Nonlinear transfer map treatment of beams through systems with absorbing material

Abstract

Summary form only given. Particle optical systems are usually comprised of electric and magnetic bending elements, focusing elements, and high-order multipoles for correction of aberrations. However, various modern systems for the transport and manipulation of large acceptance beams of rare and short-lived particles require the detailed treatment of more advanced optical elements. In particular, in recent years the reduction of the emittance of such beams has become of prime importance. The systems performing such reduction of emittance usually consist of combinations of absorbers that uniformly reduce the components of the momenta of the particles, as well as cavities that increase predominately the longitudinal components, which overall leads to a reduction of transversal emittance. For purposes of optimal focusing, frequently both cavities and absorbers are placed inside the body or at least the fringe fields of quadrupole or solenoidal focusing elements, which leads to the requirement of treating the nonlinear optics of acceleration, absorption, and focusing in a combined approach. The treatment of such systems in ray-tracing scenarios based on integration through fields and matter is very laborious and time consuming, and does not lend itself well to optimization and correction of undesirable nonlinear effects. We describe a differential algebraic method for the treatment of such nonlinear dynamics, based on the spatial and temporal form of the accelerating fields, any superimposed focusing magnetic fields, and the geometry and physical properties of the absorbing material and its possible vessel. Described by a Bethe-Bloch-Vavilov formalism, the bulk of the effects are described in terms of a high order nonlinear transfer maps. The also occurring scattering and straggling, which are inherently non-deterministic and hence not representable in the map formalism, are described in terms of a set of stochastic kicks in the transversal and longitudinal dynamics. The stochastics is propagated to the center of the occurring absorbers and thus allows a combined treatment of the tracking of both deterministic and random effects in an efficient way. ne method is implemented in the high-order code COSY INFINTIY. Examples for the application and performance of the method are given.