@MISC{_necessarycondition, author = {}, title = {NECESSARY CONDITION FOR BEAM ORDERING}, year = {} }
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Abstract
The very low momentum spread for small number of particle was reached on different storage rings. When the sudden reduction of the momentum spread ("phase transition") was observed during decreasing of the particle number it was interpreted as ordered state of ion beams. The most extensive study of ordered ion beams was done on storage rings ESR (GSI, Darmstadt) [1] and CRYRING (MSL, Stockholm) [2]. Recently, for the first time, the ordered proton beam has been observed on S-LSR (ICR, Kyoto University) [3]. This article presents the experimental investigation of low intensity proton beams on COSY (IKP, Juelich) and S-LSR which have the aim to formulate the necessary conditions for the achievement of the ordering state. The experimental studies on S-LSR and numerical simulation with the BETACOOL code [4] were done for the dependence of the momentum spread and transverse emittances on particle number with different misalignments of the magnetic field at the cooler section.