Perturbation Analysis on a Four-vane RFQ

An important issue for high intensity RFQs (tenth of mA beam current and more) is keeping beam losses as low as possible, in order to allow reliable and safe maintenance of the machine. Typically, beam dynamics outcomes driven by these constraints result both in a RFQ length that is considerably higher than the wavelength and in an intra-vane voltage admitted variation with respect to the design value that must not exceed a few percent. Therefore an analytical tool is needed in order to foresee the effect of geometric perturbations on the voltage profile, in order to give an indication on the permitted ranges of geometrical errors in the RFQ construction. In this article a five conductors transmission line equivalent circuit for the four-vane RFQ is presented and the effects of geometrical perturbations on the voltage profile are analyzed in some particular cases. The case study is the IFMIF RFQ (125 mA deuteron current, 9.8 m length, 175 MHz frequency), whose features are particularly suitable for this kind of analysis. RFQ MODELING VIA A FIVECONDUCTORS TRANSMISSION LINE A four vane RFQ can be modelled with a five conductor (the four electrodes E1, E2, E3 and E4 plus a “virtual” ground) transmission line, whose infinitesimal element of length dz is shown in Figure 1. This topology is similar to the four conductor line introduced in [1].