Open AccessThe transverse space-charge force in tri-gaussian distribution
Author(s) -
K.Y. Ng
Publication year - 2005
Language(s) - English
Resource type - Reports
DOI - 10.2172/879032
Subject(s) - sigma , physics , charge (physics) , space (punctuation) , space charge , prime (order theory) , transverse plane , beam (structure) , gaussian , distribution (mathematics) , tracking (education) , geometry , particle physics , mathematical analysis , quantum mechanics , combinatorics , mathematics , optics , electron , computer science , structural engineering , engineering , operating system , psychology , pedagogy
In tracking, the transverse space-charge force can be represented by changes in the horizontal and vertical divergences, {Delta}x{prime} and {Delta}y{prime} at many locations around the accelerator ring. In this note, they are going to list some formulas for {Delta}x{prime} and {delta}y{prime} arising from space-charge kicks when the beam is tri-Gaussian distributed. They will discuss separately a flat beam and a round beam. they are not interested in the situation when the emittance growth arising from space charge becomes too large and the shape of the beam becomes weird. For this reason, they can assume the bunch still retains its tri-Gaussian distribution, with its rms sizes {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} increasing by certain factors. Thus after each turn, {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} can be re-calculated