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Abstract
The complex number field is an associative division algebra over the real number field. In this paper we define an inner product in this field, and take this new algebraic system as a tool to study a general combined electric-magnetic focussing-deflection system with superimposed fields The relativistic third-order geometrical aberration formulas for this combined system have been derived.
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LI YU

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[1]	Liu Rong, Tian Jin-Shou, Li Hao, Wang Qiang-Qiang, Wang Chao, Wen Wen-Long, Lu Yu, Liu Hu-Lin, Cao Xi-Bin, Wang Jun-Feng, Xu Xiang-Yan, Wang Xing.Design and evaluation of a pre-traveling wave deflector magnetic solenoid lens focused streak image tube. Acta Physica Sinica, 2014, 63(5): 058501.doi:10.7498/aps.63.058501
[2]	Zhang Yi.Symmetry of Birkhoffians and conserved quantity for a relativistic mechanical system. Acta Physica Sinica, 2012, 61(21): 214501.doi:10.7498/aps.61.214501
[3]	Xu Jian-Wei, Wang Shun-Jin.Relativistic mean field theory of electron and first, second-order Rashba effects. Acta Physica Sinica, 2009, 58(7): 4878-4882.doi:10.7498/aps.58.4878
[4]	Ding Bin-Gang, Zhang Da-Li, Lu Ding-Hui.A systematic study on nuclear pairing energy under the relativistic mean-field model. Acta Physica Sinica, 2009, 58(9): 6086-6090.doi:10.7498/aps.58.6086
[5]	Zhang Kai, Feng Jun.Symmetry and stability of a relativistic birkhoff system. Acta Physica Sinica, 2005, 54(7): 2985-2989.doi:10.7498/aps.54.2985
[6]	Fang Jian-Hui, Yan Xiang-Hong, Chen Pei-Sheng.Form invariance and Noether symmetry of a relativistic mechanical system. Acta Physica Sinica, 2003, 52(7): 1561-1564.doi:10.7498/aps.52.1561
[7]	Fang Jian-Hui, Chen Pei-Sheng, Zhang Jun, Li Hong.Form invariance and Lie symmetry of relativistic mechanical system. Acta Physica Sinica, 2003, 52(12): 2945-2948.doi:10.7498/aps.52.2945
[8]	Jia Li-Qun.A theory of relativistic analytical statics of rotational systems. Acta Physica Sinica, 2003, 52(5): 1039-1043.doi:10.7498/aps.52.1039
[9]	FANG JIAN-HUI, ZHAO SONG-QING.LIE SYMMETRIES AND CONSERED QUANTITIES OF RELATIVISTIC ROTATIONAL VARIABLE MASS SYSTEM. Acta Physica Sinica, 2001, 50(3): 390-393.doi:10.7498/aps.50.390
[10]	LUO SHAO-KAI, FU JING-LI, CHEN XIANG-WEI.BASIC THEORY OF RELATIVISTIC BIRKHOFFIAN DYNAMICS OF ROTATIONAL SYSTEM. Acta Physica Sinica, 2001, 50(3): 383-389.doi:10.7498/aps.50.383
[11]	LUO SHAO-KAI, GUO YONG-XIN, CHEN XIANG-WEI.INTEGRATION THEORY OF THE DYNAMICS OF A ROTATIONAL RELATIVISTIC SYSTEM. Acta Physica Sinica, 2001, 50(11): 2053-2058.doi:10.7498/aps.50.2053
[12]	LIU LU-XIN.APPLICATIONS OF THE THEORY OF RELATIVISTIC THERMODYNAMICS TO THE SCHWARZSCHILD MATTER SYSTEM IN THE GRAVITATIONAL FIELD. Acta Physica Sinica, 1997, 46(12): 2300-2304.doi:10.7498/aps.46.2300
[13]	ZENG GUI-HUA, YU WEI, SHEN BAI-FEI, XU ZHI-ZHAN.HIGH-ORDER RELATIVISTIC GENERATION BY INTENSE LASER PULSE. Acta Physica Sinica, 1996, 45(9): 1487-1491.doi:10.7498/aps.45.1487
[14]	LI YU.ON THE RELATIVISTIC FIFTH ORDER GEOMETRICAL ABERRATION EQUATION OF A COMBINED FOCUSING-DEFLECTION SYSTEM. Acta Physica Sinica, 1986, 35(11): 1488-1495.doi:10.7498/aps.35.1488
[15]	Ai Ke-cong, Ximen Ji-ye, Zhou Li-wei.RELATIVISTIC ABERRATION THEORY FOR A COMBINED ELECTROMAGNETIC FOCUSING-DEFLECTION SYSTEM POSSESSING A SPHERICAL CATHODE LENS. Acta Physica Sinica, 1986, 35(9): 1210-1222.doi:10.7498/aps.35.1210
[16]	DING SHOU-QIAN.A GENERALIZED FORMULA OF THE THIRD ORDER ELECTRICAL DEFLECTION ABERRATION COEFFICIENTS AND THEIR RELATION WITH THE RASTER PATTERN. Acta Physica Sinica, 1983, 32(2): 145-155.doi:10.7498/aps.32.145
[17]	ZHOU LI-WEI, AI KE-CONG, PAN SHUN-CHEN.ON ABERRATION THEORY OF THE COMBINED ELECTROMAGNETIC FOCUSSING CATHODE LENSES. Acta Physica Sinica, 1983, 32(3): 376-392.doi:10.7498/aps.32.376
[18]	LI YU, XIMEN JI-YE.ON THE RELATIVISTIC ABERRATION THEORY OF A COMBINED FOCUSING-DEFLECTION SYSTEM WITH MULTI-STAGE DEFLECTORS. Acta Physica Sinica, 1982, 31(5): 604-614.doi:10.7498/aps.31.604
[19]	XIMEN JI-YE.THE ELECTRON-OPTICAL CHARACTERS AND ABBERATION THEORY OF A COMBINED SYSTEM CONSISTS OF ELECTROSTATIC ROUND LENS AND MAGNETIC DEFLECTOR. Acta Physica Sinica, 1978, 27(3): 247-259.doi:10.7498/aps.27.247
[20]	XIMEN JI-YE.THE ELECTRON OPTICAL PROPERTIES AND ABERRATION THEORY OF A COMBINED MAGNETIC ROUND LENS AND DEFLECTION SYSTEM. Acta Physica Sinica, 1977, 26(1): 34-53.doi:10.7498/aps.26.34

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Vol. 30, Issue 9 - 1981-05-05

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