A MODIFIED SPACE-CHARGE ROUTINE FOR HIGH-INTENSITY BUNCHED BEAMS

In 1991 a space charge calculation for bunched beam with a three-dimen sional ellipsoid was proposed, replacing the usual SCHEFF routines. It removes the cylindrical symmetry required in SCHEFF and avoids the po int to point interaction computation, whose number of simulation point s is limited. This routine has now been improved with the introduction of two or three ellipsoids giving a good representation of the comple x non-symmetrical form of the bunch (unlike the 3-d ellipsoidal assump tion). The ellipsoidal density distributions are computed with a new m ethod, avoiding the difficulty encountered near the centre (the axis i n 2-d problems) by the previous method. It also provides a check of th e ellipsoidal symmetry for each part of the distribution. Finally, the Fourier analysis reported in 1991 has been replaced by a very conveni ent Hermite expansion, which gives a simple but accurate representatio n of practical distributions. Comparisons with other space charge rout ines have been made, particularly with the ones applying other techniq ues such as SCHEFF. Introduced in the versatile beam dynamics code DYN AC, it should provide a good tool for the study of the various paramet ers responsible for the halo formation in high intensity linacs. Impro vements of the method are under development by the authors. These impr ovements, which might lead to a new step in space charge computations, are however beyond the scope of this article.