A modified space charge routine for high intensity bunched beams

In 1991 a space charge calculation for bunched beam with a three-dimensional ellipsoid was proposed, replacing the usual SCHEFF routines. It removes the cylindrical symmetry required in SCHEFF and avoids the point to point interaction computation, whose number of simulation points is limited. This routine has now been improved with the introduction of two or three ellipsoids giving a good representation of the complex non-symmetrical form of the bunch (unlike the 3-d ellipsoidal assumption). The ellipsoidal density distributions are computed with a new method, avoiding the difficulty encountered near the centre (the axis in 2-d problems) by the previous method. It also provides a check of the ellipsoidal symmetry for each part of the distribution. Finally, the Fourier analysis reported in 1991 has been replaced by a very convenient Hermite expansion, which gives a simple but accurate representation of practical distributions. Comparisons with other space charge routines have been made, particularly with the ones applying other techniques such as SCHEFF. Introduced in the versatile beam dynamics code DYNAC, it should provide a good tool for the study of the various parameters responsible for the halo formation in high intensity linacs. Improvements of the method are under development by the authors. These improvements, which might lead to a new step in space charge computations, are however beyond the scope of this article.