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

EQUATION OF BEAM ENVELOP FUNCTIONS AND THEIR APPROXIMATE SOLUTIONS

  •  Institute of High Enerqy Physics, Academia Sinica

  • The normalized equations of beam envelop functions βu(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.
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    [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.

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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
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Received: 1980-09-08
Revised: 1900-01-01
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EQUATION OF BEAM ENVELOP FUNCTIONS AND THEIR APPROXIMATE SOLUTIONS

  • 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 βu(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.

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