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D. Li 1*, M. Hangyo 2, Z. Yang 3, Y. Tsunawaki 4, Y. Wei 3, Y. Wang 3, S. Miyamoto 5, M. R. Asakawa 4, and K. Imasaki 1
1 Institute for Laser Technology, Suita, Osaka 565-0871, Japan
2 Institute of Laser Engineering, Osaka University, Suita, Osaka 565-0871, Japan
3 School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
4 Department of Pure and Applied Physics, Faculty of Engineering Science, Kansai University, Osaka 564-8680, Japan
5 Laboratory of Advanced Science and Technology for Industry, University of Hyogo, Ako, Hyogo 678-1205, Japan
*1 Email: Dazhi_li@hotmail.com
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Abstract: We present an analytical theory for small-signal operation of a Smith–Purcell free-electron laser with a finitely thick electron beam travelling close to the surface of a grating. The dispersion equation is derived from a self-consistent set of small-signal equations describing the dynamics of beam-wave interaction. Through the analysis of the power flow above the grating, the mechanism of beam-wave interaction in the device is explored. By solving the dispersion equation carefully, we reveal that the growth rate of the field amplitude holds a finite value at the Bragg point, which is different from previous theoretical predictions. After deriving an approximate equation to calculate the growth rate, the oscillation start current of the device is worked out by considering the power flow above the grating. The predictions of our theory are compared with those of particle-in-cell simulations, and the agreement is reasonable.
Keywords: Smith–Purcell free-electron laser, Growth rate, Start current, Particle-in-cell simulation.
Received: 2013-3-8
Published: 2013-9-30
Acknowledgments: This work is partially supported by KAKENHI (No. 24560057); Research Foundation for Opto-Science and Technology; a Grant-in-Aid for Scientific Research on Innovative Areas "Electromagnetic Metamaterials" (No. 22109003) from The Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; the National Natural Science Foundation of China (No. 61271029 and 10975031); The National High Technology Research and Development Program of China (No. 2011AA010204); and the Fundamental Research Funds for the Central Universities (No. ZYGX2009Z003).
Cite this article:
D. Li, M. Hangyo, Z. Yang, Y. Tsunawaki, Y. Wei, Y. Wang, S. Miyamoto, M. R. Asakawa, and K. Imasaki. Theoretical analysis and simulation of growth rate and start current in Smith–Purcell free-electron lasers[J]. International Journal of Terahertz Science and Technology, 2013, Vol.6, No.3: 189-205. DOI:10.11906/TST.189-205.2013.09.13
URL: http://www.tstnetwork.org/10.11906/TST.189-205.2013.09.13
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