Chinese Physics C > 1981, Vol. 5 > Issue(3): 328-333

THE BEAM ENVELOP ANALYSIS FOR NONPERIODIC SYSTEMS

WEI KAI-YU

Institute of High Energy Physics, Academia Sinica

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Abstract：
The beam envelops for non-periodic alternating gradient focusing system is analysed. The accurate analytic expressions of the beam envelop function β is obtained by solving the following non-linear differential equation: (√β)^н+Q(Z)√β-1/(√β)³=0,
The conditions of existing the maximum and the minimum of beam envelop are discussed. And we have derived the accurate formulae with which one can calculate the maximum and the minimum values of envelop and their position. The method developed in this paper is different from the convintional matrix computational method. Both methods can be checked by each other.
References

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[3]	G.S.Taki¹,P.R.Sarma¹,A.G.Drentje²,T.Nakagawa³,P.K.Ray⁴,R.K.Bhandari¹. Observation of Burst Frequency in Extracted ECR Ion Current. Chinese Physics C, 2007, 31(S1): 170-173.
[4]	SONG Yuan-Jun,WANG Shun-Jin,ZHANG Guang-Biao. Nonadiabatic Geometric Phase and Hannay's Angle of the Nonautonomous Landau System in a Rotating Magnetic Field. Chinese Physics C, 2005, 29(7): 639-643.
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[8]	LV Jian-Qin,LI Chao-Long,LI Jin-Hai. Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses. Chinese Physics C, 2003, 27(1): 76-82.
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WEI KAI-YU. THE BEAM ENVELOP ANALYSIS FOR NONPERIODIC SYSTEMS[J]. Chinese Physics C, 1981, 5(3): 328-333.

WEI KAI-YU. THE BEAM ENVELOP ANALYSIS FOR NONPERIODIC SYSTEMS[J]. Chinese Physics C, 1981, 5(3): 328-333. shu

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Received: 1980-02-11
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

THE BEAM ENVELOP ANALYSIS FOR NONPERIODIC SYSTEMS

WEI KAI-YU

Institute of High Energy Physics, Academia Sinica

Received Date:1980-02-11
Accepted Date:1900-01-01
Available Online:1981-06-05

Abstract:The beam envelops for non-periodic alternating gradient focusing system is analysed. The accurate analytic expressions of the beam envelop function β is obtained by solving the following non-linear differential equation:(√β)^н+Q(Z)√β-1/(√β)³=0,
The conditions of existing the maximum and the minimum of beam envelop are discussed. And we have derived the accurate formulae with which one can calculate the maximum and the minimum values of envelop and their position. The method developed in this paper is different from the convintional matrix computational method. Both methods can be checked by each other.