EQUATION OF BEAM ENVELOP FUNCTIONS AND THEIR APPROXIMATE SOLUTIONS

WEI KAI-YU

Chinese Physics C> 1981, Vol. 5> Issue(6) : 687-693

EQUATION OF BEAM ENVELOP FUNCTIONS AND THEIR APPROXIMATE SOLUTIONS

WEI KAI-YU

Institute of High Enerqy Physics, Academia Sinica

Abstract
HTML
Reference
Related

PDF

Abstract：
The normalized equations of beam envelop functions β_u(u = x, y, z) are described. These equations can be used to describe the envelop and emittanee shape of relativistic beam and non-relativistic beam in accelerative systems and transport systems.In the paper, we also described an approximate method solving these equations in the case to take into account acceleration process and beam space charge effect, and have obtained the expressions of the approximate solutions in this case.

References

[1]

M. Kapehinskij and V. V. Vladimirakij, Int. Conf, on High Energy Accelerators and Instn· mentation, CERN, p. 274 (1959).[2] И. М. Капчинский, дииамика частиц влинейныx резонансныx ускорнтеляx, атомнздат москва, стр 191 (1966).[3] K. Batchelor, Proc. 1976 Proton Linear Accelerator Conference, AECL 5677, p.160, Chalk River, ont. (1976).[4] G. Lambertson et al., IEEE, Trans, Nucl. Sci., 24.3(1977), 993.[5] F. J. 19acherer, CERN/SI/Int, DL/70-12, (1970).[6] C. R. Emigh, Proc. 1972 Proton Linear Accelerator Conf. LA5115, p. 182, Los. Alamos (1972).[7] 谢羲等,科技,2(1978), 119.[8] 魏开嫂,带电束流传翰理论,北京电机工程学会,(1980).[9] 魏开退,高能物理与核物理,Vol. 6, No. 8, (1981), 328.

[1]	WANG Yi-Fang . Beam Matching Between SFC and SSC. Chinese Physics C, 2008, 32(S1): 223-225.
[2]	LU Jian-Qin , LI Jin-Hai . Computer Codes for the Beam Optics Calculations —Third Order Approximation. Chinese Physics C, 2006, 30(S1): 25-27.
[3]	LI Kang , WANG Jian-Hua . Green Function Solution to the Doublet Potential Equations of the Moving Dyons. Chinese Physics C, 2005, 29(8): 731-735.
[4]	Wang Lanfa , Lin Yuzheng . Potential Well Distortion Effects and Bunch Shift Compensation. Chinese Physics C, 1999, 23(10): 1024-1032.
[5]	Shi Kangiie , Li Guangliang , Fan Heng , Hou Boyu . Multi-Parameter Solution to the Reflection Equation of Z_n Belavin Model. Chinese Physics C, 1999, 23(5): 425-435.
[6]	Wang Lanfa , Lin Yuzheng , Tong Dechun . Beam Loading Effects for A Tow-Beam Ring. Chinese Physics C, 1999, 23(8): 828-834.
[7]	Guo Zhongyan , Zhan Wenlong , Sun Zhiyu , Xiao Guoqing , Jiang Shanhong , Li Jiaxing , Meng Xiangwei , Wang Jinchuan , Zhang Wansheng , Qin Lijun , Wang Quanjin . RIBLL Beam Diagnostics. Chinese Physics C, 1999, 23(3): 237-243.
[8]	Hui Ping . Fifth Order Approximate Analytic Calculation of (2+1)-D SU(2) Vacuum Wavefunction. Chinese Physics C, 1998, 22(4): 322-325.
[9]	Li Guangxiao , Fang Shouxian . Realizability of the Permanent Magnet Mini-β Scheme for the Beijing Electron Positron Collider. Chinese Physics C, 1995, 19(10): 952-958.
[10]	Bian Jianguo , Huang Tao . Pseudo-Scalar Meson Solutions of the Equal-Time Equation IN QCD. Chinese Physics C, 1994, 18(2): 127-136.
[11]	WANG Shan , LIU Yi-Ming , JIANG Yu-Zhen , CHEN Xiao-Fan . AZIMUTHAL CORRELATION FUNCTION AND THE NUCLEAR EQUATION OF STATE. Chinese Physics C, 1990, 14(10): 907-911.
[12]	MAO Nai-Feng , LI Zeng-Hai . SPLINE FUNCTION REPRESENTATION FOR TRANSFORMATION OF PHASE SPACE WITH ARBITRARY CONTOURS. Chinese Physics C, 1989, 13(5): 445-450.
[13]	DAI You-Shan , SONG Xiao-Tong . THE BETHE-SALPETER EQUATION FOR SPIN (0—3/2) ELECTROMAGNETIC BOUND SYSTEM AND ITS APPROXIMATE SOLUTION. Chinese Physics C, 1986, 10(5): 527-535.
[14]	YAN Jun-Hu . EXACT SOLUTION OF THE PAULI EQUATION IN THE FIELD OF A 'T HOOFT-POLYAKOV MONOPOLE. Chinese Physics C, 1985, 9(3): 367-370.
[15]	HUANG Nian-Ning . ON THE ONE-SOLITON SOLUTIONS OT SUPER-GORDON EGUATION. Chinese Physics C, 1985, 9(3): 382-384.
[16]	PENG SHOU-LI , ZHAO SHU-SONG . GENERAL ANALYTIC SOLUTIONS OF THE THREE DIMENSIONAL ELECTRON SHOWER EQUATIONS IN THE NON-HOMOGENEOUS MEDIUM. Chinese Physics C, 1981, 5(1): 47-54.
[17]	WEI KAI-YU . THE BEAM ENVELOP ANALYSIS FOR NONPERIODIC SYSTEMS. Chinese Physics C, 1981, 5(3): 328-333.
[18]	Li Bing-an , Xian Ding-chang , Yan Su , Chen Tian-lun , Yang Qing-zhu , Lu Jing-fa . THE INFLUENCE OF THE SELF-ENERGY DIAGRAMS ON THE SOLUTIONS OF A SCALAR BETHE SALPETER EQUATION. Chinese Physics C, 1980, 4(1): 33-42.
[19]	Tao Fu-zhen , Yao Qi-yuan , Ou Zhi , He Zhi-qiang . THE SPHERICAL SOLUTIONS OF THE SCALAR FIELD EQUATION IN SU (2) GAUGE FIELD THEORY. Chinese Physics C, 1980, 4(2): 179-185.
[20]	SHI YI-JIN , HE YIN . INVESTIGATION OF NON-LINFAR SCHRODINGER EQUATION SOLITON SOLUTION. Chinese Physics C, 1979, 3(4): 418-431.

Access

Get Citation

WEI KAI-YU. EQUATION OF BEAM ENVELOP FUNCTIONS AND THEIR APPROXIMATE SOLUTIONS[J]. Chinese Physics C, 1981, 5(6): 687-693.

WEI KAI-YU. EQUATION OF BEAM ENVELOP FUNCTIONS AND THEIR APPROXIMATE SOLUTIONS[J]. Chinese Physics C, 1981, 5(6): 687-693. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1980-09-08
Revised: 1900-01-01

Article Metric

Article Views(1478)
PDF Downloads(309)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

EQUATION OF BEAM ENVELOP FUNCTIONS AND THEIR APPROXIMATE SOLUTIONS

WEI KAI-YU

Institute of High Enerqy Physics, Academia Sinica

Received Date: 1980-09-08
Accepted Date: 1900-01-01
Available Online: 1981-12-05

Abstract: The normalized equations of beam envelop functions β_u(u = x, y, z) are described. These equations can be used to describe the envelop and emittanee shape of relativistic beam and non-relativistic beam in accelerative systems and transport systems.In the paper, we also described an approximate method solving these equations in the case to take into account acceleration process and beam space charge effect, and have obtained the expressions of the approximate solutions in this case.