SPLINE FUNCTION REPRESENTATION FOR TRANSFORMATION OF PHASE SPACE WITH ARBITRARY CONTOURS

MAO Nai-Feng; LI Zeng-Hai

Chinese Physics C> 1989, Vol. 13> Issue(5) : 445-450

SPLINE FUNCTION REPRESENTATION FOR TRANSFORMATION OF PHASE SPACE WITH ARBITRARY CONTOURS

MAO Nai-Feng ^, ,
LI Zeng-Hai

Institute of Atomic Energy,P.O.Box 275,Beijing

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Abstract：
In order to study the transport of beams with arbitary phase space contours,the spline function representation of phase space contours is proposed in this paper.Having fitted the phase space contours with spline functions,phase space transformations are reduced to spline function transformations,and the envelopes of beams can bt expressed by spline functions.Some typical examples are presented to illustrate the usefulness of this method.

References

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A. P. Banford, Tlie Transport of Charged Particle Beams. London, E. F N. Spon Limited, 1966.[2] C. Lejeune, in "Applied Charged Particle Opticsn (A. Seprier ed.), Part C, Academic Press. New York,1963, 267.[3] E. V. Shpak, Nucl. Instr. and Meth., 213(1963), 171.[4] Chen Yirbao and Xie Xi, Nucl. Instr. and .Meth., 224(1984), 27.[5] 孙家和，样条函数与计算几何，科学出版社，北京，1982，240-260.[6] K. L. Brown, SLAC-91, 1977.

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MAO Nai-Feng and LI Zeng-Hai. SPLINE FUNCTION REPRESENTATION FOR TRANSFORMATION OF PHASE SPACE WITH ARBITRARY CONTOURS[J]. Chinese Physics C, 1989, 13(5): 445-450.

MAO Nai-Feng and LI Zeng-Hai. SPLINE FUNCTION REPRESENTATION FOR TRANSFORMATION OF PHASE SPACE WITH ARBITRARY CONTOURS[J]. Chinese Physics C, 1989, 13(5): 445-450. shu

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Received: 1900-01-01
Revised: 1900-01-01

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SPLINE FUNCTION REPRESENTATION FOR TRANSFORMATION OF PHASE SPACE WITH ARBITRARY CONTOURS

MAO Nai-Feng ^,
LI Zeng-Hai

Corresponding author: MAO Nai-Feng,

Institute of Atomic Energy,P.O.Box 275,Beijing

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1989-05-05

Abstract: In order to study the transport of beams with arbitary phase space contours,the spline function representation of phase space contours is proposed in this paper.Having fitted the phase space contours with spline functions,phase space transformations are reduced to spline function transformations,and the envelopes of beams can bt expressed by spline functions.Some typical examples are presented to illustrate the usefulness of this method.