Equilibrium State of Colliding Electron Beams.

Warnock, R. L. ; Ellison, J. A.

Technical Information Center Oak Ridge Tennessee

关键词: Beam currents;    Electron beams;    Beam-beam interactions;    Distribution functions;    Integral functions;   

RP-ID  :  DE2004826599

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

We study a nonlinear integral equation that is a necessary condition on the equilibrium phase space distribution function of stored, colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in one degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, as would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.