Emittance growth in heavy ion rings due to the effects of space charge and dispersion

Abstract

We review the derivation of moment equations which include the effects of space charge and dispersion in bends first presented in ref [l] These equations generahze the famihar envelope equations to mclude the dispersive effects of bends TTe review the application of these equations to the calculation of the change m emrttance resulting from a sharp transition from a straight section to a bend section, usmg an energy conservation constramtComparisons of detailed 2D and 3D snnulatrons of intense beams m rmgs using the WARP code (refs [2;3]) are made with results obtamed from the moment equationsWe also compare the analysis carried out in ref [I], to more recent analyses, refs [4,5] We further exammr self-consistent distributions of beams m bends and discuss the relevance of these distributions to the moment equation formulation