Principles of the non-linear tuning of beam expanders

Abstract

It is now common to consider employing non-linear multipole lenses to achieve transverse uniformization of particle beams used for the irradiation of extended targets in high intensity linac installations. In a previous report [F. Méot and T. Aniel, On beam uniformization by non-linear optics, Internal report CEA/DSM/GECA/GT/95-05, CEA Saclay, July 1995] we gave an analytical treatment of the uniformization of transverse beam densities by an octupole lens, in terms of the transport of random variables and their probability density functions, in the frame of a very basic optical scheme built up to two straight sections on both sides of the non-linear lens, following a pioneering work [P.F. Meads, A nonlinear lens system to smooth the intensity distribution of a Gaussian beam, IEEE Trans. Nucl. Sci. NS- 30 (1983)]. In the present paper, we extend the method to the more realistic configuration where the non-linear lens is preceded and followed by regular first order imaging optics, which leads to analytical expressions that provide the tuning of the non-linear lens w.r.t. the dimensions and nominal uniformization of the extended beam footprint at the target. This formalism is finally applied to the computation of the particle populations in the transverse tail distributions.