BUNCHED BEAMS IN AXISYMMETRICAL SYSTEMS

We analyse, in this paper, the self field of a bunched beam in a cylin drical metallic pipe with arbitrary density. The field is calculated b y superposition of the Green's functions of the single charge in the p ipe. A general solution is given as a Bessel-Fourier expansion, which is characterised by very good convergence properties. This allows the evaluation of the dynamics of a large class of physical beams by using this kind of solution for the self field. As an example the field is calculated for the case of a parabolic radial and elliptic longitudina l density profile.