The standard approach to compute the optical parameters and the beam emittance in a transport channel is based on the analysis of the profiles measured by three monitors. This requires the independent measurement of the dispersion function at the monitor locations and the knowledge of the value of the beam's momentum spread. In this paper different approaches based on the use of more than three beam profiles are presented. These techniques allow the determination of the complete set of four optical parameters, the betatron and dispersion functions and their derivatives, along with the beam emittance and the beam's momentum spread, simultaneously and without varying the physical parameters of the transport channel or the upstream machine. A detailed description of the different methods is carried out with a particular emphasis on their accuracy. Results of numerical simulations are presented.
Accepted for publication in Nuclear Instr. and Methods in Physics Research A
IntroductionThe complexity of the new generation of high-energy superconducting machines imposes tight constraints on the whole injector chain. In order to achieve the top performance in terms of luminosity of the planned CERN LHC [1], it is mandatory to preserve the value of the beam emittance through the whole chain of low-energy machines [2,3]. Although a crucial point is to avoid beam blow-up in the circular accelerators, which is obtained by carefully tuning the machines, the matching of the transfer lines to the phase space of the preceding and the subsequent machine also play a predominant role.In fact, even neglecting emittance blow-up due to the presence of possible non-linear fields, a transfer line generates transverse or longitudinal mismatch which will produce emittance increase after beam filamentation.Hence, as a consequence of the high performance required for the physics experiments, there has been a renewed interest in optics issues in transfer lines, with special emphasis on automated algorithms to measure optical parameters with the aim of computing mismatch factors, and, eventually, of applying corrections (see Ref. [4] for an overview of this field). These algorithms are usually devoted to the correction of the beam trajectory, via dedicated steering magnets, or to reducing the injection mismatch by using quadrupole magnets. An application of these concepts to the transfer line joining the PS and the SPS machines allowed a substantial improvement of the beam quality [5].Every correction procedure is based on a set of measured parameters to be compared with their theoretical values. Two different approaches are available. The first one deals with the measurement of the optical parameters by trajectory fit on Beam Position Monitor (BPM) data [6]. It allows the reconstruction of the transfer matrices between different BPMs and, in particular, the value of the dispersion function.The second technique allows to derive not only the optical parameters α, β, γ but also the beam characteristics, emittance and beam's momentum sp...