90-96[11] Quattromini M, Artioli M, Di Palma E et al. Physical Review Special Topics-Accelerators and Beams, 2012, 15(7): 080704[12] RADIA Technical Reference Manual. ESRF, Grenoble, France[13] Freund H P, Antonsen T M. Principles of Free-Electron Lasers. Springer Verlag, 1996[14] Wiedemann H. Particle Accelerator Physics. Springer Verlag, 2007[15] Emma P, HUANG Z, Kim K J et al. Physical Review Special Topics-Accelerators and Beams, 2006, 9(8): 100702[16] Zholents A A. Physical Review Special Topics-Accelerators and Beams, 2005, 8(3): 040701[17] HUANG Z, Borland M, Emma P et al. Physical Review Special Topics-Accelerators and Beams, 2004, 7(6): 074401[18] Freund H P, Neil G R. Proceedings of the IEEE, 1999, 87(4): 782-803[19] DOU Y, SHU X, WANG Y. High Power Laser and Particle Beams, 2006, 8: 024 (in Chinese)[20] QIN B, CHEN D Z, ZHAO L C et al. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2010, 620(1): 121-127
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YANG Lei, QIN Bin, YANG Jun, LIU Xia-Ling, TAN Ping and HU Tong-Ning. Optimization of the lattice function in the planar undulator applied for terahertz FEL oscillators[J]. Chinese Physics C, 2014, 38(3): 037004. doi: 10.1088/1674-1137/38/3/037004
YANG Lei, QIN Bin, YANG Jun, LIU Xia-Ling, TAN Ping and HU Tong-Ning. Optimization of the lattice function in the planar undulator applied for terahertz FEL oscillators[J]. Chinese Physics C, 2014, 38(3): 037004.  doi: 10.1088/1674-1137/38/3/037004 shu
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Received: 2013-04-27
Revised: 1900-01-01
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Optimization of the lattice function in the planar undulator applied for terahertz FEL oscillators

    Corresponding author: QIN Bin,

Abstract: Since the beta function of the electron beam within the undulator has a great influence on the power gain of the free electron laser (FEL), optimization of the undulator lattice becomes important. In this paper, the transfer matrix of the planar undulator is obtained from differential equations of the electron motion. Based on this, the lattice function of the planar undulator in a terahertz FEL oscillator proposed by Huazhong University of Science and Technology (HUST-FEL) is optimized and the expressions of the average beta function are derived. The accuracy of the optimization result was confirmed well by the numerical method. The application range of this analytical method is given as well. At last, the emittance growth in the horizontal direction due to the attenuation of the magnetic field is discussed.

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