PROBLEM OF STABILITY OF THE EQUILIBRIUM HELICAL ORBIT IN FREE-ELECTRON LASERS

WANG CHANG-BIAO

doi:10.7498/aps.41.1092

Abstract
The problem of stability of the equilibrium helical orbit in free-electron lasers with a combined ideal helical wiggler and uniform axial guide field is successfully solved by means of the Lyapunov's stability theory of motion. The unstable region is determined with perturbation of initial energy taken into account by Lyipunov's first method. An appropriate Lyapuov's function is constructed; accordingly, the low and high guide field stable regions are shown rigorously.
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WANG CHANG-BIAO

1.
电子科技大学高能电子学研究所,成都610054
References

Cited By

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[2]	Zhang Lei, Li Hui-Wu, Hu Liang-Bin. Study of stability of persistent spin helix in two-dimensional electron gases with spin-orbit coupling. Acta Physica Sinica, 2012, 61(17): 177203. doi: 10.7498/aps.61.177203
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[4]	Han Jing-Hua, Feng Guo-Ying, Yang Li-Ming, Zhang Qiu-Hui, Jia Jun, Li Gang, Zhu Qi-Hua, Zhou Shou-Huan. Study on the critical free electron density for nanosecond laser pulse focusing in air. Acta Physica Sinica, 2008, 57(10): 6304-6310. doi: 10.7498/aps.57.6304
[5]	WANG HONG-XIA, YU JUE-BANG. ANALYSIS OF STABILITY FOR EQUILIBRIUM OFCELLULAR NEURAL NETWORKS. Acta Physica Sinica, 2001, 50(12): 2303-2306. doi: 10.7498/aps.50.2303
[6]	LI ZHI-KUAN. DAMPED MOTION OF AN ELECTRON IN FREE-ELECTRON LASER. Acta Physica Sinica, 2000, 49(5): 893-897. doi: 10.7498/aps.49.893
[7]	LI ZHI-KUAN. QUASI-DIRAC EQUATION IN FREE-ELECTRON LASER. Acta Physica Sinica, 1997, 46(7): 1349-1353. doi: 10.7498/aps.46.1349
[8]	WEN SHUANG-CHUN. HARMONICS IN NOVEL WIGGLER FREE-ELECTRON LASER. Acta Physica Sinica, 1997, 46(2): 272-278. doi: 10.7498/aps.46.272
[9]	ZHU JIA-QING. ENERGY CONVERSION OF FREE ELECTRON LASER. Acta Physica Sinica, 1996, 45(1): 52-57. doi: 10.7498/aps.45.52
[10]	MENG LIN, LIU SHENG-GANG. INFLUENCE OF UNTRAPPED ELECTRONS ON THE SIDE-BAND INSTABILITY OF ELECTROMAGNETIC WIGGLER FREE ELECTRON LASER. Acta Physica Sinica, 1994, 43(6): 904-912. doi: 10.7498/aps.43.904
[11]	ZHANG SHI-CHANG, LIU QING-XIANG, XU YONG. ENTROPY-LIKE QUANTITY OF THE EQUILIBRIUM ELECTRONS IN A FREE-ELECTRON LASER WITH REVERSED GUIDE FIELD. Acta Physica Sinica, 1994, 43(2): 225-232. doi: 10.7498/aps.43.225
[12]	XU YONG, ZHANG SHI-CHANG. PHASE ORBITS OF THE EQUILIBRIUM ELECTRONS IN A FREE-ELECTRON LASER WITH A REVERSED GUIDE FIELD. Acta Physica Sinica, 1994, 43(7): 1096-1104. doi: 10.7498/aps.43.1096
[13]	ZHANG YI-BO, JIANG HUA-BEI. A FREE-ELECTRON LASERS PUMPED BY SOLITON LASER. Acta Physica Sinica, 1992, 41(9): 1431-1435. doi: 10.7498/aps.41.1431
[14]	SHU XIAO-JIAN. ELECTRON TRAJECTORIES AND STABILITY IN FEL WITH AN AXIAL GUIDE MAGNETIC FIELD. Acta Physica Sinica, 1991, 40(10): 1624-1631. doi: 10.7498/aps.40.1624
[15]	ZHANG SHI-CHANG, HU ZHONG-XIU, WANG WEN-YAO. EVOLUTION FROM PERIODICITY TO NON-PERIODICITY OF THE ELECTRON PHASE ORBITS IN A FREE ELECTRON LASER WITH UNTAPERED WIGGLER. Acta Physica Sinica, 1990, 39(11): 1745-1750. doi: 10.7498/aps.39.1745
[16]	ZHANG ZHONG, ZHANG SHI-CHANG. EFFECT OF DC SPACE-CHARGE FIELDS ON EQUILIBRIUM ORBITS OF ELECTRONS IN FREE-ELECTRON LASERS. Acta Physica Sinica, 1989, 38(2): 285-289. doi: 10.7498/aps.38.285
[17]	ZHANG SHI-CHANG. THEORETICAL ANALYSIS FOR THE EXPERIMENTS OF RAMAN FREE ELECTRON LASERS. Acta Physica Sinica, 1988, 37(10): 1684-1689. doi: 10.7498/aps.37.1684
[18]	FANG HONG-LIE, G. T. MOORE, M. O. SCULLY. THE EFFECT OF AN INJECTION SIGNAL ON THE FREE-ELECTRON-LASER. Acta Physica Sinica, 1985, 34(1): 17-23. doi: 10.7498/aps.34.17
[19]	FANG HONG-LIE, FU SHU-FEN, G. T. MOORE. STATIONARY PULSE SOLUTIONS FOR A FREE ELECTRON LASER. Acta Physica Sinica, 1984, 33(7): 935-942. doi: 10.7498/aps.33.935
[20]	YIN YUAN-ZHAO. THEORETICAL ANALYSIS OF FREE ELECTRON LASER AMPLIFIER. Acta Physica Sinica, 1983, 32(11): 1407-1415. doi: 10.7498/aps.32.1407

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Vol. 41, Issue 7 - 1992-04-05

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PROBLEM OF STABILITY OF THE EQUILIBRIUM HELICAL ORBIT IN FREE-ELECTRON LASERS

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PROBLEM OF STABILITY OF THE EQUILIBRIUM HELICAL ORBIT IN FREE-ELECTRON LASERS

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