The Equilibrium State of Colliding Electron Beams ∗

Integral Equation for the Equilibrium State of Colliding Electron Beams

We study a nonlinear integral equation for the equilbrium phase distribution of stored colliding electron beams. It is analogous to the Haı̈ssinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. We prove existence of a unique solution, thus the existence of a unique equilibrium state, for sufficiently small current. This is done for the Chao-Ruth model ...

LONGITbDINAL EFFECTS OF COLLIDING BEAM SPACE CHARGE FORCES IN ELECTRON-POSITRON STORkE RINGS WITH CROSkNG ANGLES*

In electron-positron storage rings in which the orbits of the colliding beams cross at a substantial angle, a phase-dependent longitudinal force is exerted on the particles of each beam by the bunches of the other. The effects of this force on both incoherent and coherent longitudinal particle motion are investigated. These effects impose a limit on the number of particles which can be stored i...

Existence and Properties of an Equilibrium State with Beam - Beam Collisions

The equilbrium phase distribution of stored colliding electron beams is studied from the viewpoint of Vlasov-Fokker-Planck (VFP) theory. Numerical integration of the VFP system in one degree of freedom revealed a nearly Gaussian equilibrium with non-diagonal covariance matrix. This result is reproduced approximately in an analytic theory based on linearization of the beam-beam force. Analysis o...

Longitudinally Polarized Colliding Beams

The feasibility of experiments with the polarized colliding beams expands significantly possibilities of getting information on fundamental interactions. Even the use of the transversely polarized beams enables getting the more reliable and clear definition of spins for the intermediate states and final particles,1p2 as well as to introduce the precise absolute energy scale.3-s But only the use...

Final State Hadrons in Deep Inelastic Processes and Colliding Beams*